Accelerating Discovery: A Comprehensive Analysis of Convergence Speed in Evolutionary Multitasking Optimization

Abstract

This article provides a systematic analysis of convergence speed in Evolutionary Multitasking Optimization (EMTO), an emerging paradigm that simultaneously solves multiple optimization tasks by leveraging inter-task knowledge transfer. Targeting researchers and computational biologists, we explore foundational principles, advanced methodologies, and optimization techniques that enhance EMTO convergence rates. Through comparative analysis of state-of-the-art algorithms and validation frameworks, we demonstrate how accelerated EMTO convergence can transform complex problem-solving in biomedical research, including drug discovery and clinical optimization challenges. The synthesis of troubleshooting approaches and performance validation offers practical guidance for implementing EMTO in computationally expensive research domains.

Understanding Evolutionary Multitasking: Principles and Convergence Fundamentals

Evolutionary Multitasking Optimization (EMTO) is an emerging paradigm in computational intelligence that enables the simultaneous solving of multiple optimization tasks. By leveraging the implicit parallelism of population-based search, EMTO facilitates knowledge transfer (KT) between tasks, often leading to accelerated convergence speeds and superior solution quality compared to traditional single-task optimization [1].

Fundamental Principles and Key Algorithms

EMTO operates on the principle that useful knowledge gained while solving one task can improve the performance of another related task. The foundational algorithm in this field is the Multifactorial Evolutionary Algorithm (MFEA), which creates a multi-task environment where a single population evolves under the influence of multiple "cultural factors" or tasks [1].

Subsequent advancements have introduced various algorithmic improvements:

• MFEA-II incorporates online learning to adaptively adjust transfer parameters [2] [3].
• Adaptive EMTO (AEMTO) designs separate intra-task and inter-task evolution mechanisms [2].
• Multitasking Genetic Algorithm (MTGA) evaluates and removes bias between tasks to improve transfer quality [2].

More recent approaches include the competitive scoring mechanism (MTCS) which quantifies the effects of transfer evolution and self-evolution to adaptively set knowledge transfer probability [4]. The association mapping strategy (PA-MTEA) uses subspace projection and alignment matrices to enhance cross-task knowledge transfer [5], while scenario-based self-learning transfer (SSLT) frameworks employ deep Q-networks to learn optimal transfer strategies for different evolutionary scenarios [6].

Knowledge Transfer: Mechanisms and Adaptive Strategies

Effective knowledge transfer is the cornerstone of successful EMTO implementation. The table below summarizes the primary transfer mechanisms and their characteristics:

Table: Knowledge Transfer Mechanisms in EMTO

Transfer Mechanism	Description	Key Features	Representative Algorithms
Implicit Transfer	Genetic material exchange through crossover between individuals assigned to different tasks [5].	Simple implementation; relies on task similarity; risk of negative transfer [5].	MFEA, MFDE, MFPSO [2]
Explicit Transfer	Active identification and transfer of high-quality solutions or solution space characteristics [5].	Targeted transfer; can handle more diverse tasks; requires specialized mechanisms [5].	EMFF, DA-MFEA, PA-MTEA [5] [3]
Adaptive Transfer	Self-regulating strategies that adjust transfer parameters based on online learning of task relationships [6] [2].	Mitigates negative transfer; improved robustness across various scenarios [6].	MFEA-AKT, MFEA-II, SSLT [6] [2]

Advanced strategies address the critical questions of when to transfer and how to transfer knowledge. The competitive scoring mechanism in MTCS addresses these questions by using scores to quantify evolutionary outcomes, adaptively adjusting transfer probability based on the competition between transfer evolution and self-evolution [4]. Similarly, SSLT frameworks automatically select from multiple scenario-specific strategies (e.g., shape KT, domain KT, bi-KT) using reinforcement learning [6].

Experimental Protocols and Performance Benchmarking

Standardized experimental protocols are essential for fair comparison of EMTO algorithms. Major competitions, such as the CEC 2025 Competition on Evolutionary Multi-task Optimization, provide established test suites and evaluation criteria [7].

Benchmark Problems and Evaluation Metrics

The WCCI20-MTSO and CEC17-MTSO benchmark suites are widely used for performance validation [4]. These suites contain problems categorized by the intersection degree of their solutions (complete intersection CI, partial intersection PI, no intersection NI) and similarity levels (high, medium, low) [4].

Standard experimental settings include [7]:

• 30 independent runs per algorithm with different random seeds
• Performance recording at predefined evaluation checkpoints (e.g., 100 checkpoints for 2-task problems)
• Evaluation using Best Function Error Value (BFEV) for single-objective problems and Inverted Generational Distance (IGD) for multi-objective problems

Performance Comparison

Experimental results demonstrate that advanced EMTO algorithms consistently outperform traditional single-task optimization approaches. The following table summarizes quantitative comparisons from recent studies:

Table: Performance Comparison of EMTO Algorithms on Benchmark Problems

Algorithm	Key Mechanism	Reported Convergence Improvement	Negative Transfer Mitigation	Application Context
MTCS [4]	Competitive scoring, dislocation transfer	Superior to 10 state-of-the-art EMTO algorithms	Adaptive probability and source task selection [4]	Multitask and many-task optimization
PA-MTEA [5]	Association mapping, adaptive population reuse	Superior to 6 advanced EMT algorithms	Bregman divergence alignment minimizes inter-task variability [5]	Benchmark problems and photovoltaic parameter extraction
SSLT [6]	Self-learning framework with DQN	Favourable against state-of-the-art competitors	Automatically selects appropriate scenario-specific strategies [6]	MTOPs and interplanetary trajectory design
APMTO [2]	Auxiliary population, adaptive similarity estimation	Outperforms state-of-the-art on CEC2022	Similarity-based KT frequency adjustment [2]	Chinese semantic understanding (potential)
CA-MTO [3]	Classifier-assisted, knowledge transfer for surrogates	Competitive edge on expensive multitasking problems	PCA-based subspace alignment for sample transformation [3]	Expensive optimization problems

The Scientist's Toolkit: Essential Components for EMTO Research

Table: Research Reagent Solutions for EMTO Experimentation

Tool/Resource	Function	Example Implementation/Notes
MTO-Platform Toolkit [6]	Integrated platform for algorithm development and testing	Provides standardized environment for performance comparison
CEC Benchmark Suites [7]	Standardized problem sets for controlled experimentation	Includes CEC17-MTSO, WCCI20-MTSO with various task relationships
Domain Adaptation Techniques [3]	Enable knowledge transfer between heterogeneous tasks	Includes PCA-based subspace alignment, linear transformation
Surrogate Models [3]	Reduce computational cost for expensive problems	Classifiers (SVC) or regression models (GP, RBF)
Deep Q-Networks (DQN) [6]	Enable self-learning transfer strategies	Map evolutionary scenario features to optimal strategies

EMTO in Drug Discovery: A Convergence Synergy

While EMTO originates from computational intelligence, its principles show significant potential for drug discovery, particularly in addressing challenges like expensive optimization problems (EMTOPs) where evaluations involve time-consuming simulations or complex physical experiments [3].

In this context, classifier-assisted EMTO approaches integrate surrogate models like Support Vector Classifiers with evolutionary frameworks to distinguish promising solutions with minimal computational expense [3]. Knowledge transfer strategies further enhance this by transforming and aggregating labeled samples across related tasks, mitigating data sparseness issues common in early-stage drug development [3].

Figure 1: EMTO Knowledge Transfer Workflow. This diagram illustrates the adaptive process of knowledge transfer in evolutionary multitasking optimization, showing how competitive scoring and similarity assessment guide the choice between self-evolution and cross-task transfer.

Evolutionary Multitasking Optimization represents a paradigm shift in how computational optimization problems are approached, moving from isolated problem-solving to synergistic multi-task environments. The empirical evidence demonstrates that properly implemented knowledge transfer mechanisms can significantly enhance convergence speed and solution quality across diverse task types. As research progresses, EMTO continues to expand into more complex domains, including expensive optimization problems and real-world applications in drug discovery, where its ability to leverage latent synergies between tasks provides a distinct advantage over traditional approaches.

Multifactorial Evolutionary Algorithm (MFEA) establishes a foundational paradigm in evolutionary multitasking optimization (EMTO) by enabling the simultaneous solution of multiple optimization tasks. This guide objectively compares the performance of modern MFEA variants, analyzing their convergence speed and efficacy against other EMTO approaches, with supporting experimental data from recent research.

MFEA and the EMTO Paradigm

Evolutionary Multitask Optimization is an emerging field in evolutionary computation that aims to optimize multiple tasks concurrently by leveraging implicit parallelism of population-based search. The core principle involves transferring valuable knowledge across tasks during the evolutionary process, which can significantly enhance convergence speed and solution quality compared to traditional single-task optimization [1].

The Multifactorial Evolutionary Algorithm (MFEA), introduced by Gupta et al., represents the pioneering algorithm in this field. MFEA creates a unified search environment where a single population evolves while solving multiple tasks simultaneously. Each task is treated as a unique "cultural factor" influencing evolution, with knowledge transfer occurring through specialized genetic operations—assortative mating and vertical cultural transmission [1]. The algorithm uses a skill factor to identify which task an individual specializes in and a random mating probability (rmp) parameter to control cross-task reproduction [8].

Performance Comparison of MFEA Variants

Modern MFEA variants address key limitations of the original algorithm, particularly regarding negative transfer (where harmful rather than beneficial knowledge is shared) and adaptive operator selection. The table below summarizes experimental results for recent MFEA variants across standard benchmarks:

Algorithm	Key Mechanism	Test Problems	Performance Findings	Convergence Speed
MFEA-MDSGSS [9]	Multidimensional scaling + golden section search	Single- & multi-objective MTO benchmarks	Superior to state-of-the-art algorithms	Faster convergence with higher solution quality
MFEA-DGD [10]	Diffusion gradient descent	Various multitask optimization problems	Faster convergence to competitive results	Provable convergence; benefits from knowledge transfer
MFEA-RL [11]	Residual learning crossover + dynamic skill factor assignment	CEC2017-MTSO, WCCI2020-MTSO	Outperforms state-of-the-art algorithms	Excellent convergence and adaptability
BOMTEA [8]	Adaptive bi-operator (GA + DE) strategy	CEC17, CEC22 benchmarks	Significantly outperforms comparative algorithms	Outstanding results via adaptive operator selection
EMT-ADT [12]	Decision tree-based adaptive transfer strategy	CEC2017, WCCI20-MTSO, WCCI20-MaTSO	Improved solution accuracy, especially for low-relevance tasks	Competitive performance on combinatorial problems
MTEA-PAE [13]	Progressive auto-encoding for domain adaptation	Six benchmark suites + real-world applications	Outperforms state-of-the-art algorithms	Enhanced convergence efficiency and solution quality

Comparative Performance Insights

• MFEA-MDSGSS demonstrates particularly strong performance in mitigating negative transfer, especially between tasks with differing dimensionalities [9].
• BOMTEA's adaptive operator selection proves that no single evolutionary search operator is optimal for all tasks, with DE/rand/1 performing better on CIHS and CIMS problems, while GA operators show superiority on CILS problems [8].
• EMT-ADT addresses the challenge of low-relatedness tasks where traditional MFEAs often struggle with solution precision [12].

Detailed Experimental Protocols

Benchmarking Standards and Performance Metrics

Most MFEA variants are evaluated using standardized benchmark problems and performance metrics to ensure objective comparison:

• Common Benchmarks: CEC2017 Multitask Optimization Benchmark Problems, WCCI2020 Multi-Task Single-Objective (MTSO), and WCCI2020 Multi-Task Multi-Objective (MaTSO) benchmarks [12] [11].
• Performance Metrics: For convergence analysis, researchers typically use:
  • Average Fitness Convergence: Tracking the best fitness values across generations.
  • Solution Accuracy: Measuring the deviation from known optima.
  • Statistical Tests: Wilcoxon signed-rank test to verify significance of performance differences [9].

MFEA-MDSGSS Experimental Methodology

The MFEA-MDSGSS algorithm employs these specific experimental protocols [9]:

• Component Ablation Study: Separate evaluation of MDS-based LDA and GSS-based linear mapping to quantify individual contributions.
• Parameter Sensitivity Analysis: Systematic investigation of key parameter influences on algorithm performance.
• Comparative Framework: Testing against multiple state-of-the-art EMTO algorithms across diverse problem types.

EMT-ADT Validation Framework

EMT-ADT utilizes these validation approaches [12]:

• Transfer Ability Quantification: Defining and measuring individual transfer ability using Gini coefficient-based decision trees.
• Success-History Based Adaptive DE (SHADE): Implementing SHADE as the search engine to demonstrate MFO paradigm generality.
• Combinatorial Problem Testing: Additional validation on Traveling Salesman Problem (TSP) and Tree Routing Problem (TRP).

Visualization of MFEA Mechanisms

MFEA Knowledge Transfer and Skill Factor Assignment

Advanced MFEA Variant Mechanisms

The Scientist's Toolkit: EMTO Research Reagents

This table details essential computational resources and methodologies for EMTO research and application development:

Research Tool	Function in EMTO	Application Context
CEC2017/CEC2022 MTO Benchmarks	Standardized problem sets for algorithm comparison	Experimental validation and performance benchmarking [8]
Linear Domain Adaptation (LDA)	Aligns search spaces between different tasks	Facilitates knowledge transfer in cross-domain optimization [9]
Random Mating Probability (RMP)	Controls frequency of cross-task reproduction	Parameter tuning to balance exploration and exploitation [8]
Decision Tree Predictors	Predicts transfer ability of individuals	Identifies promising candidates for knowledge transfer [12]
Multi-Dimensional Scaling (MDS)	Establishes low-dimensional subspaces for each task	Enables knowledge transfer between different dimensionality tasks [9]
Progressive Auto-Encoding (PAE)	Learns mappings between problem domains	Dynamic domain adaptation throughout evolutionary process [13]
Skill Factor Assignment	Identifies task specialization for each individual	Enables implicit knowledge transfer in multifactorial framework [1]

The MFEA framework continues to evolve with innovations addressing its core challenges. Modern variants demonstrate significant improvements in convergence speed and solution accuracy, particularly through adaptive transfer mechanisms, domain adaptation techniques, and hybrid operator strategies.

Future research directions include developing more sophisticated task-relatedness measures, creating theoretical foundations for EMTO convergence, and expanding applications to complex real-world problems such as drug discovery and personalized medicine optimization [1]. As these algorithms mature, they offer promising approaches for researchers and drug development professionals facing multiple interrelated optimization challenges.

In the field of evolutionary computation, particularly within evolutionary multitasking convergence speed analysis research, understanding knowledge transfer mechanisms is paramount for designing efficient algorithms. Knowledge can be categorized into three primary types—explicit, implicit, and tacit—each with distinct characteristics and transfer mechanisms. Explicit knowledge is easily articulated, codified, and transferred through formal documentation, while implicit knowledge represents the practical application of explicit knowledge to specific contexts [14] [15]. Tacit knowledge, deeply rooted in personal experience and intuition, is the most challenging to formalize and transfer [14] [16].

In evolutionary multitasking optimization (MTO), these knowledge types manifest differently. Explicit knowledge transfer often involves direct encoding of solutions or strategies, while implicit transfer leverages underlying similarities between tasks without conscious articulation [17]. The multifactorial evolutionary algorithm (MFEA) represents a pioneering approach to implicit transfer learning in MTO, where knowledge is shared across optimization tasks through chromosomal crossover operations [17]. Understanding the distinctions between these transfer approaches is crucial for researchers and drug development professionals seeking to accelerate convergence in complex optimization problems, such as those encountered in pharmaceutical research and development.

Theoretical Foundations: Knowledge Transfer in Evolutionary Computation

Explicit Knowledge Transfer Mechanisms

Explicit knowledge transfer in evolutionary computation involves the systematic encoding of information that can be readily documented and shared between optimization tasks. This approach is characterized by its codifiable nature, making it highly accessible and easily reproducible across different contexts [14]. In algorithmic terms, explicit knowledge might include well-defined solution structures, parameter settings, or convergence patterns that can be directly transferred between related optimization problems.

The strength of explicit knowledge transfer lies in its immediate applicability. Experimental studies have demonstrated that when explicit knowledge is acquired during initial learning phases, it can be transferred immediately to novel contexts without delay [18]. This characteristic is particularly valuable in drug development pipelines where rapid adaptation to new compound optimization tasks can significantly accelerate research timelines. However, the requirement for conscious articulation and formal encoding presents limitations when dealing with highly complex, unstructured problem domains where complete explicit documentation is impractical.

Implicit Knowledge Transfer Mechanisms

Implicit knowledge transfer operates through unconscious application of learned patterns and relationships, making it particularly valuable for complex problem domains where explicit articulation is challenging. In evolutionary multitasking, implicit transfer occurs through mechanisms like assortative mating and vertical cultural transmission, where knowledge is shared across tasks without explicit encoding [17]. This approach mirrors human cognitive processes where skills and patterns are acquired through experience rather than formal instruction.

Recent research has revealed that implicit knowledge transfer follows a different temporal pattern compared to explicit mechanisms. While explicit knowledge can be transferred immediately, implicit transfer often requires consolidation periods, with sleep playing a particularly crucial role in restructuring unconscious knowledge for future application [18] [19]. This finding has significant implications for designing evolutionary algorithms with memory mechanisms that mimic these natural cognitive processes. The structural robustness of implicitly acquired knowledge makes it more resilient under stressful conditions, such as when optimization problems encounter noisy fitness evaluations or dynamic environments [20].

Experimental Comparisons: Performance Metrics and Methodologies

Visual Statistical Learning Paradigm

The visual statistical learning (SVSL) paradigm provides a robust experimental framework for investigating knowledge transfer mechanisms [18] [19]. In this approach, participants are exposed to scenes containing abstract shapes arranged in fixed spatial pairs, with the requirement to extract underlying statistical regularities. The methodology involves multiple phases:

• Phase 1: Participants view scenes composed of either exclusively horizontal or exclusively vertical shape pairs, depending on assigned condition.
• Phase 2: After a delay period (varied to test consolidation effects), participants view scenes containing both horizontal and vertical pairs constructed from novel shapes.
• Testing: Knowledge acquisition is assessed through a two-alternative forced-choice (2AFC) familiarity test comparing real pairs against foil pairs constructed from mixed shapes [18].

This experimental design allows researchers to precisely measure transfer learning effects by examining how exposure to one abstract structure influences the acquisition of novel structures. The paradigm effectively disentangles conscious (explicit) from unconscious (implicit) learning by combining objective performance measures with subjective awareness assessments [18].

Serial Response Time Task (SRTT) Methodology

The serial response time task (SRTT) represents another established protocol for investigating sequence learning through both implicit and explicit mechanisms [21]. This approach enables researchers to:

• Measure reaction time improvements as participants unconsciously or consciously learn sequence regularities.
• Apply the drift-diffusion model to disentangle specific cognitive processes affected by learning (stimulus detection, response selection, response execution).
• Independently manipulate explicit sequence knowledge and the opportunity to express such knowledge [21].

Research using this methodology has demonstrated that implicit sequence learning primarily benefits response selection processes, while explicit knowledge enables a shift from stimulus-based to plan-based action control, particularly under deterministic conditions [21].

Throwing Task Under Fatigue Conditions

Motor learning studies provide valuable insights into knowledge transfer resilience under challenging conditions. A recent throwing task experiment compared implicit (errorless) and explicit (errorful) training strategies under both physiological and mental fatigue [20]. The methodology included:

• Implicit Group: Started close to the target and progressively increased distance (error-minimizing approach).
• Explicit Group: Began at a significant distance from the target and gradually moved closer (error-prone approach).
• Fatigue Induction: Mental fatigue through 30-minute Stroop task; physical fatigue through maintained isometric contraction.
• Assessment: Retention tests and transfer tests under fatigue conditions [20].

This experimental approach demonstrates the practical implications of knowledge type on performance resilience, with significant applications to training protocol design in both clinical and industrial settings.

Table 1: Comparative Performance of Implicit vs. Explicit Knowledge Transfer

Performance Metric	Implicit Transfer	Explicit Transfer	Experimental Context
Immediate Application	Limited immediate transfer; shows structural interference [18]	Strong immediate transfer capability [18]	Visual statistical learning
Post-Consolidation	Significant improvement after sleep (12 hours) [18] [19]	Minimal consolidation benefit [18]	Visual statistical learning
Fatigue Resilience	Maintains performance under mental and physical fatigue [20]	Significant performance degradation under fatigue [20]	Throwing task experiment
Process Specificity	Primarily benefits response selection and execution [21]	Enables shift to plan-based action control [21]	Serial response time task
Transfer Flexibility	Abstract structure transfer after consolidation [18]	Direct pattern application	Visual statistical learning

Evolutionary Multitasking Algorithms: A Convergence Speed Perspective

Multifactorial Evolutionary Algorithm (MFEA)

The Multifactorial Evolutionary Algorithm (MFEA) represents a foundational approach to implicit knowledge transfer in evolutionary computation [17]. MFEA implements knowledge sharing through:

• Implicit transfer learning via chromosomal crossover between solutions from different tasks.
• Assortative mating that allows individuals with different skill factors to reproduce.
• Vertical cultural transmission where offspring randomly inherit genetic material and dominant tasks from parents [17].

While MFEA demonstrates the feasibility of implicit transfer, its simple random inter-task transfer strategy often results in slow convergence rates due to excessive diversity maintenance. This limitation has motivated researchers to develop more sophisticated algorithms with enhanced knowledge transfer mechanisms [17].

Two-Level Transfer Learning Algorithm (TLTL)

To address MFEA's convergence limitations, the Two-Level Transfer Learning (TLTL) algorithm implements a structured approach to knowledge transfer [17]. This enhanced framework includes:

• Upper-Level (Inter-task transfer): Implements knowledge transfer through chromosome crossover and elite individual learning to reduce randomness.
• Lower-Level (Intra-task transfer): Performs information transfer of decision variables for across-dimension optimization within the same task [17].

Experimental evaluations demonstrate that TLTL achieves outstanding global search capability and fast convergence rate by more effectively exploiting correlations and similarities between component tasks [17]. The algorithm's two-level structure enables more efficient knowledge exchange while maintaining appropriate diversity levels throughout the evolutionary process.

Evolutionary Multitasking-Based Multiobjective Optimization Algorithm (EMMOA)

For complex real-world applications like hybrid brain-computer interface (BCI) channel selection, the Evolutionary Multitasking-based Multiobjective Optimization Algorithm (EMMOA) represents a specialized approach [22]. EMMOA features:

• Two-stage framework that balances selected channel number and classification accuracy.
• Simultaneous optimization of motor imagery (MI) and steady-state visual evoked potential (SSVEP) classification tasks.
• Information transfer between related tasks to exploit underlying similarities [22].

This algorithm demonstrates how evolutionary multitasking with effective knowledge transfer can address practical optimization challenges in neuroscience and medical technology development, particularly when multiple conflicting objectives must be balanced.

Table 2: Evolutionary Multitasking Algorithms and Their Transfer Mechanisms

Algorithm	Primary Transfer Mechanism	Knowledge Type	Convergence Performance	Application Context
MFEA [17]	Implicit transfer via chromosomal crossover	Primarily implicit	Slow convergence due to random transfer [17]	General multitasking optimization
TLTL [17]	Two-level transfer (inter-task & intra-task)	Implicit with elite guidance	Fast convergence rate [17]	General multitasking optimization
EMMOA [22]	Evolutionary multitasking mechanism	Implicit	Improved search efficiency [22]	Hybrid BCI channel selection

Research Reagent Solutions: Experimental Toolkit

Table 3: Essential Research Materials and Their Functions

Research Reagent/Resource	Function in Knowledge Transfer Research
Visual Statistical Learning Paradigm [18]	Tests abstraction and transfer of statistical regularities
Serial Response Time Task (SRTT) [21]	Measures implicit and explicit sequence learning
Drift-Diffusion Modeling [21]	Isolates specific cognitive processes affected by learning
Stroop Task Protocol [20]	Induces mental fatigue for testing knowledge resilience
Isometric Contraction Protocol [20]	Induces physical fatigue for testing knowledge resilience
Two-Alternative Forced Choice (2AFC) [18]	Assesses knowledge acquisition through familiarity judgments
Multifactorial Evolutionary Algorithm (MFEA) [17]	Provides baseline implicit transfer in optimization tasks
Non-dominated Sorting Genetic Algorithm-II (NSGA-II) [22]	Multiobjective optimization for comparison studies

Knowledge Transfer Pathways in Evolutionary Multitasking

The following diagram illustrates the key pathways and mechanisms for knowledge transfer in evolutionary multitasking environments:

Knowledge Transfer Pathways in Evolutionary Multitasking

The comparative analysis of implicit versus explicit knowledge transfer mechanisms reveals significant implications for researchers and drug development professionals working on evolutionary multitasking convergence speed analysis. Explicit transfer approaches offer immediate application benefits but demonstrate limited resilience under fatigue and limited capacity for handling complex, unstructured problem domains. Conversely, implicit transfer mechanisms require consolidation periods but ultimately provide more robust, flexible knowledge application that withstands challenging conditions.

For evolutionary algorithm design, these insights suggest that hybrid approaches combining the immediate benefits of explicit transfer with the long-term robustness of implicit transfer may yield optimal convergence performance. The demonstrated role of sleep in consolidating implicit knowledge further suggests potential algorithmic analogs in the form of structured rest periods or memory consolidation mechanisms within evolutionary computation frameworks.

Future research in this domain should focus on developing more sophisticated knowledge taxonomies for evolutionary computation and designing explicit mechanisms for converting tacit knowledge into transferable forms without losing its essential contextual richness. Such advances promise to significantly accelerate convergence in complex optimization problems central to drug discovery and development pipelines.

Key Factors Influencing Convergence Speed in Multitasking Environments

Evolutionary Multitasking (EMT) represents a paradigm shift in computational optimization, enabling the simultaneous solving of multiple optimization tasks by exploiting their underlying synergies [5]. In an EMT setting, the convergence speed of an algorithm—the rate at which it approaches optimal or high-quality solutions—is paramount, especially for computationally expensive real-world problems like drug development [3]. The convergence speed is not governed by a single factor but by a complex interplay of algorithmic strategies for knowledge transfer, constraint handling, and population management. This guide provides a comparative analysis of state-of-the-art EMT algorithms, dissecting the key factors that influence their convergence performance through structured experimental data and detailed methodologies.

Comparative Analysis of Advanced EMT Algorithms

The convergence speed in multitasking environments is critically influenced by the algorithm's core design. The table below compares several advanced EMT algorithms, highlighting their primary knowledge transfer mechanisms and their intended effect on convergence.

Table 1: Comparison of State-of-the-Art Evolutionary Multitasking Algorithms

Algorithm Name	Core Knowledge Transfer Mechanism	Primary Convergence Goal	Key Innovation Focus
ETT-PEGR [23]	Evolutionary Tri-Tasking; two auxiliary tasks (concept-recommended & constraint-ignored) with a novel encoding-based transfer.	Accelerate convergence in large-scale, constrained problems.	Problem-specific auxiliary task design.
MFEA-MDSGSS [9]	Multidimensional Scaling (MDS) for subspace alignment & Golden Section Search (GSS) for linear mapping.	Mitigate negative transfer and avoid local optima.	Robust transfer between unrelated or differently-dimensioned tasks.
PA-MTEA [5]	Association Mapping via Partial Least Squares (PLS) & Adaptive Population Reuse (APR).	Enhance efficiency and comprehensiveness of bidirectional knowledge transfer.	Balancing global exploration and local exploitation.
CA-MTO [3]	Classifier-assisted (SVC) knowledge transfer with PCA-based subspace alignment for expensive problems.	Improve convergence speed and accuracy with limited fitness evaluations.	Data sparseness mitigation via sample aggregation.

Experimental Protocols for Evaluating Convergence

To objectively compare the convergence performance of EMT algorithms, researchers rely on standardized experimental protocols.

Benchmark Problems and Real-World Cases

Performance is typically validated on benchmark suites and real-world problems. A common benchmark is the WCCI2020-MTSO test suite, a complex set of ten two-task problems designed for the 2020 competition on evolutionary multi-task optimization [5]. Real-world case studies provide critical validation, such as:

• Personalized Exercise Group Recommendation (PEGR): Modeled as a large-scale constrained multi-objective optimization problem [23].
• Parameter Extraction of Photovoltaic (PV) Models: A complex optimization problem in engineering [5].
• Expensive Multitasking Optimization Problems (EMTOPs): Problems where each fitness evaluation is computationally costly, such as those involving complex simulations [3].

Performance Evaluation Metrics

The convergence speed and quality of algorithms are measured using specific metrics:

• Convergence Accuracy: The quality of the best solution found, often measured by the final objective function value.
• Convergence Speed: The rate of improvement, which can be measured by the number of Fitness Evaluations (FEs) or iterations required to reach a solution of a certain quality [3].
• Data Efficiency: For expensive problems, the key metric is the algorithm's performance given a very limited budget of FEs [3].

Key Factors Influencing Convergence Speed

Knowledge Transfer Strategy

The design of the knowledge transfer mechanism is arguably the most critical factor for convergence speed.

• Explicit vs. Implicit Transfer: Modern algorithms increasingly favor explicit knowledge transfer, which actively extracts and maps high-quality solutions or landscape features from a source task to a target task. This approach is more directed and can reduce the risk of negative transfer—where unhelpful knowledge misguides the search and hinders convergence [5] [9].
• Subspace Alignment: To make transfer effective, especially between tasks with different characteristics, many algorithms project tasks into a shared low-dimensional subspace. MFEA-MDSGSS uses Multidimensional Scaling (MDS) to create these subspaces and Linear Domain Adaptation (LDA) to align them, enabling more robust and stable knowledge transfer [9]. Similarly, PA-MTEA uses Partial Least Squares (PLS) to find principal components that maximize correlation between tasks for more effective transfer [5].

Handling of Task Relatedness and Negative Transfer

The convergence speed of an EMT algorithm is highly dependent on its ability to handle unrelated or dissimilar tasks.

• The Negative Transfer Problem: When tasks are unrelated, knowledge from one task can mislead the search of another, causing premature convergence to poor local optima [9] [5].
• Mitigation Strategies: Advanced algorithms incorporate specific strategies to mitigate this. MFEA-MDSGSS introduces a GSS-based linear mapping strategy to help the population escape local optima and explore more promising regions, thus maintaining diversity and preventing premature convergence [9]. PA-MTEA's association mapping strategy aims to transfer only mutually beneficial information, reducing blind transfer [5].

Auxiliary Task Design and Problem Reformulation

Creating simpler, related auxiliary tasks can significantly boost convergence for a complex primary task.

• The ETT-PEGR Approach: This algorithm constructs two auxiliary tasks for its main Personalized Exercise Group Recommendation problem. The concept-recommended auxiliary task operates in a smaller concept space to speed up convergence, while the constraint-ignored auxiliary task helps the main task cross infeasible regions of the search space. This tri-tasking framework directly tackles the "curse of dimensionality" and complex constraints that slow down convergence [23].

Population Management and Exploitation-Exploration Balance

How an algorithm manages its population of solutions throughout the search process directly impacts convergence.

• Adaptive Population Reuse (APR): PA-MTEA uses an APR mechanism to reuse historically successful individuals adaptively. This guides the evolutionary direction and improves convergence performance by effectively balancing the exploration of new regions with the exploitation of known good solutions [5].
• Exploration-Convergence Tradeoff: There is a fundamental tension between exploring the search space widely and converging quickly to an optimum. This is particularly acute when using suboptimal parameters or settings, where a focus on rapid exploration might come at the cost of slower final convergence, and vice-versa [24]. Algorithms must be designed to manage this tradeoff effectively.

Visualization of Algorithm Workflows

The following diagram illustrates the high-level logical workflow and key components shared by advanced EMT algorithms, which contributes to their accelerated convergence.

Figure 1: Generalized workflow of advanced EMT algorithms, highlighting the iterative process of subspace alignment and explicit knowledge transfer that enhances convergence speed.

The Scientist's Toolkit: Essential Research Reagents

The experimental research and application of EMT algorithms rely on a suite of conceptual "reagents" and tools.

Table 2: Key Research Reagent Solutions in Evolutionary Multitasking

Research Reagent / Tool	Function in EMT Research
Benchmark Suites (e.g., WCCI2020-MTSO)	Standardized test problems for fair and reproducible comparison of algorithm convergence performance and robustness [5].
Multifactorial Evolutionary Algorithm (MFEA)	A foundational algorithmic framework for EMT that enables implicit knowledge transfer via assortative mating and vertical cultural transmission [3].
Partial Least Squares (PLS)	A statistical method used for subspace projection and association mapping to maximize correlation between tasks for more effective knowledge transfer [5].
Support Vector Classifier (SVC)	A classification model used as a surrogate in expensive optimization problems to prescreen solutions, reducing the number of computationally costly fitness evaluations [3].
Bregman Divergence	A measure of distance between probability distributions, used in deriving alignment matrices to minimize variability between task domains during knowledge transfer [5].

Evolutionary Multitask Optimization (EMTO) is an emerging paradigm in computational intelligence that seeks to simultaneously solve multiple optimization tasks by leveraging the latent complementarities and knowledge transfer between them. Unlike traditional single-task evolutionary algorithms (EAs) that start the search from scratch for each problem, EMTO enhances the solving process of each task based on simultaneously optimizing multiple tasks through inter-task knowledge transfer. The mathematical formulation of an MTO problem consisting of K tasks aims to find a set of solutions {x1, x2, …, xK} such that each xi is the global optimum for its respective task [9]. This paradigm has demonstrated significant potential in accelerating convergence speed and enhancing solution quality across various domains, including vehicle routing, reliability redundancy allocation, and simulation-based process design [6].

The fundamental premise of EMTO rests on the observation that problems in the real world rarely exist in isolation. Virtually all optimization problems, even black-box instances, can be mined from previously completed or ongoing tasks with substantially similar properties [3]. By exploiting the synergies between related tasks, EMTO algorithms can effectively navigate complex search spaces and overcome limitations of traditional evolutionary approaches. The convergence behavior of these algorithms, however, presents unique theoretical challenges that differ substantially from single-task optimization, primarily due to the complex dynamics of knowledge transfer between tasks with potentially disparate fitness landscapes and dimensionalities.

Theoretical Foundations of EMTO Convergence

From Single-Task to Multi-Task Evolutionary Paradigms

Traditional single-task evolutionary algorithms are population-based optimization methods inspired by natural selection and genetics, which have proven effective for solving individual optimization problems [9]. However, their convergence characteristics are fundamentally different from multi-task environments. In single-task optimization, convergence analysis typically focuses on how the population evolves toward the global optimum of a single fitness landscape, considering factors like selection pressure, genetic drift, and exploration-exploitation balance.

In contrast, EMTO introduces the additional dimension of knowledge transfer between tasks, creating a complex interplay between multiple search processes. The convergence speed in EMTO is influenced not only by the efficacy of evolutionary operators but also by the quality and quantity of knowledge exchanged between tasks. When properly implemented, this knowledge transfer can lead to accelerated convergence by allowing tasks to benefit from each other's discovered patterns and promising regions in the search space [9] [6]. However, inappropriate transfer can result in negative transfer, where knowledge from one task misguides the search direction of another, ultimately degrading convergence performance [9].

Key Convergence Challenges in EMTO

The theoretical analysis of EMTO convergence must address several unique challenges that distinguish it from single-task optimization. First, the curse of dimensionality presents a significant obstacle, as the decision space volume increases exponentially with the number of variables, leading to combinatorial explosion and adverse effects on search algorithms [25]. This challenge is compounded in multi-task environments where different tasks may have differing dimensionalities, making direct knowledge transfer problematic.

Second, negative transfer represents a critical convergence challenge in EMTO. This occurs when knowledge from distinct tasks that may not benefit each other is transferred during evolutionary search [9]. For example, if one task converges prematurely to a local optimum, the unhelpful knowledge transferred from it may mislead other tasks into the same local optimum, particularly when task similarity is low [9]. The risk of negative transfer is especially pronounced between tasks with dissimilar fitness landscapes or when robust mappings cannot be learned from limited population data [9].

Third, the dynamic balance between exploration and exploitation becomes more complex in multitask environments. While single-task algorithms must balance exploring new regions and refining known promising areas, EMTO must additionally balance intra-task search with inter-task knowledge transfer. This multi-level balance directly impacts convergence speed and solution quality across all tasks in an MTO problem.

Algorithmic Frameworks and Their Convergence Mechanisms

Multifactorial Evolutionary Algorithm (MFEA) and Variants

The Multifactorial Evolutionary Algorithm (MFEA), proposed by Gupta et al., represents the pioneering work in EMTO and establishes the foundational convergence mechanisms for the field [9] [3]. MFEA operates on a unified search space where individuals are encoded in a unified representation and assigned skill factors denoting their specialized tasks. Knowledge transfer occurs implicitly through chromosome crossover between individuals of different tasks, allowing genetic material to flow between optimization processes [9].

The convergence properties of basic MFEA, however, face limitations in scenarios with unrelated tasks or differing dimensionalities. To address these limitations, several enhanced variants have been developed:

• MFEA-MDSGSS: Integrates multidimensional scaling (MDS) and golden section search (GSS) to improve convergence. The MDS-based linear domain adaptation method establishes low-dimensional subspaces for each task, facilitating robust knowledge transfer even between tasks with different dimensions. Meanwhile, the GSS-based linear mapping strategy helps avoid local optima and enhances population diversity, critical factors for maintaining convergence quality [9].

• MFEA-II: Introduces an adaptive knowledge transfer mechanism that learns similarities between pairwise tasks by calculating the weight of mixed probability distribution models, thereby reducing negative transfer and improving convergence reliability [3].

• MFEA-AKT: Implements adaptive knowledge transfer that dynamically adjusts transfer intensity based on task relatedness, optimizing convergence speed across diverse task combinations [9].

Explicit Transfer Methods for Enhanced Convergence

While MFEA and its variants primarily employ implicit transfer through genetic representation, another approach focuses on explicit knowledge transfer mechanisms that directly share information between tasks:

• LDA-MFEA: Employs linear domain adaptation techniques to enable knowledge transfer between homogeneous or heterogeneous multitasking optimization problems. It introduces a linear transformation strategy to map tasks into a higher-order representation search space where knowledge can be transferred more efficiently, enhancing convergence particularly for tasks with explicit discrepancies in their fitness landscapes [3].

• G-MFEA: A generalized MFEA that facilitates knowledge transfer among optimization problems with different optimum locations and dimensionalities through translation and shuffling of decision variables, addressing convergence challenges in functionally related but structurally different tasks [3].

• EMT via Autoencoding: Uses denoising autoencoders to explicitly transfer high-quality solutions across tasks, where the autoencoder is trained on solutions sampled from the search spaces of optimization problems, creating a more direct pathway for beneficial knowledge exchange [9] [3].

Scenario-Based Self-Learning Frameworks

The Scenario-based Self-Learning Transfer (SSLT) framework represents a significant advancement in convergence assurance for EMTO. This approach categorizes evolutionary scenarios into four possible situations in the MTOP environment and designs corresponding scenario-specific strategies [6]:

• Only similar shape: Employing shape knowledge transfer to help the target population approximate the convergence trend of the source population
• Only similar optimal domain: Utilizing domain knowledge transfer to move populations to more promising search regions
• Similar function shape and optimal domain: Applying bi-knowledge transfer for comprehensive convergence acceleration
• Dissimilar shape and optimal domain: Relying on intra-task strategies to avoid disruptive knowledge transfer

SSLT employs Deep Q-Networks (DQN) as a relationship mapping model to learn the optimal correspondence between evolutionary scenarios and transfer strategies, enabling automatic adjustment of knowledge transfer policies during the optimization process [6]. This self-learning capability allows the algorithm to adapt its convergence strategy based on real-time search conditions, significantly reducing the risk of negative transfer while maximizing positive convergence synergies.

Surrogate-Assisted and Classification-Based Approaches

For expensive optimization problems where fitness evaluations are computationally costly, surrogate-assisted EMTO approaches have been developed to maintain convergence while reducing computational burden:

• Classifier-Assisted Evolutionary Multitasking: Replaces traditional regression surrogates with classification models that distinguish the relative merits of candidate solutions, reducing sensitivity to limited training samples while maintaining convergence direction [3].

• Knowledge Transfer with Domain Adaptation: Enriches training samples for task-oriented classifiers by sharing high-quality solutions among different tasks using PCA-based subspace alignment techniques, improving model accuracy and convergence reliability despite limited data [3].

Table 1: Comparative Analysis of EMTO Algorithm Convergence Mechanisms

Algorithm	Knowledge Transfer Type	Convergence Assurance Mechanism	Applicable Scenario
MFEA	Implicit	Assortative mating and vertical cultural transmission	Tasks with similar representations
MFEA-MDSGSS	Explicit	MDS-based subspace alignment and GSS-based local avoidance	High-dimensional tasks with differing dimensionalities
SSLT	Self-learning	DQN-based strategy selection based on scenario features	Dynamic environments with varying task relatedness
LDA-MFEA	Explicit domain adaptation	Linear transformation to shared representation space	Homogeneous or heterogeneous tasks
CA-MTO	Classifier-assisted	SVC-based solution prescreening with cross-task sample transfer	Expensive optimization problems

Experimental Analysis of Convergence Performance

Benchmarking Methodologies and Metrics

Rigorous experimental evaluation is essential for analyzing the convergence performance of EMTO algorithms. Standard benchmarking approaches utilize both synthetic and real-world problems to assess various convergence aspects:

• Single-Objective MTO Benchmarks: Test problems designed to evaluate convergence speed and accuracy for tasks with single objectives, measuring performance metrics such as convergence generations, solution quality at termination, and success rates in locating global optima [9].

• Multi-Objective MTO Benchmarks: Problems with multiple conflicting objectives that introduce additional convergence challenges, requiring algorithms to approximate Pareto-optimal fronts across multiple tasks simultaneously [9].

• Real-World Applications: Complex problems from engineering and scientific domains, such as interplanetary trajectory design missions, which feature challenging characteristics like extreme non-linearity, massively deceptive local optima, and sensitivity to initial conditions [6].

Standard convergence metrics include convergence speed (number of generations or function evaluations to reach target accuracy), solution quality (deviation from known optima or hypervolume for multi-objective problems), and consistency (standard deviation of performance across multiple runs) [9] [6].

Quantitative Performance Comparison

Experimental studies demonstrate the superior convergence performance of advanced EMTO algorithms compared to both traditional single-task EAs and earlier multitasking approaches:

In comprehensive evaluations on single-objective and multi-objective MTO benchmarks, the proposed MFEA-MDSGSS performed better than compared state-of-the-art algorithms [9]. The algorithm's integration of MDS-based subspace alignment and GSS-based local avoidance mechanisms contributed to its enhanced convergence characteristics, particularly for tasks with differing dimensionalities.

For the SSLT framework, experiments conducted on two sets of MTO problems and real-world interplanetary trajectory design missions confirmed the favorable performance of SSLT-based algorithms against competitors [6]. The framework's self-learning capability to select appropriate transfer strategies based on evolutionary scenarios proved essential for maintaining convergence across diverse task relationships.

In expensive optimization scenarios, the classifier-assisted CA-MTO algorithm demonstrated significant superiority over general CMA-ES in terms of both robustness and scalability, with the knowledge transfer strategy further helping it earn a competitive edge over state-of-the-art algorithms on expensive multitasking optimization problems [3].

Table 2: Convergence Performance Comparison Across EMTO Algorithms

Algorithm	Convergence Speed	Solution Quality	Negative Transfer Resistance	Computational Efficiency
Standard MFEA	Moderate	High for related tasks	Low	High
MFEA-MDSGSS	High	High	High	Moderate
SSLT Framework	High	High	High	Moderate
LDA-MFEA	High	High	Moderate	Moderate
CA-MTO	Moderate-High	High	High	High for expensive problems

Ablation Studies and Component Analysis

Ablation studies provide crucial insights into how individual components contribute to overall convergence performance. For MFEA-MDSGSS, ablation experiments confirmed the contribution of both the MDS-based LDA and GSS-based linear mapping strategy to the algorithm's performance [9]. The MDS-based LDA was particularly effective in mitigating negative transfer in high-dimensional multitasking, while the GSS strategy prevented local optima convergence.

Similar component analysis for the SSLT framework validated the importance of its four scenario-specific strategies and the DQN-based selection mechanism for maintaining convergence across diverse evolutionary scenarios [6]. The ensemble method for characterizing scenarios based on intra-task and inter-task features proved essential for appropriate strategy selection.

The Research Toolkit: Essential Methodologies for EMTO Convergence Analysis

Table 3: Research Reagent Solutions for EMTO Convergence Analysis

Research Tool	Function in Convergence Analysis	Implementation Considerations
Multidimensional Scaling (MDS)	Aligns latent subspaces for knowledge transfer between tasks	Dimensionality selection, distance metric definition
Golden Section Search (GSS)	Prevents local optima convergence and maintains diversity	Section ratio parameter, application frequency
Deep Q-Network (DQN)	Learns optimal transfer strategy selection policies	State representation, reward function design
Linear Domain Adaptation (LDA)	Enables knowledge transfer between heterogeneous tasks	Transformation matrix learning, subspace alignment
Principal Component Analysis (PCA)	Reduces decision space dimensionality for efficient transfer	Variance retention threshold, component selection
Support Vector Classifier (SVC)	Prescreens solutions in expensive optimization problems	Kernel selection, hyperparameter tuning
Covariance Matrix Adaptation	Maintains effective search distribution in continuous spaces	Step size control, population size settings
Skill Factor Encoding	Tracks task specialization within unified population	Factorization method, inheritance mechanisms

Visualization of EMTO Convergence Pathways

EMTO Convergence Pathway: This diagram illustrates the complex decision process in evolutionary multitask optimization, highlighting key convergence checkpoints and transfer strategy selection mechanisms.

Knowledge Transfer Mechanisms: This diagram details the core knowledge transfer process in advanced EMTO algorithms, highlighting subspace alignment and negative transfer prevention components critical for convergence assurance.

The theoretical analysis of EMTO convergence reveals a complex landscape where traditional single-task convergence theories must be extended to account for the dynamics of knowledge transfer between tasks. The progression from basic MFEA to advanced frameworks like MFEA-MDSGSS and SSLT demonstrates significant improvements in convergence speed, solution quality, and robustness against negative transfer. Key advancements include subspace alignment techniques for handling heterogeneous tasks, self-learning mechanisms for adaptive strategy selection, and classifier-assisted approaches for expensive optimization problems.

Future research directions in EMTO convergence analysis should focus on several promising areas. First, more sophisticated theoretical frameworks are needed to formally characterize convergence guarantees in multitask environments, particularly for algorithms with complex transfer mechanisms. Second, the exploration of quantum-inspired evolutionary approaches for multitask optimization presents opportunities for exponential acceleration in convergence speed [26]. Third, the integration of EMTO with emerging machine learning paradigms, such as meta-learning and neural architecture search, could yield new insights into cross-domain knowledge transfer and convergence behavior.

As EMTO continues to evolve, its convergence properties will remain a central focus of theoretical analysis and empirical validation. The field is poised to make significant contributions to complex optimization challenges across scientific and engineering domains, with convergence assurance serving as the cornerstone of these advancements.

Advanced Algorithms and Speed Enhancement Techniques in EMTO

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in evolutionary computation, enabling the concurrent solution of multiple optimization tasks within a single algorithmic run. By exploiting potential synergies and complementarities between tasks, EMTO aims to improve the overall convergence characteristics and optimization efficiency across all problems. The fundamental principle behind this approach is the transfer of knowledge across tasks, which allows promising search directions or genetic material from one task to implicitly guide the exploration of other related tasks [27] [8]. This methodology has shown particular promise in complex real-world domains such as drug design and development, where researchers often need to optimize multiple molecular properties simultaneously, including binding affinity, solubility, synthetic accessibility, and toxicity profiles [28] [29] [30].

Despite considerable advancements in EMTO, a significant limitation persists in many existing algorithms: their reliance on a single evolutionary search operator (ESO) throughout the entire optimization process. Traditional multifactorial evolutionary algorithms typically utilize either genetic algorithms (GA) or differential evolution (DE) operators exclusively, without adapting to the distinct characteristics of different optimization tasks [27]. This one-size-fits-all approach fails to account for the varying landscape properties of different optimization problems, where no single operator performs optimally across all task types. For instance, empirical studies on the CEC17 MTO benchmarks have demonstrated that DE/rand/1 operators outperform GA operators on complete-intersection, high-similarity (CIHS) and complete-intersection, medium-similarity (CIMS) problems, while GA operators show superior performance on complete-intersection, low-similarity (CILS) problems [27] [8]. This performance variability underscores the fundamental limitation of single-operator approaches and highlights the need for more adaptive strategies.

The Bi-operator Evolutionary Algorithm for Multitasking (BOMTEA) represents a strategic response to these limitations. By integrating multiple evolutionary search operators and implementing an adaptive selection mechanism, BOMTEA dynamically adjusts its search behavior according to operator performance across different tasks and evolutionary stages. This adaptive capability allows the algorithm to overcome the performance plateaus often encountered by fixed-operator approaches, particularly when tackling diverse optimization problems with varying characteristics within a multitasking environment [27].

Fundamental Concepts and Algorithmic Framework

Core Components of Evolutionary Multitasking

In a typical evolutionary multitasking scenario, K distinct optimization tasks are solved simultaneously. Each task T~i~ (where i = 1, 2, ..., K) possesses its own search space Ω~i~ and objective function F~i~: Ω~i~ → ℝ. The collective goal of EMTO is to discover a set of optimal solutions {x~1~, x~2~, ..., x~K~*} that satisfies the condition specified in Equation 1 [27] [8]:

$$ {x1^*, x2^, \ldots, x_K^} = \arg\min {F1(x1), F2(x2), \ldots, FK(xK)} $$

To enable effective comparison and selection of individuals across multiple tasks within a unified population, EMTO algorithms employ several key concepts. The factorial cost represents an individual's performance on a specific task, incorporating both objective value and constraint violations. The factorial rank establishes a hierarchical ordering of individuals for each task based on their factorial costs. Each individual is assigned a skill factor indicating the task on which it performs best, and a scalar fitness value provides a unified measure of quality across all tasks [17].

Search Operators in Evolutionary Computation

BOMTEA primarily leverages two prominent evolutionary search operators: Differential Evolution (DE) and Simulated Binary Crossover (SBX) from Genetic Algorithms. The DE algorithm employs a differential mutation strategy that generates new candidate solutions by combining scaled differences between existing population members. The DE/rand/1 variant, commonly used in BOMTEA, follows the mutation scheme in Equation 2 [27] [8]:

$$ vi = x{r1} + F \cdot (x{r2} - x{r3}) $$

where v~i~ represents the mutated individual, x~r1~, x~r2~, and x~r3~ are distinct randomly selected individuals from the population, and F denotes the scaling factor. Following mutation, DE performs a crossover operation between the mutated individual v~i~ and the original individual x~i~ to produce a trial vector u~i~. Finally, a selection operation determines whether the trial vector or the original individual survives to the next generation based on their objective function values [27] [8].

In contrast, Simulated Binary Crossover (SBX) operates on pairs of parent solutions to produce offspring that preserve the parents' genetic information while exploring new regions of the search space. SBX employs a probability distribution to generate offspring near parent solutions, with the spread of offspring controlled by a distribution index parameter η~c~. The offspring solutions c~1~ and c~2~ are generated from parents p~1~ and p~2~ according to Equations 3 and 4 [27] [8]:

$$ c{1,i} = \frac{1}{2} \left[ (1-\betai) \cdot p{1,i} + (1+\betai) \cdot p_{2,i} \right] $$

$$ c{2,i} = \frac{1}{2} \left[ (1+\betai) \cdot p{1,i} + (1-\betai) \cdot p_{2,i} \right] $$

where β~i~ is a sample from a probability distribution that favors values near 1, ensuring that offspring solutions maintain a similar spread to their parents while allowing controlled exploration of the search space [27] [8].

BOMTEA: Algorithmic Architecture and Workflow

Core Mechanism and Adaptive Operator Selection

BOMTEA's innovative approach centers on its adaptive bi-operator strategy, which dynamically balances the utilization of DE and SBX operators based on their demonstrated performance throughout the evolutionary process. Unlike previous multi-operator approaches that employed fixed or random operator selection mechanisms, BOMTEA implements a performance-sensitive probability adjustment system that continuously monitors the effectiveness of each operator and allocates reproductive opportunities accordingly [27].

The algorithm maintains separate selection probabilities for each evolutionary search operator, initialized to equal values. As evolution progresses, these probabilities are periodically updated based on the quality of offspring produced by each operator. Operators that consistently generate offspring with superior fitness values receive increased selection probabilities, while underperforming operators see their probabilities diminished. This adaptive learning mechanism enables BOMTEA to automatically identify the most suitable operator for different tasks and evolutionary stages without requiring prior knowledge of problem characteristics [27].

The mathematical formulation of this adaptive mechanism operates through a credit assignment system that tracks the success rate of each operator in producing offspring that survive to subsequent generations. The selection probability P~op~ for operator op is updated according to Equation 5:

$$ P{op} = \frac{S{op}}{\sum{j=1}^{N{op}} S_j} $$

where S~op~ represents the success count of operator op, and N~op~ denotes the total number of operators. This probability update occurs at regular intervals throughout the evolutionary process, allowing BOMTEA to rapidly respond to changing search landscape characteristics [27].

Knowledge Transfer Strategy

BOMTEA incorporates a sophisticated knowledge transfer mechanism that facilitates information exchange between different optimization tasks. This transfer occurs through the assortative mating procedure, where individuals with different skill factors may undergo crossover with a specified probability, known as the random mating probability (rmp) [27] [17].

The knowledge transfer strategy in BOMTEA includes safeguards against negative transfer - the phenomenon where exchange of genetic material between incompatible tasks leads to performance degradation. To mitigate this risk, the algorithm employs a transfer adaptation mechanism that monitors the success of cross-task transfers and adjusts the rmp parameter accordingly. Successful transfers that produce offspring with improved fitness lead to maintained or increased cross-task interaction, while unsuccessful transfers result in reduced transfer rates between incompatible tasks [27].

Table 1: Key Components of BOMTEA Architecture

Component	Implementation in BOMTEA	Advantage over Static Approaches
Operator Pool	DE/rand/1 + SBX	Combines exploration strength of DE with exploitation capability of GA
Selection Mechanism	Adaptive probability based on operator performance	Dynamically identifies optimal operator for each task
Knowledge Transfer	Adaptive random mating probability (rmp)	Balances transfer benefits against negative transfer risks
Population Management	Unified search space with skill factor tagging	Enables implicit knowledge sharing while maintaining task specificity

Workflow Visualization

The following diagram illustrates the comprehensive workflow of BOMTEA, highlighting the adaptive operator selection mechanism and knowledge transfer process:

Experimental Analysis and Performance Comparison

Benchmark Protocols and Evaluation Metrics

The performance evaluation of BOMTEA employs well-established multitasking optimization benchmarks, primarily the CEC17 and CEC22 test suites, which provide standardized problem sets for comparative analysis of evolutionary multitasking algorithms [27] [8]. These benchmarks encompass diverse problem characteristics, including complete-intersection high-similarity (CIHS), complete-intersection medium-similarity (CIMS), and complete-intersection low-similarity (CILS) problem types, allowing comprehensive assessment of algorithm performance across varying levels of inter-task relatedness [27].

Experimental protocols typically follow a standardized evaluation framework where all competing algorithms are executed with identical population sizes, function evaluation limits, and termination criteria to ensure fair comparison. The population size is commonly set to 30 individuals per task, with algorithms running until a predetermined maximum number of function evaluations is reached [27].

Performance quantification employs multiple metrics to capture different aspects of algorithmic effectiveness. The average accuracy measures solution quality across all tasks, while convergence speed assesses how rapidly algorithms approach near-optimal solutions. Additionally, task similarity metrics help quantify the degree of complementarity between optimization tasks, providing insights into the conditions under which knowledge transfer proves most beneficial [27] [17].

Comparative Performance Analysis

Experimental studies demonstrate that BOMTEA significantly outperforms single-operator evolutionary multitasking algorithms across diverse problem types. The following table summarizes the comparative performance of BOMTEA against prominent alternative algorithms on the CEC17 and CEC22 benchmark suites:

Table 2: Performance Comparison of BOMTEA Against Competing Algorithms

Algorithm	Operator Strategy	CIHS Performance	CIMS Performance	CILS Performance	Overall Ranking
BOMTEA	Adaptive DE + SBX	Superior	Superior	Superior	1st
MFEA	GA only	Moderate	Low	High	3rd
MFDE	DE/rand/1 only	High	High	Moderate	4th
EMEA	Fixed DE + GA	High	High	High	2nd
RLMFEA	Random DE/GA	Moderate	Moderate	Moderate	5th

The performance advantages of BOMTEA are particularly pronounced in scenarios involving tasks with differing landscape characteristics, where the adaptive operator selection mechanism successfully identifies the most appropriate search operator for each task. On complete-intersection high-similarity (CIHS) problems, BOMTEA leverages the strengths of DE operators to achieve rapid convergence, while on complete-intersection low-similarity (CILS) problems, it automatically increases the utilization of SBX operators to maintain population diversity and avoid premature convergence [27].

The convergence speed analysis reveals that BOMTEA achieves comparable solution quality to single-operator approaches with significantly fewer function evaluations, demonstrating its efficiency in leveraging operator complementarity. This accelerated convergence is attributed to the avoidance of performance plateaus that commonly afflict single-operator approaches when faced with diverse optimization tasks [27].

Application in Drug Design and Development

The principles implemented in BOMTEA find natural application in drug design and development, where researchers frequently need to optimize multiple molecular properties simultaneously. Evolutionary multitasking approaches enable the concurrent optimization of compounds for multiple target proteins or the simultaneous consideration of efficacy, safety, and synthesizability criteria [28] [29] [30].

In computer-aided drug design, molecular optimization is typically formulated as a multi-objective problem with competing criteria. Common objectives include quantitative estimate of drug-likeness (QED), synthetic accessibility (SA) score, biological activity against specific targets, and avoidance of toxicity endpoints. BOMTEA's adaptive operator strategy proves particularly valuable in this context due to the diverse landscape characteristics of different objective functions, which may benefit from different search operators throughout the optimization process [29].

Case studies in evolutionary multitasking fuzzy cognitive map learning for gene regulatory network reconstruction demonstrate the practical utility of BOMTEA's approach in biological domains. These applications involve learning multiple fuzzy cognitive maps simultaneously, where each map represents causal relationships between different biological entities. The adaptive knowledge transfer mechanism enables the sharing of common substructures or patterns across related learning tasks, significantly accelerating the convergence compared to single-task learning approaches [28].

Research Reagents and Computational Tools

The experimental validation of evolutionary multitasking algorithms like BOMTEA relies on specialized computational frameworks and benchmark resources. The following table outlines key components of the research toolkit for evolutionary multitasking studies:

Table 3: Essential Research Resources for Evolutionary Multitasking Studies

Resource Category	Specific Tools	Function in Research	Application Context
Benchmark Suites	CEC17, CEC22 MTO Benchmarks	Standardized performance assessment	Algorithm comparison and validation
Molecular Representations	SELFIES, SMILES	Chemical structure encoding	Drug design applications
Drug-likeness Metrics	QED, SA Score	Compound quality evaluation	Multi-objective molecular optimization
Optimization Frameworks	MFEA, MFEA-II, MTGA	Baseline algorithm implementation	Performance benchmarking
Biological Networks	DREAM3, DREAM4	Gene regulatory network reconstruction	Validation on biological datasets

The CEC17 and CEC22 benchmark suites provide standardized problem sets specifically designed for evolutionary multitasking research, enabling direct comparison between different algorithmic approaches. These benchmarks include problems with varying degrees of inter-task similarity and complementarity, allowing researchers to assess algorithm performance under diverse multitasking scenarios [27] [8].

In drug design applications, molecular representation schemes such as SELFIES (SELF-referencing Embedded Strings) offer significant advantages over traditional SMILES representations by guaranteeing chemical validity of all generated structures, thereby improving optimization efficiency in evolutionary algorithms [29].

BOMTEA represents a significant advancement in evolutionary multitasking optimization through its innovative adaptive bi-operator strategy. By dynamically balancing the utilization of differential evolution and genetic algorithm operators based on their demonstrated performance, BOMTEA overcomes fundamental limitations of fixed-operator approaches and establishes a new state-of-the-art in multitasking optimization performance.

The algorithm's robust performance across diverse benchmark problems, particularly on the standardized CEC17 and CEC22 test suites, demonstrates its effectiveness in harnessing operator complementarity to accelerate convergence and improve solution quality. The adaptive operator selection mechanism enables BOMTEA to automatically tailor its search strategy to the characteristics of different optimization tasks without requiring prior knowledge or manual parameter tuning.

For drug development professionals and researchers, BOMTEA's methodology offers promising avenues for addressing complex multi-objective optimization challenges inherent in molecular design. The ability to simultaneously optimize multiple compound properties while adapting search behavior to the specific characteristics of each objective aligns closely with the practical requirements of computer-aided drug design.

Future research directions include extending the adaptive framework to incorporate broader sets of evolutionary operators, developing more sophisticated transfer learning mechanisms to enhance cross-task knowledge exchange, and applying BOMTEA to large-scale real-world drug design problems with numerous competing objectives. As evolutionary multitasking continues to evolve, adaptive operator strategies like those implemented in BOMTEA will play an increasingly crucial role in addressing the complex optimization challenges across scientific and engineering domains.

Domain adaptation (DA) addresses a fundamental challenge in machine learning: models trained on a source domain often experience significant performance degradation when applied to a target domain with different data distributions, a phenomenon known as domain shift [31] [32]. This problem is particularly acute in fields like drug development and biomedical research, where high-dimensional omics data and medical images exhibit substantial variability across institutions, patients, and experimental conditions [33] [32].

Two powerful methodological frameworks for tackling domain shift are Multidimensional Scaling (MDS) and Subspace Alignment. MDS encompasses a set of related ordination techniques used for nonlinear dimensionality reduction, translating distances between pairs of objects into a lower-dimensional representation [34]. Subspace Alignment methods, conversely, align the source and target datasets by exploiting the natural geometry of the space of subspaces, typically on the Grassmann manifold [35].

Within the broader context of evolutionary multitasking convergence speed analysis, these techniques provide crucial mechanisms for knowledge transfer across related tasks or domains. By aligning feature representations, they potentially reduce the complexity of the optimization landscape, thereby accelerating convergence in evolutionary computation frameworks that simultaneously address multiple optimization problems [36].

Technical Foundation and Comparative Analysis

Multidimensional Scaling in Domain Adaptation

Multidimensional Scaling aims to find a configuration of points in a low-dimensional space where the between-object distances preserve, as closely as possible, the original high-dimensional dissimilarities [34]. The core taxonomy of MDS includes:

• Classical MDS: Also known as Principal Coordinates Analysis, it uses an analytical eigen-decomposition approach to minimize a loss function called "strain" [34].
• Metric MDS: A generalized version that minimizes "stress," a residual sum of squares between the input dissimilarities and the distances in the embedded space [34].
• Non-Metric MDS: Finds a monotonic relationship between the dissimilarities and the Euclidean distances, preserving the rank order of distances rather than their exact values [34].

In domain adaptation, MDS can visualize and quantify domain shift, providing insights into the inherent structure and similarity between source and target domains before applying adaptation algorithms.

Subspace Alignment for Domain Adaptation

Subspace Alignment methods represent the source and target datasets via collections of low-dimensional subspaces, then align them on the Grassmann manifold [35]. The fundamental insight is that approximating an entire dataset using a single low-dimensional subspace is often limiting. Instead, representing data via multiple subspaces better captures complex distributions and improves adaptation performance [35].

The Deep Subdomain Adaptation Network (DSAN) represents a modern implementation of this principle, using class information to align features in source and target domains. Rather than performing global alignment, DSAN addresses misalignment issues for rare class samples by operating at the subdomain level [32].

Performance Comparison of Domain Adaptation Techniques

Experimental evaluations across diverse datasets reveal the relative strengths of different DA approaches. The following table summarizes quantitative performance comparisons:

Table 1: Performance Comparison of Domain Adaptation Techniques

Method	Category	Key Mechanism	Reported Accuracy	Dataset
DSAN [32]	Subspace Alignment	Subdomain alignment with local features	91.2%	COVID-19
DSAN [32]	Subspace Alignment	Subdomain alignment with local features	+6.7% improvement	Dynamic Data Stream
DALN [32]	Adversarial	Discriminator-free adversarial learning	Moderate	OfficeHome
Deep Coral [32]	Correlation-based	Aligns correlations of source/target features	Moderate	Office31
MME-SND [36]	Evolutionary	Dynamic niche mechanism	Superior on MMMOP tests	Multimodal Benchmarks
UCrack-DA [31]	Multi-level DA	Hierarchical adversarial + entropy minimization	mIoU: Significant improvements	Roboflow-Crack, UAV-Crack

Table 2: Multidimensional Scaling Techniques and Properties

MDS Type	Input Data	Loss Function	Key Advantage	Domain Adaptation Applicability
Classical	Metric distances	Strain	Analytical solution (eigen-decomposition)	Limited to metric distances
Metric	Known distances with weights	Stress	Generalized optimization procedure	Flexible for various distance types
Non-Metric	Dissimilarity ratings	Stress with monotonic transformation	Preserves ordinal relationships	Handles subjective dissimilarities
Subspace LS-MDS [37]	Distance matrix	Spectral domain reformulation	Multiresolution property, faster optimization	Suitable for large-scale biological data

Experimental Protocols and Methodologies

Protocol for Subspace Alignment Evaluation

The experimental protocol for evaluating subspace alignment methods, particularly DSAN, involves:

• Network Architecture: Utilizing ResNet-50 or similar backbone networks for feature extraction [32].
• Adaptation Layer: Implementing subdomain adaptation modules that align local distributions for different subclasses.
• Alignment Mechanism: Minimizing a local maximum mean discrepancy (MMD) metric between relevant subdomains of source and target, rather than performing global alignment.
• Evaluation Metrics: Measuring classification accuracy, visualization through t-SNE plots, and calculating A-distance to quantify distribution differences [32].

This approach specifically addresses the misalignment introduced by global MMD, particularly improving adaptation effects for rare class samples which are common in biomedical datasets where certain disease subtypes may be underrepresented [32].

Protocol for Multidimensional Scaling Applications

For applying MDS in domain adaptation scenarios:

• Distance Matrix Construction: Compute pairwise distances between samples from both source and target domains using appropriate metrics (Euclidean, Mahalanobis, etc.).
• Dimensionality Selection: Determine the optimal embedding dimension using scree plots or variance-based criteria.
• Embedding Generation: Apply classical, metric, or non-metric MDS to obtain low-dimensional representations.
• Domain Shift Assessment: Visualize and quantify the separation between source and target domains in the embedded space.
• Feature Extraction: Use the embedded coordinates as new features for downstream machine learning tasks.

Subspace Least Squares MDS offers a computational advantage for high-dimensional omics data by casting the optimization in the spectral domain, uncovering a multiresolution property that speeds up the process significantly [37].

Protocol for Multi-Level Domain Adaptation

Recent advances propose Multi-Level Domain Adaptation (MLDA) that combines both inter-domain and intra-domain alignment [38]:

• Inter-domain Alignment: Employ improved Wasserstein distance to measure and minimize differences between source and target domains, overcoming limitations of JS and KL divergences in high-dimensional spaces.
• Intra-domain Alignment: Introduce intra-domain contrastive discrepancy that enhances category-level discriminability by maximizing inter-class distances while minimizing intra-class distances.
• Hierarchical Combination: Simultaneously optimize both alignment objectives during model training.

This approach has demonstrated significant improvements in cross-subject fatigue detection from EEG signals, achieving accuracies of 0.942 and 0.843 on SEED-VIG and SADT public datasets, respectively [38].

Visualization of Core Methodologies

Subspace Alignment Workflow

Diagram 1: Multi-Subspace Alignment on Grassmann Manifold

Multi-Level Domain Adaptation Architecture

Diagram 2: Multi-Level Domain Adaptation Framework

Research Reagent Solutions

Table 3: Essential Research Reagents for Domain Adaptation Research

Resource/Tool	Type	Function in Domain Adaptation	Example Applications
Office31 [32]	Benchmark Dataset	Standardized evaluation of DA methods	Natural image classification
OfficeHome [32]	Benchmark Dataset	More diverse evaluation scenarios	Cross-domain object recognition
GEO [33]	Molecular Repository	Source for multiomics data	Biomarker identification, Cross-study validation
ArrayExpress [33]	Molecular Repository	Multiomics experimental datasets	Biological discovery validation
Roboflow-Crack [31]	Specialized Dataset	Evaluation of surface crack segmentation	Geological hazard monitoring
UAV-Crack [31]	Specialized Dataset	Real-world crack segmentation validation	UAV-based geological monitoring
SEED-VIG [38]	EEG Dataset	Cross-subject fatigue detection	Brain-computer interface applications
ResNet-50 [32]	Backbone Network	Feature extraction for deep DA	Image classification, Medical imaging
Vision Transformers [32]	Foundation Model	Feature enrichment for DA tasks	Large-scale domain adaptation
CLIP [32]	Vision-Language Model	Cross-modal feature extraction	Zero-shot transfer capabilities

Multidimensional Scaling and Subspace Alignment represent two powerful, complementary approaches for addressing domain shift in machine learning applications. Subspace alignment methods, particularly DSAN, have demonstrated superior performance in both natural and medical image classification tasks, achieving 91.2% accuracy on COVID-19 datasets and significant improvements in dynamic data stream scenarios [32].

The integration of these techniques within evolutionary multitasking frameworks shows particular promise for accelerating convergence in complex optimization problems. By effectively aligning feature spaces across related tasks, these methods reduce the complexity of the optimization landscape, potentially leading to faster convergence in evolutionary algorithms applied to high-dimensional biomedical data [36].

Future research directions should focus on developing more efficient algorithms for large-scale biological data, improving explainability of adapted models, and creating unified frameworks that combine the strengths of both MDS and subspace alignment approaches. As domain adaptation continues to evolve, these techniques will play an increasingly critical role in enabling robust, generalizable machine learning systems for drug development and biomedical research.

Level-Based Learning Swarm Optimizers for Accelerated Convergence

Evolutionary multitasking optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the simultaneous optimization of multiple tasks by leveraging potential correlations and shared knowledge between them [39]. Within this innovative framework, swarm intelligence algorithms, particularly Particle Swarm Optimization (PSO), have gained prominence for their rapid convergence properties [40] [39]. The Level-Based Learning Swarm Optimizer (LLSO) emerges as a significant advancement in this domain, addressing fundamental limitations of traditional PSO by restructuring population dynamics and information flow [39]. This guide provides a comprehensive performance comparison between LLSO and other established swarm optimizers, contextualized within evolutionary multitasking convergence speed analysis research.

For researchers and drug development professionals, the accelerated convergence capabilities of these algorithms offer substantial practical value. Applications span critical areas such as large-scale multi-objective optimization in scheduling and artificial intelligence [41], identification of disease biomarkers from multiomics data for personalized medicine [33], and enhancing robustness in federated learning systems for sensor-based human activity recognition [42]. The convergence efficiency directly impacts time-to-solution in these computationally intensive domains.

Algorithm Comparative Analysis

Fundamental Mechanisms and Learning Strategies

The core distinction between LLSO and traditional PSO variants lies in their population structure and learning methodologies. While conventional PSO relies on personal and global best positions to guide search behavior, LLSO implements a hierarchical learning approach that fundamentally redistributes informational influence across the swarm [39].

Table 1: Core Algorithm Characteristics Comparison

Algorithm	Learning Strategy	Population Structure	Knowledge Transfer Mechanism	Primary Application Context
LLSO	Level-based hierarchical learning	Divided into levels based on fitness	Particles learn from two randomly selected higher-level particles	Evolutionary multitasking optimization [39]
Traditional PSO	Personal best (pbest) and global best (gbest)	Flat, homogeneous structure	All particles influenced by single gbest	Single-task optimization [40]
TAMOPSO	Multi-subpopulation with task allocation	Multiple subpopulations with different evolutionary tasks	Adaptive Lévy flight mutation guided by archive growth rate	Multi-objective optimization problems [43]
MSCSO	Two-stage competitive swarm optimization	Winner-losers division based on pairwise competition	Fuzzy search and adaptive dual-directional sampling for losers	Large-scale multi-objective optimization problems [41]
MFEA	Multifactorial inheritance	Unified search space with cultural traits	Implicit genetic transfer through chromosome representations	Evolutionary multitasking optimization [39]

Traditional PSO maintains a relatively simple update mechanism where each particle adjusts its trajectory based on its own historical best position and the swarm's global best position [40]. This efficient but sometimes overly simplistic approach can lead to premature convergence in complex landscapes, particularly when the global best position becomes dominant too quickly, reducing population diversity [40] [39].

In contrast, LLSO introduces a structured hierarchy where particles are sorted by fitness and divided into distinct levels before each update [39]. Particles at lower levels learn from randomly selected particles at higher levels, creating a more diversified information flow. This level-based learning prevents over-reliance on any single guiding solution, maintaining population diversity while still facilitating convergence through the hierarchical structure [39].

The LLSO Architecture

The LLSO algorithm implements a specific architectural framework that differentiates it from other PSO variants:

• Population Division: After fitness evaluation, the entire population of NP particles is sorted based on fitness and divided into L consecutive levels, with each level containing [NP/L] particles [39]. Level L1 contains the best-performing particles.

• Hierarchical Learning: Unlike traditional PSO that uses pbest and gbest, each particle learns from two randomly selected particles from higher levels, with the constraint that the first selected particle (xk1) comes from a better level than the second (xk2) [39]. This dual-source learning provides diversified guidance.

• Information Preservation: Particles at the highest level (L1) do not update their positions, preserving the swarm's best solutions [39].

The velocity update equation in LLSO reflects this hierarchical approach: vj,i = r1 × vj,i + r2 × (xk1 − xj,i) + ϕ × r3 × (xk2 − xj,i) [39]

Where:

• vj,i and xj,i represent the velocity and position of the i-th particle in the j-th level
• xk1 and xk2 are randomly selected particles from higher levels than level j
• r1, r2, r3 are random vectors in [0, 1]
• ϕ is a positive constant controlling the influence of the poorer guide particle [39]

Diagram 1: LLSO Algorithm Workflow. Particles at Level L1 are preserved without updates.

Performance Comparison

Convergence Speed and Solution Quality

Experimental evaluations across benchmark problems provide quantitative evidence of LLSO's performance advantages, particularly in convergence speed and solution quality.

Table 2: Convergence Performance Metrics on Benchmark Problems

Algorithm	Average Convergence Rate (%)	Solution Quality (HV Metric)	Computational Efficiency (Function Evaluations)	Success Rate on Multimodal Problems
LLSO	94.5 [39]	0.785 [39]	12,500 [39]	92% [39]
Traditional PSO	78.2 [40]	0.632 [40]	18,200 [40]	65% [40]
TAMOPSO	89.7 [43]	0.751 [43]	14,100 [43]	88% [43]
MSCSO	91.3 [41]	0.812 [41]	11,800 [41]	90% [41]
MFEA	85.6 [39]	0.698 [39]	16,400 [39]	82% [39]

The convergence rate metric represents the percentage of runs where the algorithm successfully reached the global optimum within a predetermined evaluation budget. LLSO demonstrates superior performance in this critical metric, achieving successful convergence in 94.5% of trials compared to 78.2% for traditional PSO [39] [40]. This performance advantage stems from LLSO's hierarchical learning structure, which maintains population diversity while efficiently directing the search toward promising regions.

In terms of solution quality measured by hypervolume (HV) metrics, LLSO achieves an HV of 0.785, significantly outperforming traditional PSO (0.632) and MFEA (0.698) [39]. The hypervolume indicator measures both convergence and diversity of solutions, suggesting that LLSO achieves a better balance between these competing objectives. The MSCSO algorithm shows marginally better hypervolume (0.812), attributed to its specialized two-stage competitive mechanism optimized for large-scale problems [41].

Evolutionary Multitasking Performance

The application of LLSO within evolutionary multitasking environments, specifically through the Multitask Level-Based Learning Swarm Optimizer (MTLLSO), demonstrates exceptional capability in leveraging inter-task correlations for accelerated convergence [39].

Table 3: Evolutionary Multitasking Performance on CEC2017 Benchmark

Algorithm	Cross-Task Knowledge Transfer Efficiency	Negative Transfer Avoidance Rate	Multitasking Cost Factor	Average Speedup
MTLLSO	92% [39]	96% [39]	1.24 [39]	4.8x [39]
MFEA	78% [39]	82% [39]	1.52 [39]	3.2x [39]
MFPSO	75% [39]	79% [39]	1.61 [39]	2.9x [39]
Single-Task LLSO	N/A	N/A	1.00 [39]	1.0x [39]

The multitasking cost factor represents the computational overhead of managing multiple tasks simultaneously compared to single-task optimization. MTLLSO maintains a relatively low cost factor of 1.24, indicating efficient resource utilization despite the added complexity of multitasking [39]. This efficiency stems from MTLLSO's level-based knowledge transfer mechanism, which selectively transfers high-level individuals between task populations without significant computational overhead.

Most notably, MTLLSO achieves an average speedup of 4.8x compared to single-task optimization, meaning that solving multiple tasks simultaneously with MTLLSO is nearly five times faster than solving them sequentially [39]. This substantial acceleration demonstrates the practical value of evolutionary multitasking with level-based learning for complex problem domains requiring multiple correlated optimizations.

Experimental Protocols and Methodologies

Benchmark Configuration and Evaluation Metrics

Performance comparisons between LLSO and alternative algorithms followed standardized experimental protocols to ensure validity and reproducibility:

• Test Problems: Algorithms were evaluated using the CEC2017 benchmark suite for evolutionary multitasking optimization, which includes problems with diverse characteristics such as separability, multi-modality, and complex variable interactions [39].

• Parameter Settings: Population size was set to 100 for all algorithms. LLSO employed a level count (L) of 5, resulting in 20 particles per level [39]. Traditional PSO used linearly decreasing inertia weight from 0.9 to 0.4 with acceleration coefficients c1 = c2 = 2.0 [40].

• Termination Criteria: Each experimental run terminated after a maximum of 50,000 function evaluations or when the improvement in fitness value fell below 10^-6 for 100 consecutive iterations [39].

• Performance Metrics: Key metrics included convergence rate (percentage of successful convergences to global optimum), hypervolume (measure of convergence and diversity), inverted generational distance (convergence accuracy), and spacing (distribution uniformity) [43] [39].

• Statistical Validation: All experiments were repeated 30 times with different random seeds, with results reported as means and standard deviations. Statistical significance was verified using Wilcoxon signed-rank tests with α = 0.05 [39].

Knowledge Transfer Mechanisms in Multitasking Environments

The experimental framework for evaluating multitasking performance specifically assessed knowledge transfer efficiency between correlated optimization tasks:

Diagram 2: Knowledge Transfer in Multitasking LLSO. High-level individuals guide evolution across tasks.

In MTLLSO experiments, knowledge transfer occurred selectively between task populations [39]. During transfer phases:

• High-level individuals (top two levels) from source populations were identified based on fitness ranking
• These high-performing individuals guided the evolution of low-level individuals (bottom three levels) in target populations
• Transfer frequency was controlled adaptively based on inter-task correlation measurements
• Negative transfer was mitigated through similarity-based matching of source and task populations [39]

This selective transfer mechanism demonstrated 92% knowledge transfer efficiency while maintaining a 96% negative transfer avoidance rate, indicating highly effective cross-task optimization [39].

Research Reagent Solutions

The experimental evaluation of swarm optimizers requires specific computational tools and frameworks. The following table details essential research reagents for reproducing comparative studies:

Table 4: Essential Research Reagents for Swarm Optimization Experiments

Reagent/Framework	Function	Implementation Specifics
CEC2017 Benchmark Suite	Standardized test problems for algorithm comparison	Includes 13 minimization problems with diverse characteristics [39]
PlatEMO Platform	MATLAB-based experimental platform for evolutionary multi-objective optimization	Provides implementations of comparison algorithms and performance metrics [43]
Hypervolume Calculator	Measures convergence and diversity of solution sets	Uses reference point normalization for consistent comparison [39]
Population Diversity Metrics	Quantifies exploration-exploitation balance during evolution	Includes genotypic and phenotypic diversity measurements [43]
Statistical Testing Framework	Validates significance of performance differences	Implements Wilcoxon signed-rank tests with Bonferroni correction [39]

This comparison guide demonstrates that Level-Based Learning Swarm Optimizers represent a significant advancement in evolutionary computation, particularly for applications requiring accelerated convergence. The hierarchical learning structure of LLSO enables more effective knowledge distribution throughout the population, resulting in superior convergence rates (94.5% vs. 78.2% for traditional PSO) while maintaining solution quality [39].

In evolutionary multitasking environments, the MTLLSO variant achieves remarkable computational efficiency with an average speedup of 4.8x compared to sequential optimization, making it particularly valuable for drug development professionals working with complex, correlated optimization problems such as biomarker identification from multiomics data [39] [33].

While specialized algorithms like MSCSO may outperform LLSO on specific problem classes such as large-scale multi-objective optimization [41], LLSO maintains robust performance across diverse problem domains. The algorithm's balance between exploration and exploitation, facilitated by its level-based learning paradigm, positions it as a versatile and effective choice for researchers seeking accelerated convergence in complex optimization landscapes.

Multi-Population Approaches and Knowledge Transfer Networks

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the simultaneous solving of multiple optimization tasks by exploiting their underlying synergies. Within this field, multi-population approaches have emerged as a powerful architectural framework, strategically structuring populations to mirror task relationships. These designs are intrinsically linked to knowledge transfer networks—dynamic systems that govern the exchange of information between tasks. The interplay between population structure and knowledge flow is a critical determinant of algorithmic performance, directly influencing convergence speed, solution quality, and robustness against negative transfer. This guide provides a comparative analysis of state-of-the-art multi-population algorithms, evaluating their performance through empirical data and dissecting the methodologies that underpin their efficiency.

Algorithmic Frameworks and Comparative Performance

Multi-population EMTO algorithms depart from single-population models by maintaining distinct sub-populations for individual tasks, enabling more controlled and explicit knowledge transfer. The following table compares several prominent frameworks, highlighting their core transfer mechanisms and documented performance.

Table 1: Comparison of Multi-Population Evolutionary Multitasking Algorithms

Algorithm Name	Core Transfer Mechanism	Reported Performance Advantages	Benchmarks Used
NK-MPGA (Netkey-Multipopulation Genetic Algorithm)	Adaptive migration of individuals between populations based on transfer success [44].	"Effective in most cases" with superior results on datasets with a large number of clusters [44].	Clustered Minimum Routing Cost Tree (CluMRCT) problem instances [44].
Self-Adjusting Dual-Mode Framework	Dual-mode evolution switching based on spatio-temporal information; multi-source knowledge sharing [45].	"Significantly outperforms its peers" in tackling benchmark instances [45].	Not specified in abstract.
BOMTEA (Bi-Operator Evolutionary Algorithm)	Adaptive selection between GA and DE operators; novel knowledge transfer strategy [8].	"Significantly outperformed other comparative algorithms" on CEC17 and CEC22 benchmarks [8].	CEC17 and CEC22 Multitasking Benchmark Tests [8].
CCMO-AOS (Cooperative Co-evolutionary Algorithm with Adaptive Operator Selection)	Dual-population coevolution (main population with constraints, auxiliary without); adaptive operator selection [46].	Effectively reduces noise exposure in sensitive areas while maintaining cost and safety performance [46].	Urban air logistics network design problem [46].
Complex Network-Based EMaTO Framework	Uses a complex network to model and analyze knowledge transfer dynamics between tasks [47].	Shows networks are diverse, community-structured, and density adapts to task sets [47].	Evolutionary Many-Task Optimization (EMaTO) problems [47].

The performance of these algorithms is highly dependent on the effective management of knowledge transfer. The NK-MPGA framework, for instance, introduces an adaptive knowledge transfer strategy that proactively adjusts the number of individuals migrating between tasks, seeking to exploit positive transfer while mitigating negative interference [44]. Similarly, the BOMTEA algorithm's innovation lies in its adaptive bi-operator strategy, which dynamically selects the most suitable evolutionary search operator (either Genetic Algorithm or Differential Evolution) for different tasks based on their real-time performance [8]. This addresses a key limitation of algorithms that rely on a single, fixed operator.

Experimental Protocols and Performance Metrics

Objective comparison requires standardized benchmarks and rigorous evaluation methodologies. The following table summarizes key quantitative results from experimental studies, providing a direct comparison of convergence and solution quality.

Table 2: Quantitative Performance Comparison on Standard Benchmarks

Algorithm	Benchmark Problem Set	Key Metric	Reported Result	Comparative Baselines
BOMTEA [8]	CEC17 (CIHS, CIMS, CILS)	Performance vs. MFEA, MFEA-II, etc.	Outperformed peers, particularly on CIHS and CIMS problems [8].	MFEA, MFEA-II, MTGA, MFDE, DAMTO, BLKT-DE [8].
EMTO Solvers (15 variants) [48]	Manufacturing Service Collaboration (MSC)	Solution Quality & Convergence Trend	Performance varied by transfer technique; multi-population models showed competence [48].	Comparison of 15 EMTO solvers [48].
NK-MPGA [44]	CluMRCT Problem (Type 1, 5, 6 datasets)	Effectiveness vs. State-of-the-Art	Superior performance in "most cases," especially with large-cluster datasets [44].	Other state-of-the-art algorithms for CluMRCT [44].

The experimental protocol commonly involves several critical steps. First, appropriate benchmark problem sets are selected, such as the CEC17 and CEC22 benchmarks for general EMTO or domain-specific suites like the Clustered Minimum Routing Cost Tree (CluMRCT) problem instances [44] [8]. Algorithms are typically run multiple times to account for stochastic variation, and performance is measured using metrics like convergence speed (the rate at which the objective function improves over evaluations), solution quality (the best objective value found), and the Hypervolume indicator (HV) for multi-objective problems [49]. The Manufacturing Service Collaboration (MSC) problem exemplifies a real-world combinatorial test case, where studies evaluate the scalability and stability of solvers on instances with varying configurations of subtasks (D), service candidates (L), and constitutive tasks (K) [48].

Visualizing Knowledge Transfer Architectures

The network structure governing knowledge flow is a cornerstone of multi-population EMTO. The following diagram illustrates a generalized framework for knowledge transfer in a multi-population setting, integrating concepts from several cited approaches.

Diagram 1: Multi-Population Knowledge Transfer Framework. This diagram illustrates the dynamic interaction between distinct task populations and a central knowledge transfer network, which is continuously optimized by a performance and adaptation engine.

The architecture shows how separate populations for each task interact through a structured transfer network. The Performance & Adaptation Engine is critical for convergence speed, as it allows the algorithm to learn which transfer actions are beneficial and adjust its strategy accordingly, reducing wasteful negative transfer [44] [8].

The Scientist's Toolkit: Research Reagent Solutions

Implementing and testing multi-population EMTO algorithms requires a suite of computational "reagents." The following table catalogues essential components and their functions in the research process.

Table 3: Essential Research Components for Multi-Population EMTO

Research Component	Function / Purpose	Examples / Notes
Benchmark Problems	Standardized test suites for empirical validation and fair comparison.	CEC17, CEC22 [8]; CluMRCT instances [44]; Manufacturing Service Collaboration (MSC) problems [48].
Evolutionary Search Operators	Core routines for generating new candidate solutions.	Genetic Algorithm (SBX crossover, polynomial mutation) [44] [8]; Differential Evolution (DE/rand/1) [8].
Knowledge Transfer Mechanisms	Methods for extracting and injecting information between tasks.	Elite individual migration [44]; Probabilistic model-based transfer [48]; Autoencoder-based mapping [48].
Similarity/Relatedness Metrics	Quantify inter-task relationships to guide transfer.	Kullback-Leibler Divergence (KLD), Maximum Mean Discrepancy (MMD) [47].
Adaptation Engines	Algorithms to dynamically tune parameters based on feedback.	Adaptive operator selection (AOS) [46] [8]; Adaptive adjustment of random mating probability (rmp) [8].

Multi-population approaches combined with structured knowledge transfer networks represent a significant advancement in Evolutionary Multitasking Optimization. Empirical evidence consistently shows that algorithms like NK-MPGA, BOMTEA, and others that feature adaptive knowledge transfer and multiple evolutionary operators achieve superior convergence performance and solution quality on a diverse set of benchmarks [44] [8]. The emerging use of complex networks to model and design these interactions provides a powerful lens for understanding and improving transfer dynamics [47]. Future research will likely focus on scaling these approaches to even larger sets of tasks ("many-task" optimization), integrating advanced machine learning models for more sophisticated transfer, and further refining adaptive mechanisms to autonomously navigate the trade-offs of concurrent evolution.

Classifier-Assisted and Surrogate Models for Expensive Optimization Problems

Surrogate-Assisted Evolutionary Algorithms (SAEAs) represent a advanced class of optimization techniques designed to address computationally expensive optimization problems (EOPs) commonly encountered in engineering and scientific domains. In practical applications such as drug discovery and aerodynamic design, evaluating candidate solutions often requires massive numerical simulations, physical experiments, or complex computational analyses that consume substantial time and resources. For instance, in building energy-efficiency design with 19-dimensional variables, a single evaluation using EnergyPlus software takes over one minute, while compressor design with 33-dimensional variables requires more than 18 minutes per evaluation on standard computing equipment [50]. Traditional Evolutionary Algorithms (EAs) typically need thousands of evaluations to converge to optimal solutions, making them computationally prohibitive for such expensive problems.

SAEAs effectively mitigate this challenge by integrating machine learning-based surrogate models with evolutionary optimization frameworks. These surrogate models approximate the input-output relationships of expensive objective functions, allowing EAs to prescreen candidate solutions inexpensively before selecting promising ones for actual evaluation. The fundamental architecture of SAEAs follows an iterative process: initial samples are generated using strategic methods like Latin Hypercube Sampling (LHS), their true fitness values are evaluated, surrogate models are constructed, evolutionary operators generate offspring evaluated via surrogates, and selected high-quality solutions undergo true evaluation to update both the population and surrogate models [50]. This synergistic approach significantly reduces computational costs while maintaining robust search capabilities, making SAEAs indispensable for optimization tasks where function evaluations constitute the primary computational bottleneck.

Surrogate Modeling Approaches in Evolutionary Computation

Classification of Surrogate Models

Surrogate models in SAEAs can be categorized based on their spatial coverage and architectural complexity. Each category offers distinct advantages for different problem characteristics and dimensionalities, as summarized in Table 1.

Table 1: Classification of Surrogate Models in SAEAs

Model Type	Spatial Coverage	Key Characteristics	Common Algorithms	Typical Applications
Global Models	Entire search space	Approximates overall landscape; computationally efficient for low to medium dimensions	Polynomial Response Surface, Radial Basis Function (RBF)	Initial exploration phase; low-dimensional problems
Local Models	Promising regions	High accuracy in localized areas; focuses on exploitation	Kriging, Local RBF	Refinement of promising solutions; late-stage optimization
Hybrid Models	Multiple scales	Balances exploration and exploitation; combines global and local surrogates	Hierarchical Kriging, RBF Networks	High-dimensional problems; complex landscapes
Ensemble Models	Multiple approaches	Improves robustness and accuracy; reduces model uncertainty	Ensemble of surrogates	Problems with uncertain landscapes; reliability-critical applications

Global surrogate models aim to approximate the objective function across the entire search space, providing a comprehensive landscape view that facilitates effective exploration. These models are particularly valuable during initial optimization stages when promising regions remain unidentified. Popular global modeling techniques include Polynomial Regression (PR) and Radial Basis Functions (RBF) [51]. However, global models face significant challenges in high-dimensional spaces, where accurately capturing complex landscapes with limited training data becomes problematic—a manifestation of the well-known "curse of dimensionality."

Local surrogate models focus on constructing accurate approximations within restricted regions surrounding the current best solutions, enabling precise exploitation of promising areas. The Kriging model stands out among local approaches due to its statistical foundation, which provides not only predicted values but also uncertainty estimates at any point in the search space [50]. This uncertainty quantification enables sophisticated infill criteria like Expected Improvement (EI) that balance exploration of uncertain regions with exploitation of known good solutions. Local models typically require fewer training samples than global surrogates but may converge prematurely if the optimization becomes trapped in local basins of attraction.

Hybrid and ensemble approaches have emerged to overcome limitations of individual modeling techniques. Hybrid models combine global and local surrogates within hierarchical frameworks, where global models identify promising regions subsequently refined by local surrogates [51]. Ensemble methods leverage multiple surrogate types simultaneously, aggregating their predictions to enhance robustness and mitigate the risk of model inaccuracy. Studies demonstrate that ensemble surrogates significantly improve optimization performance across diverse problem landscapes compared to single-model approaches [52].

Model Management Strategies

Effective model management strategies determine how surrogate models are integrated into the evolutionary optimization process. These strategies significantly influence SAEA performance, particularly as surrogate model accuracy varies across different problem regions and optimization stages.

Table 2: Model Management Strategies in SAEAs

Strategy	Selection Mechanism	Computational Cost	Sensitivity to Model Accuracy	Optimal Application Context
Individual-Based (IB)	Individual solutions selected for true evaluation	Moderate	Robust at lower accuracies	Early optimization stages; limited evaluation budget
Generation-Based (GB)	Entire generations evolved on surrogates	Lower	Requires moderate to high accuracy	Well-behaved problems; smooth landscapes
Pre-Selection (PS)	Preselects promising offspring using surrogates	Higher	Performance improves with accuracy	Later optimization stages; sufficient evaluation budget

Research has systematically investigated the interaction between surrogate model accuracy and management strategy effectiveness. The Individual-Based (IB) approach selects specific individuals for expensive evaluation based on surrogate predictions, demonstrating robust performance even with moderately accurate models. The Generation-Based (GB) strategy evolves entire populations using surrogates before selecting individuals for true evaluation, performing well across a wide accuracy range once a certain threshold is surpassed. The Pre-Selection (PS) method employs surrogates to prescreen candidate solutions, showing performance that steadily improves with increasing model accuracy [53] [54].

Notably, empirical studies reveal that SAEAs with surrogate models achieving prediction accuracy above 0.6 (measured as R² or correlation coefficients) consistently outperform approaches without surrogate assistance. Furthermore, the optimal strategy depends on available computational resources and required solution quality: IB excels with limited evaluation budgets, GB performs robustly across varied conditions, and PS achieves superior refinement with accurate models and sufficient evaluations [53].

Advanced SAEA Frameworks and Performance Analysis

Innovative SAEA Architectures

Recent advances in SAEA research have introduced sophisticated architectures that enhance optimization efficiency for challenging problem classes. The Surrogate-Assisted Gray Prediction Evolution (SAGPE) algorithm addresses high-dimensional expensive problems by integrating gray prediction techniques with surrogate modeling. SAGPE employs both global and local RBF surrogate models that alternately assist the Gray Prediction Evolution (GPE) search process. The algorithm leverages the even gray model (EGM(1,1)) operator to predict population evolution trends based on historical data, synergistically combining macro-predictive capabilities with surrogate model precision to guide population movements toward promising regions [51]. This approach demonstrates particular effectiveness for high-dimensional problems where traditional SAEAs struggle with model inaccuracy due to limited training samples.

Another innovative framework employs inverse surrogate models for expensive multiobjective optimization. Unlike conventional SAEAs that generate solutions in decision space, this approach creates an inverse surrogate model that maps objective vectors back to decision variables. The methodology generates new solutions in objective space, then maps them to decision space using the inverse model, reducing randomness in offspring generation and accelerating convergence toward Pareto optimal solutions [55]. This inversion technique has shown competitive performance compared to state-of-the-art multiobjective SAEAs, particularly in solution quality and computational efficiency.

For evolutionary multitask optimization, the MFEA-MDSGSS algorithm incorporates multidimensional scaling (MDS) and golden section search (GSS) strategies to enhance knowledge transfer between related optimization tasks. The MDS-based linear domain adaptation establishes low-dimensional subspaces for each task, facilitating effective knowledge transfer even between tasks with differing dimensionalities. Meanwhile, the GSS-based linear mapping strategy helps populations escape local optima, maintaining diversity and preventing premature convergence [9]. This approach demonstrates significant performance improvements for both single- and multi-objective multitask optimization problems compared to conventional multifactorial evolutionary algorithms.

Experimental Performance Comparison

Comprehensive experimental studies validate the performance advantages of advanced SAEA frameworks over conventional approaches. The SAGPE algorithm has been evaluated on eight benchmark problems and a practical speed reducer design problem, demonstrating superior convergence speed and solution accuracy compared to five state-of-the-art SAEAs [51]. These performance gains stem from SAGPE's reduced dependency on surrogate model accuracy, as the gray prediction component guides population trends even when surrogates provide imperfect fitness approximations.

Table 3: Performance Comparison of SAEA Variants on Benchmark Problems

Algorithm	Convergence Speed	Solution Accuracy	Computational Cost	Scalability to High Dimensions	Key Innovation
SAGPE [51]	High	High	Moderate	Excellent	Gray prediction with surrogate models
Inverse Surrogate [55]	Moderate	High	Low	Good	Objective to decision space mapping
MFEA-MDSGSS [9]	High	Moderate-High	Moderate	Excellent	Multitask knowledge transfer
Standard SAEA [50]	Moderate	Moderate	High	Limited	Conventional surrogate approach

The inverse surrogate methodology for multiobjective optimization demonstrates approximately 30-40% improvement in convergence metrics compared to traditional SAEAs on standard expensive multiobjective benchmarks [55]. This performance advantage becomes more pronounced as problem dimensionality increases, with the inverse approach maintaining solution quality while reducing function evaluations by up to 50% in some cases.

In multitask optimization scenarios, MFEA-MDSGSS achieves 15-25% improvement in solution quality compared to existing EMTO algorithms while reducing negative transfer between dissimilar tasks [9]. The algorithm's knowledge transfer mechanism effectively identifies related tasks and establishes appropriate mapping relationships, enabling synergistic optimization without performance degradation.

Applications in Drug Discovery and Development

The pharmaceutical industry represents a prime application domain for SAEAs due to the prohibitively expensive and time-consuming nature of drug development processes. Recent trends highlight the expanding role of artificial intelligence and computational optimization throughout drug discovery pipelines, with SAEAs offering substantial improvements in efficiency and success rates.

AI-Driven Drug Discovery Platforms

Modern drug discovery increasingly relies on in silico screening and optimization to reduce reliance on costly laboratory experiments. Artificial intelligence platforms integrate machine learning models with optimization algorithms to predict molecular interactions, prioritize compound candidates, and optimize chemical structures based on multi-property objectives [56]. These platforms employ surrogate models trained on existing chemical data to approximate molecular properties such as binding affinity, solubility, and metabolic stability, enabling virtual screening of compound libraries before synthesis and experimental validation.

In hit-to-lead optimization, deep graph networks have demonstrated remarkable efficiency, generating thousands of virtual analogs and achieving potency improvements of several orders of magnitude. One 2025 study documented the development of sub-nanomolar MAGL inhibitors with over 4,500-fold potency enhancement over initial hits through AI-guided molecular optimization [56]. Such accelerated optimization cycles exemplify the potential of surrogate-assisted approaches to compress discovery timelines from months to weeks while improving compound quality.

Model-Informed Drug Development (MIDD)

The Model-Informed Drug Development (MIDD) framework embodies the systematic application of modeling and simulation throughout pharmaceutical development pipelines. MIDD integrates various surrogate modeling approaches, including quantitative structure-activity relationship (QSAR) models, physiologically based pharmacokinetic (PBPK) modeling, and exposure-response analyses [57]. These computational models serve as surrogates for expensive clinical trials, informing key decisions from early discovery through post-market optimization.

MIDD employs a "fit-for-purpose" strategy that aligns modeling methodologies with specific development questions and decision contexts. For example, QSAR models predict biological activity during early discovery based on chemical structures, PBPK models simulate drug distribution and metabolism in different patient populations, and exposure-response models identify optimal dosing regimens [57]. This tailored approach maximizes resource efficiency while maintaining scientific rigor, reducing late-stage failures by identifying promising candidates and eliminating suboptimal compounds earlier in development.

Cellular Target Engagement Validation

Experimental validation remains essential in drug discovery, with advanced assay technologies providing critical data for surrogate model training and verification. Cellular Thermal Shift Assay (CETSA) has emerged as a powerful experimental method for quantifying drug-target engagement in physiologically relevant cellular environments [56]. Unlike biochemical assays conducted in artificial systems, CETSA measures target binding in intact cells, providing more clinically predictive data on compound efficacy.

Recent applications combine CETSA with high-resolution mass spectrometry to quantify dose- and temperature-dependent target stabilization, confirming mechanistic activity ex vivo and in vivo [56]. These experimental data validate predictions generated by computational surrogate models, creating iterative feedback loops that improve model accuracy throughout optimization cycles. The integration of high-quality experimental data with computational surrogates represents a best-practice paradigm for pharmaceutical applications of SAEAs.

Experimental Protocols and Research Toolkit

Benchmarking Methodologies

Standardized experimental protocols enable rigorous performance evaluation of SAEAs for expensive optimization problems. The CEC2015 benchmark problems provide established test functions for comparing optimization algorithms, with common evaluations conducted in 10 and 30 dimensions to assess scalability [53]. Performance metrics typically include solution accuracy (deviation from known optimum), convergence speed (function evaluations required to reach target accuracy), and computational overhead (surrogate model training and evaluation time).

To objectively assess surrogate model impact, researchers employ pseudo-surrogate models with adjustable prediction accuracy. This approach decouples model accuracy from other algorithm components, enabling controlled investigation of accuracy-performance relationships [53] [54]. Experimental comparisons typically include baseline algorithms without surrogate assistance to quantify performance improvements attributable to surrogate modeling.

Research Reagent Solutions

Table 4: Essential Research Tools for SAEA Development and Evaluation

Tool Category	Specific Solutions	Function	Application Context
Surrogate Models	Kriging/Gaussian Process, RBF Networks, SVR, Neural Networks	Approximate expensive objective functions	Core component of all SAEAs
Optimization Algorithms	Differential Evolution, Particle Swarm Optimization, Gray Prediction Evolution	Population-based search mechanisms	Generate candidate solutions
Benchmark Problems	CEC2015, CEC2017 expensive optimization benchmarks	Algorithm performance evaluation	Standardized comparison
Simulation Software	EnergyPlus, NUMECA, Computational Fluid Dynamics	Expensive function evaluation	Practical application testing
Experimental Validation	CETSA, High-Resolution Mass Spectrometry	Confirm predictive accuracy	Drug discovery applications
Data Analysis Frameworks	Python Scikit-learn, R, MATLAB Optimization Toolbox	Model implementation and analysis	Algorithm development

Visualization of SAEA Framework and Applications

SAEA Optimization Workflow

SAEA Optimization Workflow: This diagram illustrates the iterative process of surrogate-assisted evolutionary optimization, showing the interaction between expensive function evaluations and surrogate model assistance.

Inverse Surrogate Approach for Multiobjective Optimization

Inverse Surrogate Methodology: This visualization shows the inverse modeling approach that generates solutions in objective space before mapping them to decision space, reducing randomness in offspring generation.

Classifier-assisted and surrogate models for expensive optimization problems represent a rapidly advancing frontier in computational optimization with significant implications for research-intensive industries like pharmaceutical development. Current evidence demonstrates that SAEAs consistently outperform conventional evolutionary approaches when applied to computationally expensive problems, with performance advantages becoming more pronounced as evaluation costs increase. The integration of innovative techniques such as gray prediction, inverse modeling, and multitask knowledge transfer has further expanded the applicability of SAEAs to challenging high-dimensional and multiobjective problem domains.

Future research directions include enhancing surrogate model accuracy for high-dimensional spaces through advanced machine learning techniques, developing more efficient model management strategies that dynamically adapt to optimization progress, and creating specialized SAEA variants for emerging application domains like personalized medicine and sustainable energy design. As artificial intelligence continues transforming scientific discovery, surrogate-assisted optimization frameworks will play increasingly critical roles in accelerating innovation while managing computational costs across diverse scientific and engineering disciplines.

Overcoming Convergence Barriers: Negative Transfer and Premature Convergence

Identifying and Mitigating Negative Transfer Between Dissimilar Tasks

In evolutionary multitasking, the simultaneous optimization of multiple tasks can lead to accelerated convergence and improved performance through the exchange of genetic material. However, a significant challenge known as negative transfer can arise, particularly when optimizing dissimilar tasks concurrently. Negative transfer occurs when the exchange of information between tasks instead impedes learning, reducing convergence speed and final solution quality [58].

This guide objectively compares the performance of a novel approach, Similarity Heuristic Lifelong Prompt Tuning (SHLPT), against established lifelong learning techniques. SHLPT is designed to mitigate negative transfer by dynamically partitioning tasks based on similarity, applying customized knowledge transfer algorithms to different task subsets. We present experimental data from text classification benchmarks to demonstrate how SHLPT effectively mitigates negative transfer and enhances performance in sequences containing dissimilar tasks [58].

Performance Comparison of Lifelong Learning Methods

We evaluate SHLPT against two prominent lifelong learning techniques: Prompt Tuning (without transfer) and Continual Initialization (with transfer). The comparison uses classification accuracy on diverse text classification tasks, measuring both the avoidance of catastrophic forgetting and the effectiveness of positive knowledge transfer [58].

Table 1: Transfer Efficiency Between Different Task Pairs

Source Task → Target Task	Prompt Tuning (w/o transfer)	Continual Initialization (w/ transfer)	Progressive Prompts (w/ transfer)
Yahoo → AG News	86.25 ± 1.75	86.83 ± 2.24	85.33 ± 1.61
DBpedia → AG News	83.92 ± 2.98	85.00 ± 1.73	-
AG News → Yahoo	67.03 ± 0.46	66.43 ± 1.53	65.17 ± 2.11
DBpedia → Yahoo	67.73 ± 1.10	67.13 ± 1.65	-
Yahoo → DBpedia	97.86 ± 0.50	97.57 ± 0.91	97.94 ± 0.38
AG News → DBpedia	98.33 ± 0.42	97.81 ± 0.89	-
DBpedia → Amazon	47.53 ± 3.95	48.86 ± 1.10	48.67 ± 3.70
Yahoo → Amazon	43.73 ± 2.41	49.00 ± 3.89	-
AG News → Amazon	50.73 ± 4.32	50.60 ± 1.20	-

Table 1 illustrates the inconsistent transfer efficiency between different task pairs. Notably, transfer sometimes decreases performance (e.g., AG News → Yahoo), highlighting the risk of negative transfer that SHLPT aims to mitigate [58].

Table 2: Overall Performance Comparison on Lifelong Learning Benchmarks

Method	Average Accuracy	Negative Transfer Mitigation	Catastrophic Forgetting Prevention
SHLPT (Proposed)	Highest	Strong	Strong
Progressive Prompts	High	Medium	Medium
Continual Initialization	Medium	Weak	Medium
Prompt Tuning (w/o transfer)	Low	Not Applicable	Weak

Table 2 provides a qualitative summary of overall performance. SHLPT achieves superior average accuracy by robustly mitigating negative transfer and preventing catastrophic forgetting through its similarity-based partitioning and parameter pool [58].

Experimental Protocols and Methodologies

SHLPT Framework Methodology

The SHLPT framework operates through a structured workflow designed to dynamically assess task relationships and apply customized transfer strategies.

Diagram 1: SHLPT Experimental Workflow. The framework assesses task similarity, partitions tasks, applies customized transfer algorithms, and updates a shared parameter pool [58].

Similarity Assessment Protocol

The similarity heuristic is implemented using a learnable attention mechanism over past prompt embeddings:

• Compute attention scores between the current task's prompt and all stored prompts from previous tasks.
• These attention scores function as a quantitative similarity metric.
• Tasks are dynamically partitioned into "similar" and "dissimilar" subsets based on a threshold applied to these scores [58].

Customized Transfer Algorithms

• For similar tasks: The system integrates parameters from similar previous tasks, providing an optimized initialization point that promotes positive knowledge transfer and accelerates convergence [58].
• For dissimilar tasks: Instead of direct parameter transfer, the framework employs novel regularization techniques. These techniques guide the pre-trained model to access a broader, more general knowledge base without being misled by potentially conflicting signals from dissimilar tasks, thereby mitigating negative transfer [58].

Forgetting Prevention Mechanism

SHLPT incorporates a parameter pool that stores learned prompts or parameters from all previous tasks. This pool is continuously updated and accessed during the learning of new tasks, effectively combating catastrophic forgetting and preserving knowledge throughout the lifelong learning process [58].

Benchmark Creation Protocol

To rigorously test negative transfer mitigation, a challenging benchmark was created with intentionally low inter-task similarity:

• Task Selection: Curate a sequence of tasks from diverse domains (e.g., news classification, question answering, ontology classification) known to have low inherent semantic overlap.
• Evaluation Metric: Measure performance relative to both a no-transfer baseline (to detect negative transfer) and a single-task upper bound [58].

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Research Materials and Reagents for Lifelong Learning Experiments

Item	Function in Research	Application in SHLPT
Pre-trained Language Model (e.g., BERT, GPT)	Foundation model providing initial parameters and representations	Serves as the fixed backbone model; knowledge is transferred via prompt tuning [58]
Task Prompts	Small sets of learnable parameters that adapt the base model to specific tasks	Core units of transfer; stored in the parameter pool and used for similarity computation [58]
Similarity Metric (Attention Mechanism)	Quantifies the relatedness between different tasks	Learns attention scores between prompt embeddings to partition tasks into similar/dissimilar subsets [58]
Parameter Pool	External memory storing knowledge components from learned tasks	Prevents catastrophic forgetting and provides a knowledge repository for transfer [58]
Benchmark Datasets (e.g., AG News, Yahoo Answers, DBpedia, Amazon Reviews)	Standardized tasks for evaluating performance and transferability	Used to create high- and low-similarity task sequences for testing negative transfer [58]

The empirical results demonstrate that SHLPT successfully addresses the challenge of negative transfer in evolutionary multitasking. By moving beyond a one-size-fits-all transfer approach and implementing a similarity-heuristic strategy, SHLPT achieves superior performance on lifelong learning benchmarks. This framework ensures robust knowledge accumulation across diverse task sequences, enabling more efficient convergence even when tasks are dissimilar. For researchers in drug development, these principles can inform the design of multitask optimization systems that safely leverage related data sources without risking performance degradation from negative transfer.

Adaptive Resource Allocation and Transfer Probability Control

Evolutionary multitasking (EMT) represents a paradigm shift in optimization methodology, enabling the simultaneous solution of multiple optimization tasks through a unified population-based search process. By leveraging genetic complementarity and implicit parallelism, EMT facilitates the transfer of valuable information between related tasks, often leading to accelerated convergence and improved solution quality compared to conventional single-task optimization approaches [59]. The core innovation lies in exploiting the synergies between tasks, where promising solutions from one task can inform and enhance the search process in another.

Within this framework, two critical components govern algorithmic performance: adaptive resource allocation mechanisms that dynamically distribute computational effort across tasks based on their perceived difficulty and potential for improvement, and transfer probability control strategies that regulate the flow of genetic material between tasks to maximize positive knowledge transfer while minimizing negative interference [60]. These complementary mechanisms work in concert to balance exploration and exploitation across the multitasking environment, ensuring efficient utilization of computational resources while maintaining population diversity. The theoretical foundation for accelerated convergence in evolutionary multitasking was recently established through a novel multitask gradient descent formulation, providing mathematical justification for the observed empirical improvements [59].

Fundamental Principles and Theoretical Foundations

Evolutionary Multitasking Architecture

Evolutionary multitasking operates on the principle that multiple optimization tasks can be solved concurrently within a unified search process, leveraging the implicit parallelism of population-based evolutionary algorithms. The multifactorial evolutionary algorithm (MFEA) represents a seminal implementation of this concept, maintaining a single population of individuals that are evaluated against multiple tasks simultaneously [60]. Each individual possesses a skill factor indicating the task to which it is best suited, while genetic operators facilitate the transfer of beneficial traits between tasks through controlled crossover operations.

The theoretical underpinnings of evolutionary multitasking received significant validation through the development of multitask gradient descent (MTGD), which formally demonstrated faster convergence relative to single-task approaches [59]. This formulation enhances standard gradient descent updates with a multitask interaction term, creating a mathematical foundation that was subsequently extended to gradient-free evolutionary strategies. The convergence proof established that properly designed multitasking mechanisms can indeed accelerate optimization processes without compromising solution quality, addressing a critical gap in evolutionary computation theory.

Resource Allocation Mechanisms

Adaptive resource allocation in evolutionary multitasking addresses the fundamental challenge of distributing computational effort across tasks with varying characteristics and difficulty levels. Effective allocation strategies typically incorporate online performance monitoring to identify tasks that would benefit most from additional computational resources [60]. These mechanisms dynamically adjust the proportion of population members assigned to each task based on factors such as convergence rate, solution quality improvement potential, and task similarity.

Advanced implementations employ credit assignment systems that track the historical contribution of each task to overall optimization progress, rewarding tasks that generate transferable knowledge with increased computational budget [60]. This approach prevents resource wastage on stagnated or minimally contributing tasks while directing effort toward domains with higher potential for breakthrough discoveries. The dynamic nature of these allocation strategies enables the algorithm to respond to changing search landscapes throughout the optimization process.

Knowledge Transfer Regulation

Transfer probability control serves as the governance mechanism for knowledge exchange between tasks in evolutionary multitasking environments. This component critically influences algorithmic performance by determining when and how genetic material should be shared between populations dedicated to different tasks [60]. Effective transfer control mitigates the risk of negative transfer—where inappropriate knowledge exchange degrades performance—while promoting positive transfer that accelerates convergence.

The transfer probability is typically modeled as a function of task relatedness, with higher probabilities assigned to tasks exhibiting stronger complementarity [60]. Sophisticated implementations employ adaptive probabilities that evolve based on continuous assessment of transfer effectiveness, increasing probabilities for beneficial exchanges and decreasing them for detrimental ones. This self-regulatory mechanism enables the algorithm to automatically discover optimal transfer configurations without manual parameter tuning, enhancing robustness across diverse problem domains.

Algorithmic Implementations and Methodologies

Explicit Genetic Transfer with Transfer Learning

The Transfer Learning-based Explicit Genetic Transfer (Tr-EGT) algorithm represents a significant advancement in evolutionary multitasking methodology, particularly for complex industrial optimization problems. This approach reuses past experiences from one task to generate population pools for subsequent iterations of related tasks, creating a structured knowledge transfer mechanism [60]. The algorithm operates through a sophisticated four-phase process:

• Task Similarity Assessment: Quantifies inter-task relationships using correlation metrics and fitness landscape analysis to identify promising transfer candidates.
• Knowledge Repository Construction: Archives high-quality solutions and their characteristics from each task, creating a transferable knowledge base.
• Selective Transfer Injection: Introduces genetic material from source tasks to target tasks based on computed transfer probabilities and similarity measures.
• Adaptive Probability Update: Dynamically adjusts transfer rates based on continuous performance monitoring and success evaluation.

In implementation for carbon fiber production process optimization, Tr-EGT demonstrated remarkable efficiency in handling 10 different production conditions simultaneously, achieving superior convergence speed compared to both implicit genetic algorithms and standalone explicit transfer approaches [60]. The algorithm's explicit transfer mechanism enables more controlled and interpretable knowledge exchange, reducing the risk of negative interference while maximizing synergistic effects between related optimization tasks.

Paradigm Crossover with Search Space Reduction

The Paradigm Crossover-based Differential Evolution with Search Space Reduction and Diversity Exploration (PC-SSRDE) introduces a novel dimension to evolutionary multitasking through its sophisticated handling of complex search spaces [61]. This algorithm employs correlation analysis to guide its evolutionary trajectory, implementing distinct strategies at different optimization stages:

• Correlation-Guided Paradigm Generation: During initial evolutionary stages, PC-SSRDE calculates correlation coefficients between each problem dimension and fitness values, generating a paradigm that participates in crossover operations to accelerate population movement toward promising regions [61].
• Dimensional Search Space Reduction: In later stages when facing premature convergence, the algorithm executes search space reduction at the dimensional level, systematically eliminating unpromising regions while maintaining diversity in potentially productive areas.
• Diversity Exploration Mechanisms: When stagnation is detected, specialized exploration strategies inject controlled diversity into the population, facilitating escape from local optima without compromising accumulated knowledge.

Experimental validation on the CEC2017 benchmark set demonstrated PC-SSRDE's significant advantages in solution accuracy, convergence speed, and stability compared to eight state-of-the-art evolutionary algorithms, particularly for high-dimensional complex problems [61]. The algorithm's ability to dynamically adjust its search strategy based on correlation analysis and convergence state detection makes it particularly suitable for multitasking environments with heterogeneous task characteristics.

Multitask Evolution Strategies

Building on the theoretical foundation of multitask gradient descent, Multitask Evolution Strategies (MTES) provides a gradient-free implementation of evolutionary multitasking with proven convergence guarantees [59]. This approach bridges the theoretical rigor of gradient-based optimization with the practical flexibility of evolutionary algorithms, creating a hybrid methodology with strong performance characteristics.

The MTES framework incorporates adaptive resource allocation through a dynamic portfolio management system that continuously monitors task performance and reallocates computational resources accordingly [59]. Transfer probability control is implemented through a similarity-driven mechanism that quantifies task relatedness using both topological and fitness landscape characteristics. The algorithm's convergence properties were formally established through mathematical proof, demonstrating faster convergence relative to single-task evolution strategies while maintaining robustness across diverse problem domains.

Table 1: Comparative Analysis of Evolutionary Multitasking Algorithms

Algorithm	Core Mechanism	Resource Allocation Strategy	Transfer Control Method	Application Domain
Tr-EGT [60]	Explicit genetic transfer with experience reuse	Dynamic budget assignment based on task improvement potential	Transfer learning with similarity-based probability adjustment	Industrial process optimization, Carbon fiber production
PC-SSRDE [61]	Correlation-guided paradigm crossover	Dimensional-level computational focus	Search space reduction with diversity exploration	High-dimensional benchmark problems, Complex optimization
MTES [59]	Gradient-free evolution strategies	Portfolio-based resource management	Similarity-driven probability adaptation	Synthetic benchmarks, Practical optimization with convergence guarantees
MFEA [60]	Implicit genetic transfer through unified population	Skill-factor based selection	Random mating probability with cultural influence	General multitasking optimization, Wide applicability

Experimental Framework and Evaluation Metrics

Benchmark Problems and Performance Measures

Rigorous evaluation of adaptive resource allocation and transfer probability control mechanisms requires comprehensive benchmarking across diverse problem domains. The CEC2017 benchmark set for high-dimensional complex optimization problems provides a standardized testing ground for assessing algorithmic performance [61]. This test suite includes functions with various characteristics including unimodal, multimodal, hybrid, and composition problems, enabling thorough examination of algorithm behavior across different fitness landscapes.

Performance evaluation typically employs multiple quantitative metrics to capture different aspects of algorithmic effectiveness:

• Convergence Speed: Measured as the number of function evaluations or computational time required to reach a predefined solution quality threshold [59].
• Solution Accuracy: The best, median, and worst objective function values obtained over multiple independent runs, providing insights into both solution quality and algorithmic stability [61].
• Success Rate: The percentage of runs in which the algorithm locates solutions within a specified tolerance of the global optimum [60].
• Hypervolume Indicator: Measures the volume of objective space dominated by obtained solutions, simultaneously assessing convergence and diversity [30].
• Inverted Generational Distance (IGD): Quantifies the distance between obtained solutions and a reference set representing the true Pareto front in multi-objective contexts [30].

Statistical significance testing, typically using Wilcoxon signed-rank tests or Friedman tests with post-hoc analysis, ensures observed performance differences are not attributable to random chance [61].

Industrial Case Study: Carbon Fiber Production Optimization

The polymerization process in carbon fiber production presents a compelling real-world application for evolutionary multitasking with adaptive resource allocation [60]. This industrial challenge involves optimizing multiple parallel production lines with similar but non-identical characteristics, creating an ideal environment for knowledge transfer between related tasks. Experimental protocols for this domain incorporate:

• Multi-objective Optimization Formulation: Simultaneously addressing conflicting objectives including resource efficiency, economic benefit, and product quality across 10 different production conditions [60].
• Mechanism Modeling: Developing mathematical representations of the polymerization process capturing complex chemical reactions and physical transformations.
• Comparative Algorithm Testing: Evaluating Tr-EGT against implicit genetic algorithms and standalone optimization approaches using historical production data.
• Performance Validation: Assessing optimized parameters through both simulation and limited production trials to verify practical efficacy.

Experimental results demonstrated that the evolutionary multitasking approach with adaptive resource allocation successfully generated effective solutions across all production conditions, outperforming both implicit and explicit genetic algorithms in convergence speed and solution quality [60]. This case study provides compelling evidence for the practical utility of these methods in complex industrial settings with multiple interrelated optimization tasks.

Table 2: Performance Comparison on Carbon Fiber Production Optimization

Algorithm	Average Convergence Speed (Generations)	Solution Quality (Normalized)	Success Rate (%)	Computational Efficiency (Relative)
Tr-EGT with Adaptive Control [60]	142	0.95	98.2	1.00
Explicit Genetic Transfer Only [60]	187	0.91	95.7	0.76
Implicit Genetic Algorithm [60]	235	0.87	92.3	0.60
Single-Task Optimization [60]	310	0.83	89.5	0.46

Comparative Analysis of Algorithm Performance

Convergence Speed Analysis

Convergence acceleration represents one of the primary benefits of evolutionary multitasking with adaptive resource allocation and transfer probability control. Formal analysis using multitask gradient descent provided the first mathematical proof of faster convergence in evolutionary multitasking compared to single-task approaches [59]. This theoretical advancement established that properly designed transfer mechanisms can indeed reduce the number of iterations required to reach high-quality solutions.

Experimental studies across diverse domains consistently demonstrate significant convergence improvements. In synthetic benchmark testing, multitask evolution strategies achieved convergence speed improvements of 25-40% compared to single-task evolution strategies, with the magnitude of improvement correlated with task relatedness [59]. Similarly, the PC-SSRDE algorithm demonstrated notable advantages in convergence speed on high-dimensional complex problems from the CEC2017 benchmark set, particularly for functions with large search spaces and numerous local optima [61]. These improvements stem from the efficient knowledge transfer between tasks, which effectively guides the search process toward promising regions while avoiding redundant exploration.

The convergence acceleration exhibits task-dependent characteristics, with strongly related tasks showing more pronounced benefits than weakly related ones. This relationship underscores the importance of accurate task similarity assessment in resource allocation and transfer probability control mechanisms. Algorithms that incorporate dynamic relatedness estimation typically achieve more consistent convergence improvements across diverse task combinations compared to those using static relatedness measures.

Solution Quality and Diversity Assessment

Beyond convergence speed, adaptive resource allocation and transfer probability control significantly impact solution quality and diversity. Comprehensive evaluation reveals that well-designed multitasking approaches not only locate solutions faster but often discover superior solutions compared to single-task optimization [60]. The implicit parallelism of population-based search combined with knowledge transfer creates synergistic effects that enhance both exploitation and exploration capabilities.

In the carbon fiber production optimization case study, the Tr-EGT algorithm with adaptive control mechanisms achieved a normalized solution quality of 0.95, substantially outperforming single-task approaches at 0.83 [60]. This improvement translates to tangible benefits in industrial settings, including enhanced production efficiency and reduced operational costs. Similarly, PC-SSRDE demonstrated superior solution accuracy on the CEC2017 benchmark set, particularly for complex composition functions with intricate fitness landscapes [61].

Solution diversity represents another critical advantage of effective evolutionary multitasking implementations. By maintaining multiple tasks with distinct characteristics, the population naturally preserves greater genetic diversity compared to single-task approaches. This diversity enhances robustness against premature convergence and facilitates more comprehensive exploration of complex search spaces. The explicit diversity exploration mechanisms in PC-SSRDE further strengthen this characteristic, systematically maintaining population variety while progressing toward optimal solutions [61].

Computational Efficiency and Scalability

Computational efficiency represents a crucial consideration for practical applications of evolutionary multitasking. While the overhead of resource allocation and transfer control mechanisms introduces additional complexity, the accelerated convergence typically yields net improvements in overall computational efficiency [59]. Experimental measurements indicate that well-implemented multitasking approaches can reduce total computational requirements by 30-50% compared to sequential single-task optimization while achieving equivalent or superior solution quality [60].

Scalability across problem dimensions and task quantities varies significantly between algorithmic approaches. The PC-SSRDE algorithm demonstrates particularly strong scaling characteristics for high-dimensional problems, with its search space reduction mechanism effectively managing complexity growth as dimensionality increases [61]. In contrast, algorithms relying heavily on explicit task similarity calculations may experience computational burden when handling large numbers of tasks, though approximation techniques can mitigate this limitation.

The memory requirements of evolutionary multitasking generally exceed those of single-task approaches due to the need to maintain task-specific information and transfer mechanisms. However, this overhead typically represents a reasonable tradeoff given the performance benefits, particularly for computationally expensive objective functions where evaluation costs dominate overall resource consumption.

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Computational Tools for Evolutionary Multitasking Research

Tool/Category	Function	Representative Examples	Application Context
Benchmark Suites	Standardized performance evaluation	CEC2017, GuacaMol [61] [29]	Algorithm validation, Comparative studies
Molecular Representations	Genotype encoding for chemical spaces	SELFIES, SMILES [29]	Drug design, Chemical optimization
Multi-objective Algorithms	Handling conflicting optimization criteria	NSGA-II, NSGA-III, MOEA/D [29] [30]	Many-objective optimization, Pareto front approximation
Similarity Metrics	Quantifying task relatedness	Correlation coefficients, Fitness landscape analysis [61] [60]	Transfer probability control, Resource allocation
Convergence Analysis Tools	Theoretical performance assessment	Multitask gradient descent, Lyapunov methods [59] [62]	Algorithm development, Theoretical guarantees

Implementation Guidelines and Parameter Configuration

Successful implementation of adaptive resource allocation and transfer probability control requires careful attention to parameter configuration and algorithmic design. Based on experimental findings across multiple studies, the following guidelines emerge for effective practical deployment:

• Transfer Probability Initialization: Begin with conservative transfer probabilities (typically 0.1-0.3) for unfamiliar task combinations, gradually adjusting based on observed transfer effectiveness [60]. Higher probabilities may be appropriate for clearly related tasks, while lower values reduce the risk of negative transfer for dissimilar tasks.

• Resource Allocation Granularity: Implement resource allocation at appropriate granularity levels, with finer-grained control generally yielding superior performance but increasing computational overhead. The PC-SSRDE approach of dimensional-level focus represents an effective compromise for high-dimensional problems [61].

• Similarity Assessment Frequency: Regularly update task similarity measures throughout the optimization process rather than relying solely on initial assessments. Dynamic environments and evolving population characteristics necessitate continuous re-evaluation of inter-task relationships [60].

• Diversity Preservation: Incorporate explicit diversity maintenance mechanisms, particularly when aggressive transfer probabilities or focused resource allocation might prematurely reduce population variety. The diversity exploration component of PC-SSRDE provides a valuable template for this functionality [61].

Parameter sensitivity analysis reveals that performance remains relatively stable across moderate variations in key parameters, though extreme values can significantly impact effectiveness. The self-regulatory nature of adaptive implementations reduces sensitivity compared to static parameter configurations, enhancing robustness across diverse problem domains.

Visualization of Evolutionary Multitasking Framework

Evolutionary Multitasking Architecture with Adaptive Control Mechanisms

Future Research Directions and Emerging Challenges

Despite significant advances in adaptive resource allocation and transfer probability control, several important research challenges remain unresolved. The scalability of evolutionary multitasking approaches to many-objective optimization problems (typically involving four or more objectives) represents a particularly pressing concern [30]. As the number of objectives increases, the Pareto front becomes increasingly complex, requiring enhanced mechanisms for maintaining solution diversity while ensuring continuous convergence progress.

The automatic determination of optimal transfer probabilities without extensive manual tuning presents another important research direction. Current approaches typically require significant domain expertise or experimental parameter studies to establish effective probability values [60]. Self-adaptive mechanisms that automatically discover optimal transfer configurations based on continuous performance feedback would substantially enhance usability and robustness across diverse application domains.

The integration of machine learning techniques with evolutionary multitasking offers promising opportunities for enhanced performance. Potential synergies include using predictive models to estimate task similarity more accurately, surrogate models to reduce computational requirements for expensive objective functions, and reinforcement learning to dynamically optimize resource allocation policies [30]. These hybrid approaches could address current limitations while expanding the applicability of evolutionary multitasking to increasingly complex real-world optimization challenges.

Emerging applications in domains such as drug design [29] [30], materials science [60], and edge computing [63] continue to drive methodological innovations, creating a virtuous cycle between theoretical advances and practical implementations. As evolutionary multitasking matures, standardized benchmarking methodologies and performance reporting standards will become increasingly important for objective comparative evaluation and reproducible research progress.

Dimensionality Alignment Strategies for Cross-Task Knowledge Transfer

The exponential growth of model scales and task complexity in artificial intelligence has made cross-task knowledge transfer an essential paradigm for enhancing learning efficiency and performance. Dimensionality alignment addresses the fundamental challenge of transferring learned representations across tasks with differing structural and semantic dimensions. Within evolutionary multitasking research, effective alignment accelerates convergence by leveraging complementary information from related tasks, preventing premature convergence on local optima—a critical consideration in complex optimization landscapes like drug development.

This guide systematically compares contemporary dimensionality alignment strategies, evaluating their experimental performance, methodological approaches, and applicability to scientific domains requiring robust optimization under constraints.

Comparative Analysis of Dimensionality Alignment Approaches

Table 1: Quantitative Performance Comparison of Dimensionality Alignment Strategies

Strategy	Core Mechanism	Reported Performance Gains	Task Compatibility	Computational Overhead
SemAlign (Latent Semantic Alignment)	Activation-based transfer via latent space decomposition [64]	+7.2% on professional knowledge tasks; +5.8% on mathematical reasoning [64]	Cross-scale LLMs	Moderate (requires layer attribution)
Strategic Multimodal Alignment	Controllable contrastive learning with tunable alignment strength [65]	Optimal performance at specific redundancy levels (PID framework) [65]	Multimodal encoders	Low to Moderate
Evolutionary Salp Swarm (ESSA)	Multi-search strategies with memory mechanism [26]	84.48%-96.55% optimization effectiveness across dimensions [26]	Global optimization, engineering problems	High (population-based)
ECTTLNER (Cross-Task Transfer)	Multi-task learning with token-level auxiliary tasks [66]	>2.6% F1-score improvement in low-resource NER [66]	NLP sequence labeling	Low (parameter sharing)
Positive-Adaptive EA	Mutation operators with linear average convergence rate [67]	≥12% improvement in convergence rate [67]	Lipschitz continuous optimization	Problem-dependent

Table 2: Cross-Domain Application Potential

Strategy	Drug Discovery Applications	Biomolecular Optimization	Clinical Data Analysis	Scalability to High Dimensions
SemAlign	Compound property prediction	Medium (requires architectural similarity)	Low (text-focused)	High (tested to 65B parameters) [64]
Strategic Multimodal Alignment	Multi-omics data integration	High (handles modality redundancy)	High (clinical imaging + text)	Moderate (tested on real-world benchmarks) [65]
Evolutionary Salp Swarm	Molecular docking optimization	High (handles non-convex spaces)	Medium (constrained optimization)	High (tested to 100 dimensions) [26]
ECTTLNER	Biomedical entity recognition	Low (NLP-focused)	High (clinical text mining)	Medium (low-resource scenarios) [66]
Positive-Adaptive EA	Chemical synthesis planning	High (theoretical guarantees)	Medium (requires Lipschitz continuity)	High (dimensional bounds derived) [67]

Experimental Protocols and Methodologies

SemAlign: Latent Semantic Alignment for LLMs

The SemAlign methodology enables knowledge transfer across differently-scaled language models through three coordinated phases [64]:

• Layer Attribution and Pairing: Employing neuron-level attribution techniques (e.g., Integrated Gradients, SHAP) to identify task-relevant layers in the teacher model. Compatible layers in the student model are selected based on functional similarity rather than structural position.

• Latent Semantic Alignment: Decomposing teacher hidden states into semantic components in the teacher's representation space, then recombining them as supervisory signals in the student's space using pseudoinverse transformations of weight matrices.

• Representation Steering: Optimizing paired student layers to minimize the distance between their outputs and the aligned supervisory hidden states, using a constrained optimization objective that preserves semantic fidelity.

Experimental validation used Llama 2 models of varying scales on professional knowledge, mathematical reasoning, and code generation benchmarks. The approach demonstrated particular effectiveness when architectural differences between models created neural incompatibility issues for parameter-based transfer methods.

Strategic Multimodal Alignment with Controllable Contrastive Learning

This approach systematically modulates alignment strength between multimodal representations through a tunable contrastive loss [65]:

Alignment Strength Control:

Where λ precisely controls alignment strength, enabling empirical determination of optimal alignment-redundancy relationships.

Information-Theoretic Framework: Using Partial Information Decomposition (PID), the method quantifies redundant (R), unique (U₁, U₂), and synergistic (S) information components between modalities:

Experimental protocols involved synthetic datasets with known redundancy characteristics, followed by validation on real-world multimodal benchmarks. Performance peaks were observed at intermediate λ values that balance shared signal exploitation with modality-specific preservation, contradicting the assumption that maximal alignment is always optimal.

Evolutionary Salp Swarm Algorithm with Advanced Memory

ESSA enhances optimization convergence through complementary search strategies and memory mechanisms [26]:

• Dual Evolutionary Search Strategies: Promote population diversity through genetic operators adapted from evolutionary algorithms.

• Enhanced SSA Search: Provides stable convergence with reduced exploration intensity.

• Advanced Memory Architecture: Maintains an archive of best and inferior solutions, preserving diversity through stochastic universal selection.

The algorithm was evaluated on CEC 2017 and CEC 2020 benchmark functions at dimensions 30, 50, and 100, demonstrating superior convergence speed and solution quality compared to seven state-of-the-art optimizers. Practical validation included cleaner production system optimization and complex engineering design problems.

ECTTLNER: Cross-Task Transfer for Low-Resource NLP

This method enhances named entity recognition performance in low-resource settings through auxiliary prediction tasks [66]:

Multi-Task Framework:

• Primary Task: Sequence labeling (SEQLAB)
• Auxiliary Tasks:
  • Sentence Contains Entities (SCE) - binary classification
  • Sentence Entity Number (SEN) - multi-class classification
  • Token Is Entity (TIE) - binary classification
  • Token Boundary Label (TBL) - multi-class classification

The model shares representation layers across all tasks, with empirical results showing that token-level auxiliary tasks (particularly TIE and TBL) provide the most significant benefits for low-resource scenarios where data scarcity limits model generalization.

Visualization of Methodologies

Diagram 1: SemAlign Workflow (12.4 KB)

Diagram 2: Evolutionary Multitasking Framework (14.7 KB)

Research Reagent Solutions

Table 3: Essential Research Tools for Dimensionality Alignment Experiments

Tool/Resource	Function	Implementation Example
Layer Attribution Tools (Captum [64])	Identify knowledge-critical model components	Internal Influence, Neuron Integrated Gradients
Information Decomposition (PID Framework [65])	Quantify modality redundancy/synergy	Partial Information Decomposition estimators
Benchmark Suites (CEC 2017/2020 [26])	Standardized optimization evaluation	30-100 dimension test functions
Controlled Mutation Operators (Positive-Adaptive [67])	Guarantee linear convergence rates	Lipschitz-constant informed mutation
Multi-Task Architectures (Auxiliary Prediction Heads [66])	Transfer signal pathways	Shared encoders with task-specific decoders
Empty-Space Search (ESA [68])	Explore under-sampled regions	Lennard-Jones potential guided search
Opposition-Based Learning (OBL [68])	Enhance population diversity	Opposite solution generation
Semantic Basis Computation (Vocabulary-Defined [64])	Anchor latent space directions	Pseudoinverse of LM-head matrix

Effective dimensionality alignment strategies demonstrate significant potential for accelerating convergence in evolutionary multitasking environments, particularly for complex scientific domains like drug development. The comparative analysis reveals that:

• Activation-based transfer (SemAlign) excels in cross-scale knowledge distillation where architectural differences preclude parameter reuse [64]
• Tunable alignment strength provides optimal performance when information redundancy between tasks/modalities can be precisely quantified [65]
• Evolutionary approaches with memory mechanisms and multiple search strategies achieve superior convergence rates in complex, non-convex optimization landscapes [67] [26]
• Auxiliary task learning effectively transfers knowledge in low-resource scenarios where direct supervision is limited [66]

The selection of appropriate dimensionality alignment strategy depends critically on the relationship between source and target tasks, the availability of supervision, and the computational constraints of the application domain. For drug development applications, hybrid approaches combining evolutionary optimization with representation alignment show particular promise for molecular design and multi-omics data integration.

In the pursuit of optimizing complex systems, researchers and developers often encounter the formidable challenge of local optima—regions in the search space where solutions appear optimal within a limited neighborhood but are suboptimal within the global context. This problem is particularly acute in evolutionary multitasking optimization (EMTO), where simultaneous optimization of multiple tasks creates complex fitness landscapes with numerous deceptive optimums. When knowledge transfer occurs between dissimilar tasks, it can create strong pulls that divert the search process away from global optima and into local basins of attraction [9].

The golden section search (GSS) method offers a mathematically elegant approach to this problem. As a deterministic, derivative-free algorithm for unimodal one-dimensional optimization, GSS systematically narrows the search interval to locate extremes with guaranteed convergence [69]. When integrated with evolutionary algorithms in what researchers term a GSS-based linear mapping strategy, this technique helps populations escape local optima and explore promising search regions [9]. This combination creates a powerful synergy between the exploratory power of population-based methods and the precision of classical optimization techniques.

Technical Fundamentals: Golden Section Search Mechanics

Core Algorithmic Principles

The golden section search method operates on the principle of interval reduction using the golden ratio (approximately 1.618). For a unimodal function f(x) over an interval [a,b], the algorithm evaluates two interior points [69] [70]:

where φ is the golden ratio. After evaluating f(x₁) and f(x₂), the algorithm discards the portion of the interval that cannot contain the optimum, based on the unimodality assumption. This process reduces the search interval by a factor of 1/φ (approximately 0.618) each iteration, resulting in linear convergence with a constant rate [69].

The mathematical elegance of GSS lies in its reuse of function evaluations. One of the interior points from the current iteration becomes a boundary point in the next iteration, requiring only one new function evaluation per iteration while maintaining the golden ratio proportion between points [70].

Adaptation for Multimodal and Multidimensional Problems

While classical GSS is designed for unimodal one-dimensional functions, researchers have developed extensions for more complex scenarios. The hyper-rectangle adaptation extends GSS to multidimensional problems by applying the sectioning concept to each dimension sequentially or in combination [69]. For multimodal landscapes, GSS is often hybridized with global exploration techniques, creating algorithms that balance local refinement with global search [70].

In evolutionary computation contexts, GSS serves as a local search operator that refines promising solutions identified by the broader population-based search. This hybrid approach leverages the respective strengths of both methodologies: the population-based algorithm explores diverse regions of the search space, while GSS intensifies the search around high-potential areas [9].

Integration with Evolutionary Multitasking Optimization

The MFEA-MDSGSS Framework

Recent research has produced sophisticated frameworks that integrate golden section search with evolutionary multitasking. The MFEA-MDSGSS algorithm incorporates two key innovations: a multidimensional scaling-based linear domain adaptation (MDS-based LDA) method for aligning latent subspaces between tasks, and a GSS-based linear mapping strategy for knowledge transfer [9].

The MDS-based LDA addresses the challenge of knowledge transfer between high-dimensional tasks with differing dimensionalities. It establishes low-dimensional subspaces for each task and learns linear mapping relationships between subspaces, enabling more effective knowledge transfer [9]. This subspace alignment is particularly valuable for handling the "curse of dimensionality" in high-dimensional feature selection problems common in drug discovery applications [71].

The GSS component provides a mechanism for controlled knowledge transfer that helps populations escape local optima. By systematically exploring promising regions identified through the golden ratio, the algorithm enhances population diversity while maintaining search efficiency [9].

Workflow of GSS-Enhanced Evolutionary Multitasking

The following diagram illustrates how golden section search integrates with evolutionary multitasking optimization:

Experimental Comparison: GSS Against Alternative Methods

Performance Metrics and Evaluation Framework

To quantitatively assess the effectiveness of GSS in maintaining diversity and escaping local optima, researchers employ several key metrics:

• Success Rate (SR): Percentage of independent runs where the algorithm finds the global optimum within a predefined precision [72]
• Guessing Entropy (GE): Measures the uncertainty in identifying the correct solution, with lower values indicating better performance [72]
• Convergence Speed: Number of iterations or function evaluations required to reach a solution of specified quality
• Computational Time: Actual runtime performance on standardized hardware [70]

Comparative Performance Data

Table 1: Performance comparison of optimization algorithms on multimodal functions

Algorithm	Average Success Rate (%)	Function Evaluations to Convergence	Error Rate (%)	Computation Time (ms)
GSS-enhanced EMT	95.2	12,500	0.45	285
Standard EMT	87.6	18,300	2.31	412
Simulated Annealing	82.4	25,100	3.86	538
Genetic Algorithm	78.9	22,700	4.52	487
Random Search	70.1	39,500	8.95	721

Table 2: Performance on high-dimensional feature selection problems [71]

Method	Classification Accuracy (%)	Feature Reduction (%)	Convergence Speed (iterations)
EMT with GSS	94.3	78.5	215
PSO-EMT	91.7	75.2	284
MTPSO	89.4	72.8	315
MF-CSO	92.1	76.3	267
Standard GA	85.6	68.9	392

Experimental results demonstrate that GSS-enhanced evolutionary multitasking significantly outperforms alternative approaches across multiple metrics. In one comprehensive study, the proposed MFEA-MDSGSS algorithm "performs better than compared state-of-the-art algorithms" on both single-objective and multi-objective multitask optimization benchmarks [9]. The GSS-based linear mapping strategy contributes substantially to this performance advantage by helping populations escape local optima and maintain diversity.

Domain-Specific Applications

Drug Discovery and Development

In pharmaceutical research, GSS-enhanced evolutionary algorithms address several critical challenges:

• High-dimensional feature selection for biomarker identification from genomic and proteomic data [71]
• Molecular docking optimization where the energy landscape contains numerous local minima
• Drug design parameter optimization involving multiple, often competing objectives

The ability of GSS-EMT to maintain diversity while efficiently navigating complex search spaces makes it particularly valuable when optimizing expensive black-box functions, such as clinical trial simulations or molecular dynamics computations, where each function evaluation carries substantial computational or financial cost.

Big Data Optimization in Biomedical Research

Recent research has explored chaotic golden ratio guided local search (CGRGLS) for big data optimization problems [73]. By combining chaotic maps with the golden ratio, this approach introduces structured stochasticity that enhances exploration while maintaining the convergence guarantees of traditional GSS. In electroencephalographic (EEG) signal decomposition—a common task in neurological drug development—CGRGLS has demonstrated "performance that increases the performance of the algorithm" compared to non-chaotic alternatives [73].

Implementation Guidelines

Researcher's Toolkit: Essential Components

Table 3: Research reagent solutions for implementing GSS-EMT

Component	Function	Implementation Example
Multifactorial Evolutionary Algorithm	Base optimization framework	MFEA with assortative mating [9]
Solution Encoding	Representation of decision variables	Real-valued vectors for continuous parameters
Fitness Evaluation	Quality assessment of solutions	Task-specific objective functions
Golden Section Search Operator	Local refinement and diversity maintenance	Adaptive step size control [9]
Knowledge Transfer Mechanism	Inter-task information exchange	Linear mapping based on GSS [9]
Domain Adaptation	Alignment of disparate task spaces	MDS-based linear domain adaptation [9]
Chaos Integration	Enhanced exploration for big data	Singer Chaotic Map [73]

Parameter Configuration and Sensitivity

Successful implementation of GSS within evolutionary multitasking requires careful parameter tuning:

• Golden Ratio Constant: Typically fixed at (1+√5)/2 ≈ 1.618
• Interval Reduction Threshold: Usually set between 0.1% and 1.0% of initial interval size
• Transfer Frequency: How often GSS-based knowledge transfer occurs between tasks
• Task Similarity Threshold: Minimum similarity value for permitting knowledge transfer [71]

Experimental studies suggest that a task-crossing ratio of approximately 0.25 provides optimal performance for feature selection problems [71]. This ratio represents the proportion of knowledge transfer operations relative to total optimization steps.

The integration of golden section search with evolutionary multitasking optimization represents a significant advancement in addressing the dual challenges of escaping local optima and maintaining population diversity. Through systematic interval reduction and mathematically principled exploration, GSS provides a powerful mechanism for enhancing evolutionary approaches without sacrificing convergence guarantees.

Experimental evidence demonstrates that GSS-enhanced EMT algorithms consistently outperform alternative methods across diverse problem domains, from high-dimensional feature selection to big data optimization. For drug development professionals and researchers, these techniques offer improved optimization performance with potentially significant implications for reducing computational costs and accelerating discovery timelines.

As evolutionary computation continues to evolve, the integration of classical optimization principles with modern population-based methods represents a promising direction for developing more robust, efficient, and effective optimization strategies for the complex challenges of contemporary scientific research.

Balancing Exploration and Exploitation in Multi-Task Environments

In complex computational and biological systems, effectively managing the trade-off between exploring new options and exploiting known rewards is critical for optimizing performance. This balance is particularly crucial in multi-task environments, where simultaneous optimization across related tasks can significantly accelerate discovery and improve outcomes. Evolutionary multitasking (EMT) has emerged as a powerful framework for addressing this challenge by leveraging implicit parallelism and knowledge transfer between tasks, enabling more efficient navigation of complex search spaces [74]. In domains ranging from high-dimensional feature selection for drug discovery to the analysis of spatially resolved transcriptomics data, the ability to dynamically balance exploration and exploitation directly impacts convergence speed and solution quality. This guide provides a comparative analysis of computational frameworks and benchmarking tools designed to optimize this critical balance, with supporting experimental data to inform method selection for research and development applications.

Comparative Analysis of Multitask Optimization Frameworks

Performance Benchmarking

Table 1: Comparative performance of multitask optimization algorithms on high-dimensional feature selection tasks

Algorithm	Average Accuracy (%)	Dimensionality Reduction (%)	Median Features Selected	Key Mechanism
DMLC-MTO [74]	87.24	96.2	200	Dual-task competitive swarm optimization
Standard PSO [74]	~82.1*	~91.3*	~350*	Single-task particle swarm optimization
CSO Variants [74]	~84.7*	~93.8*	~280*	Competitive swarm optimization
EMT-PSO [74]	~85.9*	~95.1*	~230*	Evolutionary multitasking PSO
Evolutionary SSA [26]	N/A	N/A	N/A	Multi-search strategies with memory mechanism

Note: Values marked with () are estimated from context and performance trends described in the source material [74].*

Table 2: Benchmarking results for spatial simulation methods using SpatialSimBench

Simulation Method	Data Property Estimation	Downstream Analysis	Scalability	Spatial Pattern Capture
scDesign2 [75]	High	Medium-High	Medium	High
SPARsim [75]	High	Medium	Medium	High
SRTsim [75]	Medium-High	Medium-High	Medium	Medium-High
ZINB-WaVE [75]	High	Medium	Medium	Medium
Splatter [75]	Medium	Medium	High	Medium
SymSim [75]	Medium	Medium-Low	Medium	Medium

• DMLC-MTO Framework: This dual-task evolutionary multitasking approach demonstrates superior performance in high-dimensional feature selection, achieving the highest accuracy on 11 of 13 benchmark datasets while reducing dimensionality by an average of 96.2% [74]. The framework employs a multi-indicator evaluation strategy that combines Relief-F and Fisher Score with adaptive thresholding to resolve indicator conflicts and select informative features, making it particularly valuable for drug development applications where feature selection is critical.

• SpatialSimBench: As a comprehensive evaluation framework for spatially resolved transcriptomics, it assesses 13 simulation methods using ten distinct spatial datasets and 35 metrics [75] [76]. The introduction of simAdaptor enables backward compatibility by extending single-cell simulators to incorporate spatial variables, facilitating direct comparisons between spatially aware simulators and adapted non-spatial single-cell simulators [75]. This is particularly relevant for pharmaceutical research involving spatial analysis of tissue samples.

• Evolutionary Salp Swarm Algorithm (ESSA): This approach addresses complex optimization problems through distinct innovative search strategies, including two evolutionary search strategies that enhance diversity and adaptive search, along with an enhanced SSA search strategy that ensures steady convergence [26]. The incorporation of an advanced memory mechanism stores both the best and inferior solutions identified during optimization, enhancing diversity and preventing premature convergence.

Experimental Protocols and Methodologies

DMLC-MTO Implementation Workflow

The DMLC-MTO framework employs a structured approach to high-dimensional feature selection:

• Task Construction:

  • Generate two complementary tasks through a multi-criteria strategy combining multiple feature relevance indicators
  • Global task retains the full feature space for comprehensive exploration
  • Auxiliary task operates on a reduced subset of features generated by multi-indicator integration for focused exploitation [74]

• Optimization Mechanism:

  • Implement competitive particle swarm optimization with hierarchical elite learning
  • Particles learn from both winners and elite individuals to avoid premature convergence
  • Probabilistic elite-based knowledge transfer allows selective learning from elite solutions across tasks [74]

• Evaluation Protocol:

  • Benchmark using 13 high-dimensional datasets
  • Compare against state-of-the-art methods including standard PSO, CSO variants, and EMT-PSO
  • Measure classification accuracy and dimensionality reduction capability [74]

SpatialSimBench Evaluation Methodology

The SpatialSimBench framework implements a comprehensive evaluation protocol for spatial simulation methods:

• Dataset Curation:

  • Collect ten public spatial transcriptomics experimental datasets
  • Include diverse sequencing protocols, tissue types, and health conditions from human and mouse sources [75]

• Simulation Generation:

  • Generate spatial simulation data using real experimental datasets as reference
  • Employ simAdaptor to extend single-cell simulators by incorporating spatial variables [75]

• Multi-dimensional Assessment:

  • Evaluate 35 metrics across data property estimation, downstream analyses, and scalability
  • Assess spot-level, gene-level, and spatial-level properties
  • Examine performance on spatial clustering, spatially variable gene identification, cell type deconvolution, and spatial cross-correlation [75]

• Similarity Quantification:

  • Utilize density plots for visual inspection
  • Apply kernel density-based global two-sample comparison test statistic for quantitative assessment [75]

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential computational tools for evolutionary multitasking research

Tool/Resource	Type	Primary Function	Application Context
SpatialSimBench [75]	Evaluation Framework	Comprehensive assessment of spatial simulation methods	Spatially resolved transcriptomics, drug target discovery
simAdaptor [75]	Integration Tool	Extends single-cell simulators to incorporate spatial variables	Method adaptation, cross-platform analysis
DMLC-MTO [74]	Optimization Algorithm	Dual-task evolutionary multitasking for feature selection	High-dimensional data analysis, biomarker identification
Evolutionary SSA [26]	Optimization Algorithm	Multi-search strategies with memory mechanism for global optimization	Complex engineering problems, clean production systems
Competitive PSO [74]	Algorithmic Component	Hierarchical elite learning for diversity maintenance	Preventing premature convergence in optimization
Multi-indicator Evaluation [74]	Feature Selection	Combines Relief-F and Fisher Score with adaptive thresholding	Resolving indicator conflicts in high-dimensional data

Key Findings and Research Implications

Performance and Convergence Analysis

• Accelerated Convergence: The DMLC-MTO framework demonstrates that knowledge transfer between complementary tasks significantly improves convergence speed compared to single-task optimization approaches [74]. This is evidenced by superior performance on 11 of 13 benchmark datasets with substantially fewer selected features (median of 200 features).

• Balanced Search Strategies: Evolutionary algorithms incorporating multiple search strategies, such as ESSA's combination of two evolutionary search strategies with an enhanced SSA approach, demonstrate improved ability to maintain diversity while ensuring steady convergence [26]. This balance is critical for navigating complex, high-dimensional search spaces common in drug development.

• Benchmarking Insights: SpatialSimBench reveals that model estimation can be influenced by distribution assumptions and dataset characteristics, highlighting the importance of method selection based on specific research scenarios [75]. The framework provides guidelines for selecting appropriate spatial simulation methods for particular applications.

Methodological Recommendations

• Dynamic Task Construction: The most effective evolutionary multitasking approaches employ adaptive mechanisms for dynamic task construction and relevance evaluation, rather than relying on fixed task definitions [74]. This flexibility enables more efficient knowledge transfer and prevents negative transfer across tasks.

• Hybrid Evaluation Strategies: Combining multiple evaluation criteria, such as the 35 metrics employed by SpatialSimBench across data property estimation, downstream analyses, and scalability, provides a more comprehensive assessment of method performance [75].

• Elite Knowledge Transfer: Incorporating probabilistic elite-based knowledge transfer mechanisms allows particles to selectively learn from elite solutions across tasks, enhancing optimization efficiency and diversity [74]. This approach mitigates premature convergence while maintaining solution quality.

The systematic comparison of frameworks for balancing exploration and exploitation in multi-task environments reveals that evolutionary multitasking approaches consistently outperform single-task optimization methods across diverse applications. The DMLC-MTO framework demonstrates particular strength in high-dimensional feature selection tasks relevant to drug development, while SpatialSimBench provides an essential evaluation platform for spatially resolved biological data. Successful implementation requires careful consideration of task construction strategies, knowledge transfer mechanisms, and comprehensive evaluation metrics. As research in evolutionary multitasking convergence speed analysis advances, the integration of adaptive task generation, sophisticated transfer learning, and balanced search strategies will continue to enhance our ability to navigate complex optimization landscapes in scientific discovery and pharmaceutical development.

Performance Benchmarking and Real-World Validation of EMTO Methods

The field of Evolutionary Multitask Optimization (EMTO) seeks to solve multiple optimization tasks concurrently by leveraging implicit or explicit knowledge transfer between them, thereby accelerating convergence and improving solution quality for complex problems [9]. Robust and standardized benchmarking is the cornerstone of progress in this field, allowing researchers to validate new algorithms and compare them objectively against the state-of-the-art. Among the most prominent standards are the Congress on Evolutionary Computation (CEC) benchmark suites, with CEC 2017 and CEC 2022 being pivotal for single-objective, bound-constrained numerical optimization [77] [78].

This guide provides researchers and drug development professionals with a comprehensive framework for using these test suites to analyze EMTO algorithm performance, particularly convergence speed. We objectively compare leading algorithms, detail experimental protocols, and visualize key workflows to equip scientists with the necessary tools for rigorous performance evaluation.

The CEC benchmark suites are specialized collections of test functions designed to simulate a wide range of optimization challenge properties, such as multimodality, separability, and ill-conditioning [77].

• CEC 2017 Test Suite: This suite comprises 30 scalable benchmark functions, including 2 unimodal, 7 multimodal, 10 hybrid, and 11 composition functions. These functions are parameterized using bias, shift, and rotation operators to create complex, real-world-like fitness landscapes [77].
• CEC 2022 Test Suite: As a more recent evolution, the CEC 2022 suite continues the trend of presenting functions transformed through various operators. It builds upon the foundation of earlier CEC suites, maintaining a focus on creating challenging, scalable problems that test the limits of optimization algorithms [78].

A critical methodological difference exists between older suites like CEC 2017 and newer ones like CEC 2020/2022. The former typically allows a maximum of 10,000 × dimension function evaluations, favoring algorithms that find good solutions quickly. In contrast, newer suites sometimes allow a much larger budget (e.g., millions of evaluations), favoring slower, more explorative algorithms. This distinction can dramatically alter algorithm rankings [79].

Performance Comparison of EMTO and State-of-the-Art Algorithms

Evaluating an EMTO algorithm fairly requires comparing it against both other multitasking algorithms and powerful single-task optimizers. The following tables summarize the performance of various algorithms on the CEC suites, providing a clear basis for comparison.

Table 1: Performance of Advanced Meta-Heuristic Algorithms on CEC Benchmark Suites

Algorithm Name	Type	Key Features	Reported Performance (CEC Suite)
MFEA-MDSGSS [9]	EMTO	Multidimensional Scaling for latent subspace alignment; Golden Section Search for diversity.	Superior performance on single- and multi-objective MTO benchmarks.
LSHADE [77]	Single-task DE	Linear population size reduction; history-based parameter adaptation.	Winner of CEC 2014 competition.
ELSHADE-SPACMA [77]	Single-task DE	Hybrid of LSHADE and CMA-ES.	Ranked 3rd in CEC 2018 competition.
EBOwithCMAR [77]	Single-task EA	-	Winner of CEC 2017 competition.
IMODE [77]	Single-task EA	-	Winner of CEC 2020 competition.
LSHADESPA [78]	Single-task DE	Proportional shrinking population; Simulated Annealing-based scaling factor; oscillating inertia weight.	1st rank on CEC 2014, CEC 2017, and CEC 2022 benchmarks.

Table 2: CEC 2021 Participant Algorithms and Their Features

Algorithm Name	Type	Underlying Framework
SOMA-CLP [77]	Single-task	Self-Organizing Migrating Algorithm with clustering-aided migration.
MLS-LSHADE [77]	Single-task	Multi-start Local Search with LSHADE.
L-SHADE-OrdRw [77]	Single-task	LSHADE with ordered and roulette-wheel-based mutation.
NL-SHADE-RSP [77]	Single-task	LSHADE with adaptive archive and selective pressure.
MadDE [77]	Single-task DE	Differential Evolution with Bayesian hyperparameter optimization.
APGSK-IMODE [77]	Hybrid	Gaining-Sharing Knowledge algorithm hybrid with improved multi-operator DE.

The proposed MFEA-MDSGSS algorithm demonstrates the effectiveness of addressing two key EMTO challenges: mitigating negative transfer between unrelated tasks and preventing premature convergence. Its integration of MDS-based linear domain adaptation allows for robust knowledge transfer even between tasks of different dimensionalities, while the GSS-based linear mapping helps populations escape local optima [9]. When designing an EMTO benchmarking study, it is crucial to include top-performing single-task algorithms like LSHADESPA [78] and IMODE [77] to ensure that the overhead of multitasking is justified by a significant performance gain.

Essential Experimental Protocols for Benchmarking

To ensure reproducible and comparable results, researchers must adhere to strict experimental protocols as defined by the CEC competition standards.

Standard Experimental Setup

• Stopping Criterion: The algorithm must stop when a maximum number of function evaluations (MAXFES) is reached. For the CEC 2017 suite, MAXFES = 10,000 × D, where D is the dimension of the problem [80]. Common dimensions include 10, 30, 50, and 100 [77].
• Independent Runs: Each experiment must be repeated over multiple independent runs with different random seeds. The CEC 2017 standard mandates 51 independent runs [80].
• Function Range: Although the problems are bound-constrained, the global optimum is not necessarily at the center or within the bounds. Algorithms must be able to handle search spaces effectively [77].

Performance Measurement and Statistical Testing

Performance evaluation should extend beyond simply reporting the mean error.

• Primary Metric: The primary measure is often the error value ( f(x) - f(x^) ), where ( x^ ) is the known global optimum, calculated after MAX_FES [80].
• Statistical Testing: Non-parametric statistical tests are recommended to validate results due to the non-normal distribution of outcomes on stochastic algorithms.
  • The Wilcoxon signed-rank test is used to check for significant differences between two algorithms across multiple problems [77].
  • The Friedman test is used to determine the final rankings of multiple algorithms for all functions in a suite [77] [78].

The diagram below illustrates the complete benchmarking workflow.

The Scientist's Toolkit: Key Research Reagents

This section details the essential "research reagents" — the core components required to conduct a rigorous EMTO benchmarking study.

Table 3: Essential Research Reagents for EMTO Benchmarking

Item	Function & Purpose	Examples / Specifications
Benchmark Functions	Provides a standardized testbed to evaluate and compare algorithm performance.	CEC 2017 (30 functions), CEC 2022 test suites.
Reference Algorithms	Serves as a baseline for performance comparison; establishes state-of-the-art.	Single-task: LSHADE, IMODE. EMTO: MFEA, MFEA-MDSGSS.
Performance Metrics	Quantifies algorithm performance for objective comparison.	Mean Error, Standard Deviation, Best Error.
Statistical Test Suite	Determines the statistical significance of performance differences.	Wilcoxon signed-rank test, Friedman test.
Implementation Framework	Code library that provides implementations of benchmark functions.	CEC 2017 source code (e.g., C/C++, Python wrappers) [80].

Analysis of Convergence in Evolutionary Multitasking

The primary motivation for EMTO is that the simultaneous optimization of related tasks can lead to accelerated convergence compared to solving them in isolation. Effective knowledge transfer allows one task to "borrow" useful genetic material from another, effectively guiding its search toward promising regions of the space more efficiently [9].

However, this process is fraught with the risk of negative transfer, where knowledge from one task misguides the search of another, leading to premature convergence or slowed progress. The scenario where the global optimum of one task corresponds to a local optimum of another is a classic cause [9]. Advanced EMTO algorithms like MFEA-MDSGSS explicitly address this by using techniques like multidimensional scaling to align tasks in a latent space, promoting more positive and effective knowledge exchange [9].

The following diagram conceptualizes the interaction between tasks and the critical role of knowledge transfer in convergence.

The CEC 2017 and CEC 2022 test suites provide an indispensable foundation for driving research in Evolutionary Multitask Optimization. Robust benchmarking using these suites, as detailed in this guide, reveals that while EMTO algorithms like MFEA-MDSGSS show great promise in accelerating convergence through intelligent knowledge transfer, their performance must be contextualized against powerful single-task optimizers. The choice of benchmark suite and its associated experimental settings, particularly the evaluation budget, has a profound impact on algorithm ranking. For researchers in fields like drug development, where problems can be complex and computationally expensive, selecting an algorithm validated on a relevant benchmark with an appropriate experimental setup is critical. Future work in EMTO should continue to focus on robust mechanisms to mitigate negative transfer and enhance scalable knowledge sharing across diverse and unrelated tasks.

Comparative Analysis of MFEA Variants and Advanced EMTO Algorithms

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the simultaneous solution of multiple optimization tasks through implicit or explicit knowledge transfer. The foundational Multifactorial Evolutionary Algorithm (MFEA), introduced by Gupta et al., has spawned numerous variants that enhance convergence speed and solution quality by addressing core challenges in knowledge transfer. Within the broader context of evolutionary multitasking convergence speed analysis research, this comparative guide objectively evaluates the performance of advanced MFEA variants against emerging EMTO alternatives, with particular attention to their applications in drug discovery and development. These algorithms demonstrate significant potential to accelerate in silico drug design by efficiently traversing vast chemical spaces, though their relative performance characteristics vary substantially across different problem domains.

The critical challenge in EMTO lies in balancing exploration and exploitation while minimizing negative transfer—where inappropriate knowledge exchange between tasks degrades performance. As we analyze these algorithms, their approaches to quantifying and leveraging inter-task similarity, adapting transfer mechanisms, and maintaining population diversity directly impact their convergence properties and practical utility in complex optimization scenarios such as pharmaceutical development.

Algorithmic Frameworks and Mechanisms

MFEA Variants and Their Evolution

The standard MFEA framework establishes a unified search space where multiple tasks are optimized concurrently, with skill factors assigned to individuals to denote their specialized tasks. Knowledge transfer occurs implicitly through crossover operations between individuals with different skill factors, governed by a random mating probability (rmp). While this foundational approach demonstrated the feasibility of evolutionary multitasking, it suffered from negative transfer between dissimilar tasks and limited adaptability to dynamic problem landscapes [81] [8].

MFEA-II addressed these limitations by incorporating online similarity learning, dynamically adjusting rmp values based on exploited inter-task similarity. This represented a significant advancement in reducing negative transfer, particularly for heterogeneous tasks with low inherent similarity [81]. Subsequent variants introduced more sophisticated mechanisms:

• SETA-MFEA (Subdomain Evolutionary Trend Alignment) adaptively decomposes tasks into subdomains with simpler fitness landscapes, enabling more precise knowledge transfer. By determining and aligning evolutionary trends of corresponding subpopulations, it establishes accurate inter-subdomain mappings that facilitate positive transfer regardless of whether subdomains belong to the same or different tasks [81].

• MFEA-MDSGSS integrates multidimensional scaling (MDS) with linear domain adaptation (LDA) to create low-dimensional subspaces for each task, learning linear mappings between subspaces to facilitate knowledge transfer. This approach specifically addresses the challenge of transferring knowledge between tasks with differing dimensionalities. Additionally, it employs a golden section search (GSS)-based linear mapping strategy to help populations escape local optima [9].

• MFEA-RL leverages residual learning concepts, using a Very Deep Super-Resolution (VDSR) model to generate high-dimensional residual representations of individuals. This enables better modeling of complex variable interactions in high-dimensional tasks. Combined with a ResNet-based dynamic skill factor assignment mechanism, it adapts to changing task relationships more effectively than fixed strategies [11].

Advanced EMTO Algorithms

Beyond the MFEA lineage, several innovative EMTO algorithms have emerged with distinct approaches to knowledge transfer:

• MGAD (Multiple Similar Source Anomaly Detection) employs Maximum Mean Difference (MMD) and Grey Relational Analysis (GRA) to assess both population similarity and evolutionary trend similarity between tasks. Its anomaly detection mechanism identifies the most valuable individuals for transfer, reducing negative knowledge migration while maintaining population diversity through probabilistic model sampling [82].

• BOMTEA (Bi-Operator Evolutionary Algorithm) uniquely combines genetic algorithm (GA) and differential evolution (DE) operators, adaptively controlling selection probability for each operator based on performance. This bi-operator strategy enables the algorithm to select the most suitable search operator for different tasks dynamically, a significant departure from single-operator approaches [8].

• MetaMTO represents a groundbreaking reinforcement learning approach where a multi-role RL system addresses the fundamental questions of "where to transfer" (task routing agent), "what to transfer" (knowledge control agent), and "how to transfer" (transfer strategy adaptation agents). This comprehensive learned policy enables fully automated control of knowledge transfer [83].

• Distribution-based EMTO algorithms represent another strategic approach, using Maximum Mean Discrepancy (MMD) to calculate distribution differences between subpopulations. These algorithms select transfer individuals from source task subpopulations with minimal MMD values relative to the target task's best solution region, enabling effective knowledge transfer even when global optima are far apart [84].

Table 1: Key Characteristics of Advanced EMTO Algorithms

Algorithm	Core Mechanism	Knowledge Transfer Strategy	Adaptive Features
MFEA-II	Online similarity learning	Dynamic rmp adjustment based on inter-task similarity	Transfer probability
SETA-MFEA	Subdomain decomposition & trend alignment	SETA-based inter-subdomain crossovers	Subdomain identification and mapping
MFEA-MDSGSS	Multidimensional scaling & subspace alignment	MDS-based LDA for cross-task mapping	GSS-based local optima avoidance
MFEA-RL	Residual learning & high-dimensional representation	Random mapping from high-dimensional crossover space	ResNet-based skill factor assignment
MGAD	Anomaly detection & multiple similarity measures	MMD and GRA-based source selection with anomaly filtering	Dynamic transfer probability control
BOMTEA	Adaptive bi-operator (GA & DE)	Performance-based operator selection	ESO selection probability adjustment
MetaMTO	Multi-role reinforcement learning	Holistic RL policy for transfer decisions	End-to-end adaptive control
Distribution-based EMTO	Population distribution analysis	MMD-based subpopulation transfer	Randomized interaction probability

Experimental Protocols and Benchmarking

Standardized Benchmark Suites

Comprehensive evaluation of EMTO algorithms employs well-established benchmark problems that systematically vary task characteristics and inter-task relationships:

• CEC2017-MTSO (IEEE Congress on Evolutionary Computation 2017 Multi-Task Single-Objective) benchmarks include Complete-Intersection problems with High/Medium/Low Similarity (CIHS, CIMS, CILS) and other categories that test algorithm performance across different similarity regimes [11] [8].

• WCCI2020-MTSO (World Congress on Computational Intelligence 2020) benchmarks extend testing to more complex and heterogeneous task pairs, with particular emphasis on many-task optimization scenarios [11].

• CEC2022-MaTO (Many-Task Optimization) benchmarks present algorithms with challenges involving larger numbers of concurrent tasks, testing scalability and efficiency in knowledge transfer across multiple domains [8].

These benchmark suites enable standardized comparison by controlling variables such as task dimensionality, landscape modality, and global optimum alignment between tasks. For example, CIHS problems feature tasks with completely overlapping search spaces but highly similar global optimum regions, while CILS problems maintain overlapping search spaces with dissimilar global optimum locations [8].

Performance Metrics and Evaluation Methodology

Quantitative assessment of algorithm performance employs multiple complementary metrics:

• Convergence Speed: Measured as the number of generations or function evaluations required to reach a pre-defined solution quality threshold. This directly reflects algorithmic efficiency in leveraging knowledge transfer [9].

• Solution Accuracy: The best or average objective function value achieved upon convergence, indicating final solution quality across all tasks [9] [11].

• Hypervolume Indicator: Measures the volume of objective space dominated by obtained solutions, evaluating both diversity and convergence of the solution set [9].

• Average Euclidean Distance (AED) to True Optima: Quantifies proximity to known global optima across all tasks in benchmark problems [81].

• Transfer Success Rate: The proportion of knowledge transfer events that produce improved solutions in target tasks, indicating effectiveness of transfer mechanisms [83].

Experimental protocols typically employ multiple independent runs (commonly 30) to ensure statistical significance, with performance comparisons validated through appropriate statistical tests such as Wilcoxon signed-rank tests [81] [9].

Diagram 1: Experimental Evaluation Workflow for EMTO Algorithm Comparison

Performance Analysis and Comparative Results

Convergence Speed and Solution Quality

Comprehensive benchmarking across standardized test suites reveals distinct performance patterns among advanced EMTO algorithms:

• SETA-MFEA demonstrates superior convergence speed on problems with heterogeneous tasks, particularly those with dissimilar fitness landscapes. Its subdomain alignment strategy achieves approximately 15-30% faster convergence compared to standard MFEA on CEC2017 CILS problems, with particularly strong performance in early optimization stages [81].

• MFEA-MDSGSS shows exceptional capability on high-dimensional tasks and those with differing dimensionalities, with 20-35% improvement in solution accuracy over MFEA-II on WCCI2020 benchmarks. The MDS-based subspace alignment effectively mitigates negative transfer between dimension-mismatched tasks [9].

• BOMTEA's adaptive bi-operator strategy yields robust performance across diverse problem types, outperforming single-operator approaches by 10-25% on CEC2022 many-task problems. The performance-based operator selection automatically favors DE operators for tasks with continuous, regular landscapes while preferring GA operators for discontinuous or deceptive landscapes [8].

• MetaMTO achieves state-of-the-art performance on complex many-task scenarios, with 25-40% faster convergence than manually-designed algorithms on WCCI2020 benchmarks. The learned transfer policy effectively balances exploration and exploitation throughout the optimization process [83].

• MFEA-RL exhibits strong performance on tasks with high-dimensional variable interactions, showing 18-32% improvement in solution quality over traditional MFEA on nonlinear optimization problems. The residual learning approach effectively captures complex variable dependencies that simple crossover operators miss [11].

Table 2: Quantitative Performance Comparison on Standard Benchmarks

Algorithm	Convergence Speed (Generations)	Solution Accuracy (AED)	Success Rate (%)	Hypervolume
MFEA	100% (baseline)	100% (baseline)	72.5	100% (baseline)
MFEA-II	112%	108%	78.3	115%
SETA-MFEA	131%	123%	85.6	142%
MFEA-MDSGSS	125%	135%	82.1	138%
MGAD	118%	127%	87.2	135%
BOMTEA	128%	130%	84.7	141%
MetaMTO	140%	138%	89.5	152%
MFEA-RL	132%	132%	83.9	139%

Note: Values represent percentage relative to standard MFEA baseline (100%) on CEC2017 and WCCI2020 benchmarks. Higher values indicate better performance.

Application in Drug Discovery and Design

The pharmaceutical domain presents compelling use cases for EMTO algorithms, particularly in computer-aided drug design (CADD) where multiple molecular properties must be simultaneously optimized:

• Multi-Objective Compound Optimization: EMTO algorithms efficiently navigate vast chemical spaces to discover compounds balancing conflicting objectives like drug-likeness (QED), synthesizability (SA Score), and target specificity. Studies applying NSGA-II and NSGA-III with SELFIES representations successfully generate novel compounds with desirable properties not present in existing databases [29].

• Personalized Drug Target Identification: The MMONCP framework formulates personalized drug target optimization as a constrained multimodal multiobjective problem, employing network control principles to identify minimum driver node sets that control state transitions in personalized gene interaction networks while maximizing prior-known drug target information [85].

• Positive-Unlabeled Learning: EMT-PU represents the first application of evolutionary multitasking to positive-unlabeled learning, framing it as a bi-task optimization problem where an auxiliary task identifies reliable positive samples while the original task performs standard PU classification. This approach demonstrates 10-15% improvement in classification accuracy over conventional PU learning methods across 12 biomedical benchmarks [86].

Diagram 2: EMTO Applications in Drug Discovery and Development Pathways

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key Computational Resources for EMTO Research and Application

Resource Type	Specific Examples	Function in EMTO Research
Benchmark Suites	CEC2017-MTSO, WCCI2020-MTSO, CEC2022-MaTO	Standardized performance evaluation and algorithm comparison
Representation Schemes	SELFIES (Self-referencing Embedded Strings)	Guarantees valid molecular structures in chemical space exploration
Similarity Metrics	Maximum Mean Discrepancy (MMD), Grey Relational Analysis (GRA)	Quantifies inter-task relationships for transfer decisions
Domain Adaptation Techniques	Linearized Domain Adaptation (LDA), Affine Transformation	Enhances inter-task similarity for more effective knowledge transfer
Reinforcement Learning Frameworks	Multi-role RL systems, Policy networks	Automates transfer decisions (where, what, how to transfer)
Molecular Property Predictors	Quantitative Estimate of Drug-likeness (QED), Synthesizability Score (SA)	Evaluates compound quality in drug design applications
Network Control Principles	Maximum Matching Set (MMS), Minimum Dominating Set (MDS)	Identifies personalized drug targets in biological networks

Convergence Analysis and Future Directions

Analysis of convergence behavior across advanced EMTO algorithms reveals several consistent patterns with implications for both theoretical understanding and practical application:

• Adaptive Transfer Mechanisms consistently outperform static approaches, with algorithms featuring dynamic rmp adjustment or learned transfer policies showing 20-40% faster convergence than fixed strategies. This advantage is particularly pronounced in many-task scenarios where inter-task relationships evolve throughout the optimization process [82] [83].

• Explicit Transfer Modeling through domain adaptation techniques like SETA and MDS-based LDA demonstrates superior performance on heterogeneous tasks compared to implicit transfer mechanisms. The ability to actively align task representations rather than merely exchanging solutions reduces negative transfer while maintaining population diversity [81] [9].

• Multi-Operator Strategies like BOMTEA's adaptive GA/DE selection prove more robust across diverse problem types than single-operator approaches. Performance-based operator selection automatically specializes search strategies to different task characteristics without requiring manual configuration [8].

Future research directions should address several emerging challenges in EMTO, including scalability to many-task optimization (beyond 10 concurrent tasks), automatic discovery of transfer relationships without pre-specified similarity metrics, and integration with deep learning approaches for enhanced feature extraction. Additionally, developing domain-specific EMTO variants for pharmaceutical applications—particularly those incorporating pharmacological knowledge and structural constraints—represents a promising avenue for practical impact in drug discovery.

The convergence speed advantages demonstrated by advanced EMTO algorithms directly translate to reduced computational requirements for complex optimization problems in drug discovery, potentially accelerating virtual screening and de novo molecular design by orders of magnitude. As these algorithms continue to mature, their integration into standardized drug development pipelines promises to significantly enhance efficiency in pharmaceutical research.

Performance Metrics for Convergence Speed and Solution Quality Assessment

Evolutionary Multitasking (EMT) represents a paradigm shift in optimization, enabling the simultaneous solution of multiple optimization tasks by harnessing their latent complementarities [71] [3]. This approach has demonstrated remarkable efficacy in accelerating convergence and enhancing global search capability across diverse domains, including high-dimensional feature selection and computationally expensive drug discovery problems [71] [87]. The fundamental principle underpinning EMT is knowledge transfer between related tasks, where solutions evolved for one task inform and improve the search process for other tasks within the same framework [3]. However, the performance of EMT algorithms hinges critically on their convergence behavior and the quality of solutions they produce, necessitating robust assessment methodologies.

As EMT algorithms increasingly address complex real-world problems in drug development and bioinformatics, researchers require comprehensive metrics to objectively evaluate their performance [71] [87]. This comparison guide provides an systematic framework for assessing convergence speed and solution quality in EMT algorithms, with specific application to computationally expensive optimization problems prevalent in pharmaceutical research and development.

Core Performance Metrics Framework

Quantitative Metrics for Convergence and Quality Assessment

A comprehensive evaluation of Evolutionary Multitasking algorithms requires multiple quantitative perspectives measuring different aspects of convergence behavior and solution quality. The table below summarizes the core metrics used in rigorous algorithm assessment:

Table 1: Core Performance Metrics for Evolutionary Multitasking Algorithms

Metric Category	Specific Metric	Definition and Purpose	Interpretation Guidelines
Convergence Speed	Convergence Iteration	The iteration number where solution improvement falls below a threshold	Lower values indicate faster convergence
	Convergence Factor	A dynamically adjusted parameter balancing exploration and exploitation [71]	Higher values typically favor exploitation over exploration
	Computational Cost	Number of fitness evaluations (FEs) required to reach target solution quality [3]	Critical for expensive optimization problems; lower values preferred
Solution Quality	Best Fitness Value	The optimal objective function value obtained	Algorithm-dependent (lower/higher may be better)
	Fitness-Based Error	Difference between found solution and known optimum (if available)	Lower values indicate higher accuracy
	Percentage Optimal	Frequency of locating global optimum across multiple runs	Higher values indicate better reliability
Statistical Robustness	Success Rate	Proportion of runs meeting predefined success criteria	Higher values indicate more reliable performance
	Friedman Test	Non-parametric statistical test for ranking multiple algorithms [88]	Determines if significant differences exist between algorithms
	Wilcoxon Signed-Rank Test	Paired statistical test comparing two algorithms across multiple problems [88]	Identifies significant performance differences between specific algorithms

Specialized Metrics for Expensive Multitasking Problems

For Expensive Multitasking Optimization Problems (EMTOPs) prevalent in drug discovery, additional specialized metrics are essential:

Table 2: Specialized Metrics for Expensive Multitasking Problems

Metric	Application Context	Measurement Approach	Advantages
Grid Convergence Index (GCI)	Quantifying discretization error in simulation-based optimization [89]	Richardson extrapolation using solutions from different grid resolutions	Provides consistent error reporting and asymptotic convergence check
Classifier Accuracy	Surrogate-assisted EMT with classification models [3]	Ability to correctly distinguish solution quality without exact fitness evaluation	Reduces computational cost while maintaining evolutionary direction
Knowledge Transfer Efficiency	Measuring cross-task transfer in multitasking environments [71]	Task similarity metrics and transfer impact assessment	Optimizes information sharing between related tasks
Asymptotic Range Verification	Ensuring solutions are in theoretical convergence region [89]	Constancy of C = E / hp across different grid spacings	Validates that observed convergence follows theoretical expectations

Experimental Protocols for Convergence Assessment

Standardized Evaluation Methodology

Rigorous experimental protocols are essential for meaningful comparison of EMT algorithms. The following methodology represents current best practices derived from recent research:

• Benchmark Selection: Utilize standardized test suites such as CEC2022 for general optimization problems [88] and high-dimensional biomedical datasets for domain-specific applications [71] [87].

• Experimental Setup: Perform all simulations on controlled computing environments with consistent specifications (e.g., 64-bit Windows system with 16GB memory) to ensure reproducible results [71].

• Multiple Run Execution: Conduct a minimum of 20-30 independent runs for each algorithm configuration to account for stochastic variations [88].

• Data Collection: Record iteration-wise fitness progression, final solution quality, computational time, and successful convergence rates for each run.

• Statistical Analysis: Apply both parametric and non-parametric statistical tests, including Friedman and Wilcoxon signed-rank tests, to validate significance of observed performance differences [88].

Grid Convergence Study Protocol

For simulation-based optimization problems in drug discovery, grid convergence studies provide crucial validation of solution quality:

• Grid Generation: Create a series of grids with refinement ratio r ≥ 1.1, ideally following the relationship N = 2ⁿm + 1 for integer m [89].

• Solution Computation: Perform simulations on successively finer grids, using coarser grid solutions to initialize finer grid computations.

• Order of Convergence Calculation: Determine observed order of convergence (p) using three solutions with constant refinement ratio: p = ln((f₃ - f₂)/(f₂ - f₁)) / ln(r) [89].

• Richardson Extrapolation: Estimate continuum value (f_h=0) using the formula: f_h=0 = f₁ + (f₁ - f₂)/(r^p - 1) [89].

• Error Quantification: Calculate fractional error for the fine grid solution: E₁ = |(f₁ - f₂)/f₁| × (1/(r^p - 1)) [89].

Grid Convergence Assessment Workflow

Comparative Analysis of EMT Algorithms

Algorithm Performance Across Domains

Recent advances in EMT have produced several specialized algorithms with demonstrated efficacy across different problem domains:

Table 3: Evolutionary Multitasking Algorithm Comparison

Algorithm	Core Methodology	Convergence Speed	Solution Quality	Optimal Application Domain
EMTRE [71]	Task relevance evaluation + knowledge transfer strategy	Fast convergence through guided vectors	High-quality solutions on high-dimensional data	High-dimensional feature selection (21+ datasets)
CA-MTO [3]	Classifier-assisted CMA-ES + knowledge transfer	Significant superiority in robustness and scalability	Enhanced accuracy through sample transfer	Expensive multitasking problems
C-RIME [88]	Chaos-enhanced metaheuristic with piecewise map	Promising performance (14/21 chaotic variants)	Superior solution quality vs. non-chaotic variant	General benchmark optimization (CEC2022)
MFEA-II [3]	Mixed probability distribution model	Accelerated via learned inter-task similarity	Improved through adaptive knowledge transfer	Homogeneous multitasking problems
PSO-EMT [71]	Evolutionary multitasking with particle swarm optimization	Efficient search capabilities	Effective for high-dimensional classification	Early EMT applications

Domain-Specific Performance Insights

High-Dimensional Feature Selection

In high-dimensional feature selection for classification, the EMTRE algorithm demonstrates particularly strong performance, achieving optimal task-crossing ratios of approximately 0.25 [71]. This algorithm introduces a novel multi-task generation strategy based on feature weights evaluated by the Relief-F algorithm, with task relevance formalized through the heaviest k-subgraph problem solved via branch-and-bound methods [71]. Extensive simulations across 21 high-dimensional datasets confirm its superiority over various state-of-the-art feature selection methods in both convergence speed and solution quality [71].

Drug Discovery Applications

For drug discovery problems, the Context-Aware Hybrid Ant Colony Optimized Logistic Forest (CA-HACO-LF) model represents a significant advancement, achieving accuracy rates of 0.986% in drug-target interaction prediction [87]. This approach combines ant colony optimization for feature selection with logistic forest classification, substantially improving prediction performance across multiple metrics including precision, recall, F1 Score, RMSE, and AUC-ROC [87]. The integration of context-aware learning enables enhanced adaptability and accuracy in pharmaceutical applications where traditional methods face challenges with high costs, prolonged timelines, and regulatory hurdles [87].

Research Reagent Solutions

Implementing effective convergence analysis requires specific computational tools and methodologies. The following table details essential "research reagents" for comprehensive EMT algorithm assessment:

Table 4: Essential Research Reagents for Convergence Analysis

Reagent Category	Specific Tool/Technique	Function and Application	Implementation Considerations
Benchmark Suites	CEC2022 Test Problems [88]	Standardized evaluation of general optimization capabilities	Enables cross-algorithm comparisons on controlled problems
	High-Dimensional Biomedical Datasets [71]	Domain-specific performance assessment	Provides relevance to real-world drug discovery applications
	Kaggle Drug Datasets (11,000+ compounds) [87]	Validation of drug-target interaction prediction	Tests practical utility in pharmaceutical contexts
Surrogate Models	Support Vector Classifier (SVC) [3]	Replacement for expensive fitness evaluations	Reduces computational cost while maintaining search direction
	Gaussian Processes (GP) [3]	Regression surrogate for expensive problems	Provides uncertainty estimates with predictions
	Radial Basis Function (RBF) Networks [3]	Flexible approximation of complex response surfaces	Balanced between accuracy and computational cost
Chaotic Maps	Piecewise Chaotic Map [88]	Enhancement of metaheuristic diversity and local optima escape	Best-performing variant in C-RIME algorithm
	Logistic Map [88]	Introduction of stochasticity with ergodicity properties	Most frequently utilized chaotic map
	27 Standard Chaotic Maps [88]	Comprehensive exploration of chaos-enhanced optimization	Enables selection of optimal map for specific problems
Knowledge Transfer Mechanisms	PCA-Based Subspace Alignment [3]	Facilitates knowledge sharing across related tasks	Particularly effective for heterogeneous task distributions
	Guiding Vector Strategy [71]	Enables beneficial knowledge transfer between related tasks	Improves search capability and convergence speed
	Linear Transformation Strategy [3]	Maps tasks to higher-order representation space	Enhances latent synergies between distinct tasks

Convergence Pathways in Evolutionary Multitasking

The convergence behavior of EMT algorithms follows distinct pathways influenced by their knowledge transfer mechanisms and optimization strategies. The following diagram illustrates key convergence pathways and their interactions:

EMT Convergence Pathways and Assessment Framework

This comparison guide has established a comprehensive framework for assessing convergence speed and solution quality in Evolutionary Multitasking algorithms, with particular relevance to drug discovery applications. The experimental protocols and metrics outlined provide researchers with standardized methodologies for objective algorithm evaluation. Current evidence demonstrates that algorithms incorporating task relevance evaluation [71], classifier assistance [3], and chaos enhancement [88] consistently outperform traditional approaches in both convergence speed and solution quality across diverse problem domains.

The optimal application of EMT algorithms requires careful matching of algorithm strengths to problem characteristics. For high-dimensional feature selection problems, EMTRE with its explicit task relevance evaluation provides superior performance [71]. For computationally expensive drug optimization problems, classifier-assisted approaches like CA-MTO offer the best balance between computational efficiency and solution quality [3]. Future research directions should focus on adaptive knowledge transfer mechanisms, automated task similarity assessment, and improved surrogate modeling techniques to further enhance convergence behavior in complex pharmaceutical optimization problems.

Complex Network Analysis of Knowledge Transfer Efficiency

In the domains of scientific research and industrial drug development, optimizing the flow of knowledge is critical for accelerating innovation. Knowledge transfer (KT), the process of exchanging information, skills, and insights among entities, is a fundamental driver of progress [90]. However, the pathways through which knowledge travels are often complex and inefficient. Complex Network Analysis (CNA) provides a powerful quantitative framework to model these pathways, representing entities as nodes and their relationships as edges [91]. By analyzing the topology and dynamics of these Knowledge Transfer Networks (KTNs), researchers can identify bottlenecks, optimize collaboration structures, and ultimately enhance innovation efficiency [92]. This guide explores the intersection of CNA and KT, objectively comparing analytical approaches and their performance within the specialized context of evolutionary multitasking convergence speed analysis.

The rise of evolutionary multitasking optimization (MTO) presents a compelling application for CNA. MTO algorithms, such as the Multifactorial Evolutionary Algorithm (MFEA), simultaneously solve multiple optimization tasks by exploiting synergies and transferring knowledge between them [93]. The convergence speed of these algorithms is highly dependent on the efficacy of inter-task knowledge transfer. This article frames its comparison within this advanced research context, providing methodologies and data relevant to scientists developing next-generation optimization tools for complex problems like drug discovery.

Theoretical Foundations: Knowledge Transfer as a Network

A knowledge transfer network is a complex system where members (e.g., researchers, labs, firms) are connected through relationships that enable the flow of knowledge. The structure of these networks directly influences their function.

Key Network Metrics and Their Impact on Knowledge Transfer

The efficiency of a KTN can be quantified using specific network metrics, each offering a different lens on the network's topology and its potential for knowledge flow. Centrality measures a node's importance based on its connectivity, influencing its access to information [92]. Structural holes represent gaps between disconnected parts of a network; nodes that bridge these holes can control information flow and access non-redundant knowledge [92]. Modularity identifies densely connected clusters within the network, which can foster deep, specialized knowledge sharing but may also create silos if connections between clusters are weak.

The dynamic characteristics of Heterogeneous Knowledge Transfer Networks (HKTNs), which contain different types of entities and relationships, are particularly crucial. The evolution of a node's position within an HKTN—its shifting centrality and control over structural holes—significantly impacts its innovation output [92].

The Evolutionary Multitasking Connection

In evolutionary computation, Multitasking Optimization (MTO) aims to solve multiple tasks concurrently by leveraging inter-task synergies [94] [93]. The Multifactorial Evolutionary Algorithm (MFEA) is a pioneering MTO algorithm that uses implicit transfer learning, often through chromosomal crossover between individuals assigned to different tasks [93]. The convergence speed of such algorithms is critically dependent on the effectiveness of this knowledge transfer. Inefficient transfer can lead to negative transfer, where knowledge from one task hinders performance on another, thereby slowing convergence. Analyzing the "knowledge network" within the population—how solutions from different tasks interact and share genetic material—using CNA can reveal inefficiencies and guide the development of more sophisticated transfer mechanisms, such as the two-level transfer learning algorithm developed to reduce randomness and improve convergence rates [93].

Comparative Analysis of Methodological Approaches

Different methodological approaches for analyzing knowledge transfer efficiency offer varying advantages and are suited to different research scenarios. The table below provides a high-level comparison of the primary paradigms.

Table 1: Comparison of Primary Methodological Approaches for Knowledge Transfer Analysis

Methodology	Core Focus	Typical Data Sources	Key Performance Metrics	Best-Suited For
Social Network Analysis (SNA)	Mapping and measuring relationships and flows between entities.	Surveys, publication co-authorship, patent co-invention.	Centrality, Density, Structural Holes, "Small World" properties [92].	Understanding social drivers of KT, identifying key influencers.
Bibliometric Network Analysis	Mapping the structure of scientific knowledge through publication data.	Scientific papers (Web of Science, Scopus), patents.	Co-citation, Co-word analysis, Bibliographic coupling [90].	Tracking the evolution of research fields, identifying emerging topics.
Evolutionary Multitasking Algorithms	Optimizing knowledge transfer between concurrent computational tasks.	Benchmark optimization problems, real-world task suites.	Convergence Speed, Factorial Cost, Scalar Fitness [93].	Enhancing the performance of computational optimization in drug discovery.
Heterogeneous Network Modeling	Analyzing networks with multiple node and relationship types.	Complex relational data (e.g., firm-university partnerships) [92].	Dynamic centrality/structural hole metrics, Regression coefficients on innovation output [92].	Modeling real-world, multi-actor innovation ecosystems.

Performance Comparison of Advanced Network-Based Methods

For researchers requiring deeper analytical power, advanced computational methods have been developed. The following table compares two sophisticated frameworks that explicitly use network structures to improve knowledge transfer, with quantitative performance data based on established test suites.

Table 2: Performance Comparison of Advanced Network-Based KT Frameworks

Framework / Algorithm	Core Mechanism	Reported Performance Advantage	Experimental Context	Key Limitations
Network Collaborator (NC) [94]	Evolutionary multitasking framework that explicitly shares network structure (from NR task) and community partitions (from CD task).	Joint optimization shows a synergistic effect:• Community info ↑ NR accuracy.• Network structure ↑ CD quality [94].	Test suite of synthetic & real-world networks; inference models: Evolutionary Game (EG), Resistor Network (RN) [94].	Performance is sensitive to the inherent correlation between the network structure and dynamic processes.
Two-Level Transfer Learning (TLTL) [93]	Upper-level: Inter-task knowledge transfer via elite individuals.Lower-level: Intra-task transfer across dimensions.	Outperforms MFEA in global search ability and convergence rate by reducing random transfer and leveraging task similarity [93].	Various MTO benchmark problems; compared against state-of-the-art evolutionary MTO algorithms like MFEA [93].	Requires tuning of inter-task transfer probability; performance gain depends on inter-task relatedness.

Experimental Protocols for Key Methodologies

To ensure reproducibility and provide a clear guide for implementation, this section details the experimental protocols for two key methodologies referenced in the comparison tables.

Protocol for the Network Collaborator Framework

This protocol outlines the steps to implement and validate the synergistic NR-CD framework as described in [94].

• Problem Formulation & Test Suite Design: Define a set of multitasking problems where each task involves simultaneously inferring a network structure and its community partition from observed node dynamics. Construct a test suite using both synthetic networks (e.g., Lancichinetti-Fortunato-Radicchi benchmarks) and real-world network data.
• Dynamic Data Generation: Simulate interdependent dynamics on the known networks using inference models like the Evolutionary Game (EG) or Resistor Network (RN) models. The observed node dynamics serve as the input for the reconstruction tasks.
• Algorithm Initialization: Implement the Network Collaborator framework, which involves a pre-optimization stage to obtain an initial network structure. Initialize a population of candidate solutions for the joint NR-CD problem.
• Multitasking Optimization Cycle:
  • NR Task Optimization: Evolve the population to find a network structure that best explains the observed dynamics, using a multiobjective evolutionary algorithm.
  • Explicit Knowledge Transfer to CD: Transfer the superior network structures found by the NR task to the CD task.
  • CD Task from Dynamics: Model the process as a dynamic community detection problem on the evolving network.
  • Explicit Knowledge Transfer to NR: Transfer the community partitions found by the CD task to the NR task. Employ local search strategies that use this inter-community and intra-community information to refine the network structure.
• Performance Evaluation: Evaluate the accuracy of the reconstructed network against the ground truth (e.g., using AUC-ROC) and the quality of the detected communities (e.g., using Normalized Mutual Information). Compare the performance against baseline methods that perform NR and CD in isolation.

Protocol for the Two-Level Transfer Learning Algorithm

This protocol details the procedure for applying the TLTL algorithm to enhance convergence in MTO problems, as per [93].

• MTO Problem Setup: Define K distinct optimization tasks to be solved simultaneously. Each task Tj has its own objective function Fj(x) and decision space.
• Population Initialization: Initialize a population of N individuals with a unified representation. Assign a skill factor (τ_i) to each individual, denoting the task on which it performs best.
• Two-Level Evolutionary Cycle: For each generation:
  • Upper-Level (Inter-Task Transfer):
    • With a probability tp (transfer probability), select parent individuals.
    • If parents have different skill factors, perform inter-task crossover. To reduce randomness, bias the selection towards using genetic material from elite individuals of the other task.
    • The offspring inherit genetic material from both tasks and are assigned a skill factor based on their factorial rank.
  • Lower-Level (Intra-Task Transfer):
    • For each task, implement a separate EA (e.g., DE, PSO).
    • Within this EA, enable information transfer between different dimensions of the decision variables for the same task, facilitating a more efficient search across dimensions.
  • Fitness Evaluation & Selection: Calculate the factorial cost and scalar fitness for each individual. Select elite individuals for each task to form the next generation.
• Performance Measurement: Track the convergence speed (number of generations or function evaluations to reach a target solution quality) and the best factorial cost for each task over generations. Compare these metrics against the standard MFEA and other baseline MTO algorithms.

Visualization of Complex Networks and Workflows

Effective visualization is crucial for interpreting the structure of complex networks and the workflows of analytical algorithms. The following diagrams, generated using Graphviz with the specified color palette, illustrate key concepts.

Network Collaborator Multitasking Framework

The following diagram visualizes the core synergistic process of the Network Collaborator framework, where knowledge is explicitly shared between the Network Reconstruction and Community Detection tasks.

Strategies for Visualizing Complex Network Data

Displaying complex network data clearly requires specific strategies to reduce visual clutter and improve readability. This diagram outlines the three primary strategies identified in the literature [91].

The Scientist's Toolkit: Research Reagent Solutions

This section details essential computational tools, algorithms, and data sources that form the foundational "reagent solutions" for conducting complex network analysis of knowledge transfer.

Table 3: Essential Research Tools for KT-CNA

Tool / Resource	Type	Primary Function in KT-CNA	Key Features / Notes
Web of Science Core Collection [90]	Data Source	Provides high-quality publication metadata for constructing bibliometric KT networks.	Considered a relevant database for bibliometric studies due to comprehensive metadata and journal impact factors [90].
VOSviewer & SciMAT [90]	Software	Enables science mapping and visualization of bibliometric networks.	Complementary tools for performing performance analysis and science mapping in bibliometric studies [90].
Multifactorial Evolutionary Algorithm (MFEA) [93]	Algorithm	The foundational algorithm for evolutionary multitasking, enabling implicit knowledge transfer between tasks.	Uses assortative mating and vertical cultural transmission for transfer; serves as a baseline for advanced MTO algorithms [93].
Network Collaborator (NC) [94]	Software Framework	An evolutionary multitasking framework for joint Network Reconstruction and Community Detection from dynamics.	Open-source code available; demonstrates explicit, synergistic knowledge transfer between NR and CD tasks [94].
Centrality & Structural Hole Metrics [92]	Analytical Metric	Quantifies the strategic importance and information control of nodes within a KTN.	Dynamic evolution of these metrics in HKTNs is a significant predictor of firm innovation capability [92].
Negative Binomial Regression Model [92]	Statistical Model	Used to model the relationship between count-based innovation outcomes (e.g., patents) and network position variables.	Appropriate for analyzing the impact of HKTN location characteristics on firm innovation output [92].

The healthcare industry faces a critical challenge: the slow and inefficient translation of groundbreaking biomedical discoveries into timely, effective, and accessible patient treatments. Despite decades of major advances in biomedical science, systemic barriers consistently delay the adoption of innovations, from drug therapies to cell and gene therapies and new diagnostics [95]. This inefficiency has significant consequences; the U.S. healthcare system, for instance, is plagued by an estimated $800 billion of waste and inefficiency, undermining the perceived value of new innovations and contributing to poorer health outcomes compared to other high-income countries [95].

These barriers are multifaceted and include inconsistent coverage policies, imperfect information systems for decision-making, policy constraints, and fundamental infrastructure gaps [95]. For example, despite FDA approval and demonstrated clinical effectiveness, the utilization of transformative therapies like PCSK9 inhibitors for cardiovascular disease and CAR-T cell therapies for certain blood cancers remains considerably lower than expected. This is often due to strict payer coverage criteria, complex manufacturing requirements, and a shortage of qualified clinical providers [95]. Overcoming these challenges requires a new approach that optimizes the entire healthcare system, not just its individual components. This article explores how advanced computational optimization paradigms, particularly evolutionary multitasking, are being leveraged to address these very real-world problems, accelerating drug development, enhancing clinical trials, and ultimately helping to deliver on the promise of biomedical innovation.

Evolutionary Multitasking Optimization: A Primer

Evolutionary multitasking optimization (EMTO) is an emerging paradigm that rethinks how complex problems are solved. Traditionally, optimization tasks are tackled in isolation. EMTO, however, draws inspiration from the concept of transfer learning in machine learning, enabling the simultaneous solving of multiple tasks by leveraging their underlying complementarities [3]. In an EMTO framework, knowledge transfer between tasks allows the problem-solving process of one task to be enhanced by the evolutionary search of another [9].

The core mathematical principle involves optimizing multiple tasks concurrently. Suppose an MTO problem consists of K optimization tasks, where the i-th task, denoted as T_i, is defined by an objective function f_i : X_i → R over a search space X_i. The goal of MTO is to find a set of solutions {x*_1, x*_2, ..., x*_K} such that each x*_i is the global optimum for its respective task f_i [9]. This is achieved through sophisticated algorithms that manage a shared population of solutions, facilitating the exchange of beneficial genetic material across tasks.

A key challenge in this process is mitigating negative transfer, which occurs when knowledge from one task misguides or hinders the optimization of another, potentially leading to premature convergence on suboptimal solutions [9]. Modern EMTO algorithms employ various strategies to overcome this, such as:

• Domain Adaptation Techniques: Using methods like linear domain adaptation (LDA) based on multi-dimensional scaling (MDS) to align the search spaces of different tasks, enabling more robust and effective knowledge transfer, even between tasks with different dimensionalities [9].
• Diversity Preservation Mechanisms: Incorporating advanced memory mechanisms or dual-archive strategies to store both high-quality and diverse solutions, preventing the population from stagnating in local optima [26] [96].

The following diagram illustrates the core workflow and knowledge transfer process in a generalized evolutionary multitasking algorithm.

Comparative Analysis of Optimization Algorithms

The "No Free Lunch" theorem in optimization asserts that no single algorithm is universally superior for all problems [26]. Different algorithms possess distinct strengths and weaknesses, making them suited to specific types of challenges. The table below provides a structured comparison of several state-of-the-art optimization algorithms, highlighting their core mechanisms, advantages, and limitations, with a particular focus on their applicability to biomedical problems.

Table 1: Performance and Characteristic Comparison of Optimization Algorithms

Algorithm Name	Core Mechanism / Inspiration	Key Advantages	Key Limitations / Challenges	Suitability for Biomedical Problems
MFEA-MDSGSS [9]	Evolutionary Multitasking with Multi-Dimensional Scaling & Golden Section Search	Effective knowledge transfer; Mitigates negative transfer; Prevents premature convergence.	Complexity in tuning mapping parameters; Computational overhead from subspace alignment.	High - for complex, multi-faceted problems like clinical trial optimization and multi-objective drug design.
ESSA [26]	Evolutionary Salp Swarm Algorithm with Advanced Memory	Enhanced solution diversity; Prevents premature convergence; Robust performance.	May have slower convergence on simpler problems due to focus on diversity.	Medium-High - for global optimization and complex engineering design problems with noisy data.
DREA-FS [96]	Evolutionary Multitasking for Multi-Objective Feature Selection	Identifies multiple equivalent feature subsets; Enhances interpretability; Balances convergence & diversity.	Primarily designed for feature selection; May not be directly applicable to other problem types.	Very High - for high-dimensional biomarker discovery and genomic data analysis.
CA-MTO [3]	Classifier-Assisted Evolutionary Multitasking for Expensive Problems	Uses classifiers as surrogates; Reduces computational cost; Robust with limited data.	Performance depends on classifier accuracy; Knowledge transfer efficiency relies on task relatedness.	Very High - for computationally expensive problems like drug candidate simulation or protein folding.
SSA [26]	Salp Swarm Algorithm (Basic Version)	Simple structure; Few control parameters; Easy implementation.	Prone to getting trapped in local optima; Slower convergence in complex problems.	Medium - for less complex, single-objective optimization tasks.

From this comparison, it is clear that EMTO algorithms like MFEA-MDSGSS, DREA-FS, and CA-MTO offer significant advantages for the complex, interconnected, and computationally demanding problems prevalent in biomedicine. Their ability to share information across tasks and efficiently navigate high-dimensional search spaces makes them particularly powerful tools for the modern biomedical researcher.

Experimental Protocols and Performance Metrics

To objectively evaluate the performance of optimization algorithms, rigorous experimental protocols and standardized metrics are essential. The following table outlines the key performance indicators used to benchmark algorithms like those discussed, providing insights into their efficiency and robustness.

Table 2: Key Performance Metrics for Optimization Algorithm Evaluation

Metric Category	Specific Metric	Description	Interpretation in Biomedical Context
Convergence Speed	Number of Function Evaluations (FEs) to Reach Target Accuracy	Measures the number of simulations or objective function calculations required for the algorithm to find a solution of a specified quality [9].	Lower FEs mean faster, cheaper R&D cycles (e.g., quicker virtual screening of drug molecules).
Solution Quality	Best/Median/Average Objective Value	The final quality of the solution found by the algorithm after a fixed budget of FEs or upon convergence [26].	Directly relates to the efficacy of the solution (e.g., higher drug binding affinity, more accurate diagnostic model).
Statistical Robustness	Mean, Standard Deviation, and Wilcoxon Rank-Sum Test	Provides a statistical summary of performance over multiple independent runs and tests for significant differences between algorithms [26] [96].	Ensures the algorithm's performance is reliable and not due to chance, which is critical for reproducible research.
Success Rate / Optimization Effectiveness	Percentage of Successful Runs	The proportion of independent runs in which the algorithm found a solution meeting a pre-defined success criterion [26].	Indicates the probability of successfully finding a viable solution to a problem, such as a valid therapeutic antibody sequence.

Case Study: Multi-Objective Feature Selection with DREA-FS

Objective: To solve high-dimensional feature selection problems in biomedical data (e.g., genomic or proteomic data) by selecting a minimal set of features that maximizes classification accuracy [96].

Protocol:

• Task Construction: A dual-perspective dimensionality reduction strategy creates two simplified, complementary tasks from the original high-dimensional dataset.
  • Task 1: Uses an improved filter-based method to select features with high statistical scores.
  • Task 2: Uses a group-based method to cluster correlated features and select representatives [96].
• Algorithm Setup: The DREA-FS algorithm is initialized with a population of candidate feature subsets. It employs a dual-archive mechanism:
  • Elite Archive: Stores non-dominated solutions (Pareto front) to guide convergence.
  • Diversity Archive: Preserves feature subsets with equivalent classification performance but different selected features to maintain diversity and offer multiple options [96].
• Knowledge Transfer: Genetic material is exchanged between the two tasks during evolution, allowing each task to benefit from the search perspective of the other.
• Evaluation: The algorithm is run on 21 real-world datasets. Its performance is compared against state-of-the-art multi-objective feature selection algorithms using the metrics in Table 2 [96].

Key Findings:

• DREA-FS demonstrated superior classification performance compared to other algorithms.
• Critically, it successfully identified multiple, distinct feature subsets that achieved equivalent classification accuracy, providing decision-makers with diverse and interpretable options for biomarker discovery [96].

Case Study: Classifier-Assisted Multitasking for Expensive Problems

Objective: To optimize complex, computationally expensive problems (e.g., clinical trial simulations) where each function evaluation is time-consuming and resource-intensive [3].

Protocol:

• Surrogate Model Integration: Instead of using a regression model, a Support Vector Classifier (SVC) is integrated with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The SVC is trained to distinguish whether a candidate solution is better or worse than a reference point, rather than predicting its exact fitness value, which is a simpler and more robust task [3].
• Knowledge Transfer for Data Augmentation: A PCA-based subspace alignment technique is used to transform and aggregate high-quality solutions from all related tasks. This enriches the training data for each task-specific classifier, significantly improving its accuracy despite the initial scarcity of data [3].
• Optimization Loop: The classifier pre-screens promising candidate solutions, and only the most promising ones are evaluated with the expensive, true objective function.
• Evaluation: The proposed CA-MTO algorithm is tested on a suite of expensive multitasking optimization problems and benchmarked against standard CMA-ES and other state-of-the-art algorithms [3].

Key Findings:

• The SVC-assisted CMA-ES showed significant improvements in robustness and scalability over the standard version.
• The knowledge transfer strategy further enhanced performance, giving CA-MTO a competitive edge in efficiently solving expensive multitasking problems with limited evaluation budgets [3].

Clinical and Biomedical Case Studies

The theoretical advantages of advanced optimization algorithms are being realized in tangible biomedical breakthroughs. The following case studies demonstrate their impact across the drug development lifecycle.

AI-Powered Clinical Trial Optimization

Leading pharmaceutical companies are now deploying AI agents to dramatically accelerate and improve the efficiency of clinical trials. AstraZeneca, for example, has developed a "Development Assistant" powered by generative AI on AWS. This tool allows clinical operations teams to use natural language to query vast amounts of structured and unstructured clinical data, providing real-time, evidence-based insights for critical decisions like patient recruitment and site selection. Built on a strong data foundation that transforms curated sources into FAIR (Findable, Accessible, Interoperable, Reusable) data products, this system has progressed from proof-of-concept to a production-ready platform in just six months, with plans to scale to over 1,000 users [97].

Similarly, Novartis has implemented an adaptive AI strategy across its R&D pipeline to reduce drug development time by up to 19 months. Its core initiatives include "Fast-to-IND," "Enhanced Operations," and "AI-Enabled R&D." A key component is the Intelligent Decision System (IDS), which uses digital twins to simulate clinical workflows. This allows teams to forecast outcomes and test strategies before implementation, reducing risk and increasing operational efficiency [97]. The workflow for such an AI-optimized clinical trial is illustrated below.

Accelerating Antibody Discovery with High-Throughput Optimization

The integration of high-throughput experimentation and machine learning is transforming antibody discovery from a laborious, empirical process into a rational, optimized pipeline. Researchers now use techniques like next-generation sequencing (NGS) and antibody display technologies (e.g., phage, yeast display) to generate massive datasets of antibody sequences and their functional properties [98]. Machine learning models, including protein language models, are then trained on this data to predict and optimize not just affinity, but also critical therapeutic properties like specificity, stability, and manufacturability [98]. This data-driven approach allows for the in silico exploration of a vast sequence space, rapidly identifying lead candidates with high developability potential, thereby accelerating the entire discovery timeline.

CRISPR Therapy Development: Overcoming Systemic Barriers

The journey of CRISPR-based therapies from discovery to clinic highlights both the promise of biomedical innovation and the systemic barriers that optimization must address. While the first CRISPR medicine, Casgevy for sickle cell disease and beta thalassemia, has been approved, its uptake is constrained by financial and infrastructure challenges, including the high cost of treatment and the need for specialized treatment centers [99]. Furthermore, regulatory and policy constraints continue to shape the landscape. A landmark case in 2025 involved a personalized in vivo CRISPR treatment for an infant with a rare genetic disease, CPS1 deficiency. This therapy was developed and delivered in just six months, establishing a regulatory precedent for rapid approval of platform therapies [99]. This case serves as a powerful proof-of-concept but also underscores the next great challenge: scaling these bespoke optimization successes into broadly accessible "CRISPR for all" treatments, which will require further optimization of manufacturing, delivery, and reimbursement systems [99].

The Scientist's Toolkit: Key Research Reagent Solutions

The experimental and computational advances discussed rely on a suite of core technologies and reagents. The following table details some of the essential tools in the modern biomedical optimization toolkit.

Table 3: Essential Research Reagents and Platforms for Biomedical Optimization

Tool / Reagent / Platform	Primary Function	Key Application in Optimization
Amazon Web Services (AWS) & Amazon Bedrock [97]	Cloud Computing Platform & Generative AI Service	Provides scalable infrastructure for building and deploying AI agents and digital twins for clinical trial optimization and data analysis.
Next-Generation Sequencing (NGS) [98]	High-Throughput DNA/RNA Sequencing	Generates massive-scale antibody sequence and genomic data, forming the foundational dataset for training machine learning models.
Antibody Display Technologies (e.g., Yeast, Phage Display) [98]	Screening Antibody Libraries for Binders	High-throughput experimental method to generate labeled data (sequence -> binding affinity) for supervised learning in antibody optimization.
Bio-Layer Interferometry (BLI) [98]	Label-Free Analysis of Biomolecular Interactions	Provides high-throughput kinetic and affinity data (e.g., kon, koff, KD) for antibody-antigen interactions, used to validate and refine computational models.
Support Vector Classifier (SVC) [3]	Machine Learning Classification Algorithm	Acts as a robust surrogate model in evolutionary algorithms to pre-screen solutions in expensive optimization problems, reducing computational cost.
Differential Scanning Fluorimetry (DSF) [98]	High-Throughput Protein Stability Analysis	Rapidly assesses the thermal stability of hundreds of antibody variants, providing critical data for optimizing developability properties.
Lipid Nanoparticles (LNPs) [99]	In Vivo Delivery Vehicle for Therapeutics	Enables efficient delivery of CRISPR components in vivo, a critical solution to the "delivery" problem in gene therapy, allowing for systemic administration and even re-dosing.

The integration of advanced optimization strategies, particularly evolutionary multitasking, with high-throughput experimental data is ushering in a new era of efficiency in biomedical research and development. As evidenced by the case studies, from AI-accelerated clinical trials to data-driven antibody design, these approaches are moving from theoretical promise to practical impact. They directly address the core challenges of cost, time, and complexity that have long plagued the healthcare system.

The future of biomedical optimization lies in the deeper fusion of computational and experimental worlds. Explainable AI will be crucial for building trust in model-driven discoveries, while next-generation algorithms will need to grapple with even more complex, multi-scale problems that integrate genomic, clinical, and real-world data. The ultimate goal is a learning healthcare system where optimization is not just a tool for research, but an embedded, continuous process that ensures every biomedical innovation can rapidly and reliably reach the patients who need it.

Conclusion

Evolutionary Multitasking Optimization represents a paradigm shift in computational problem-solving, with convergence speed serving as the critical determinant of its practical utility. Our analysis demonstrates that strategic knowledge transfer, adaptive operator selection, and sophisticated domain adaptation techniques collectively address the fundamental challenge of negative transfer while significantly accelerating convergence. The emergence of surrogate-assisted EMTO frameworks and network-based transfer analysis opens new avenues for tackling computationally expensive biomedical problems, from drug candidate screening to treatment optimization. Future research should focus on dynamic transfer mechanisms for heterogeneous tasks, quantum-inspired EMTO frameworks, and specialized applications in personalized medicine and clinical trial optimization, potentially transforming how we approach complex biological systems and therapeutic development pipelines.

References

• 1. What makes evolutionary multi-task optimization better [https://www.sciencedirect.com/science/article/abs/pii/S156849462300563X]
• 2. Auxiliary Population Multitask Optimization Based on ... [https://www.mdpi.com/2076-3417/15/17/9746]
• 3. A classifier-assisted evolutionary algorithm with knowledge ... [https://link.springer.com/article/10.1007/s40747-025-01908-7]
• 4. An adaptive multitask optimization algorithm based on ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650224003365]
• 5. Evolutionary multitasking optimization based on cross-task ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417425031951]
• 6. Scenario-based self-learning transfer framework for multi ... [https://www.sciencedirect.com/science/article/abs/pii/S0950705125008706]
• 7. CEC 2025 Competition on “Evolutionary Multi-task ... [https://www.hou-yq.com/WCCI_CEC_2025_COMPETITION_EMO.html]
• 8. Adaptive Bi-Operator Evolution for Multitasking ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11505233/]
• 9. Enhancing evolutionary multitask optimization by ... [https://www.sciencedirect.com/science/article/abs/pii/S095741742503595X]
• 10. Multifactorial Evolutionary Algorithm Based on Diffusion ... [https://pubmed.ncbi.nlm.nih.gov/37159319/]
• 11. Residual Learning Inspired Crossover Operator and ... [https://arxiv.org/html/2503.21347v1]
• 12. Multifactorial evolutionary algorithm with adaptive transfer ... [https://link.springer.com/article/10.1007/s40747-023-01105-4]
• 13. Progressive auto-encoding for domain adaptation in ... [https://www.sciencedirect.com/science/article/abs/pii/S1568494625012293]
• 14. 10 Types of Knowledge: Explicit, Implicit, Tacit, & More [https://whatfix.com/blog/types-of-knowledge/]
• 15. Different Types of Knowledge: Implicit, Tacit, and Explicit [https://bloomfire.com/blog/implicit-tacit-explicit-knowledge/]
• 16. Understanding implicit and explicit knowledge [https://great2know.de/en/blog/understanding-implicit-and-explicit-knowledge/]
• 17. A Two-Level Transfer Learning Algorithm for Evolutionary ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC6971124/]
• 18. Structure transfer and consolidation in visual implicit learning [https://elifesciences.org/articles/100785]
• 19. Structure transfer and consolidation in visual implicit learning [https://pubmed.ncbi.nlm.nih.gov/40956297/]
• 20. Implicit and explicit learning strategies and fatigue [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2025.1438313/full]
• 21. How Implicit Sequence Learning and Explicit ... [https://journalofcognition.org/articles/10.5334/joc.439]
• 22. Evolutionary Multitasking-Based Multiobjective ... [https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2021.749232/full]
• 23. Multitasking optimization for personalized exercise group ... [https://www.sciencedirect.com/science/article/abs/pii/S0952197625028519]
• 24. Exploration vs Convergence Speed in Adaptive-Bias ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9202311/]
• 25. Decision Space - an overview | ScienceDirect Topics [https://www.sciencedirect.com/topics/computer-science/decision-space]
• 26. Evolutionary salp swarm algorithm with multi-search ... [https://www.nature.com/articles/s41598-025-09345-9]
• 27. Adaptive Bi-Operator Evolution for Multitasking ... [https://www.mdpi.com/2313-7673/9/10/604]
• 28. Evolutionary multitasking fuzzy cognitive map learning [https://www.sciencedirect.com/science/article/abs/pii/S0950705119305842]
• 29. Optimized Drug Design using Multi-Objective Evolutionary ... [https://arxiv.org/html/2405.00401v1]
• 30. Multi-and many-objective optimization: present and future ... [https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2023.1288626/full]
• 31. UCrack-DA: A Multi-Scale Unsupervised Domain ... [https://www.mdpi.com/2072-4292/17/12/2101]
• 32. Domain Adaptation Techniques for Natural and Medical ... [https://www.sciencedirect.com/science/article/abs/pii/S0020025525007418]
• 33. Multiomics with Evolutionary Computation to Identify ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11942451/]
• 34. Multidimensional scaling [https://en.wikipedia.org/wiki/Multidimensional_scaling]
• 35. Multiple Subspace Alignment Improves Domain Adaptation [https://arxiv.org/abs/1811.04491]
• 36. Goal-directed multimodal multi-objective evolutionary ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650224003341]
• 37. Subspace Least Squares Multidimensional Scaling [https://arxiv.org/abs/1709.03484]
• 38. Multi-level domain adaptation for improved generalization ... [https://www.sciencedirect.com/science/article/abs/pii/S0952197624019845]
• 39. Multitask Level-Based Learning Swarm Optimizer [https://www.mdpi.com/2313-7673/9/11/664]
• 40. Advances in Particle Swarm Optimization (2015–2025) [https://medium.com/@firestrand/advances-in-particle-swarm-optimization-2015-2025-a-theoretical-review-57c73d0a2bcb]
• 41. A multi-stage competitive swarm optimization algorithm for ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417424022784]
• 42. Robust two stages federated learning for sensor based ... [https://www.nature.com/articles/s41598-025-02395-z]
• 43. Multi-objective particle swarm optimization algorithm for ... [https://www.nature.com/articles/s41598-025-99730-1]
• 44. A multipopulation multitasking evolutionary scheme with ... [https://www.sciencedirect.com/science/article/abs/pii/S0020025523015463]
• 45. A Novel Self-Adjusting Dual-Mode Evolutionary Framework for ... [http://jas.ia.ac.cn/article/doi/10.1109/JAS.2025.125273?viewType=HTML&pageType=en]
• 46. A new perspective on designing urban low-altitude logistics ... [https://e3.eurekalert.org/news-releases/1090251]
• 47. Exploring Knowledge Transfer in Evolutionary Many-task ... [https://arxiv.org/html/2407.08918v1]
• 48. Knowledge-aware manufacturing services collaboration: A ... [https://www.sciencedirect.com/science/article/abs/pii/S1474034623004718]
• 49. Multi-objective recommendation system utilizing a ... [https://link.springer.com/article/10.1007/s40747-025-01891-z]
• 50. A review of surrogate-assisted evolutionary algorithms for ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417422025143]
• 51. A Surrogate-Assisted Gray Prediction Evolution Algorithm ... [https://www.mdpi.com/2227-7390/13/6/1007]
• 52. A survey of surrogate-assisted evolutionary algorithms for ... [https://link.springer.com/article/10.1007/s41965-024-00165-w]
• 53. Impact of surrogate model accuracy on performance and ... [https://www.sciencedirect.com/science/article/pii/S2590005625000888]
• 54. Impact of Surrogate Model Accuracy on Performance and ... [https://arxiv.org/abs/2503.00844]
• 55. Evolutionary Algorithm Based on Surrogate and Inverse ... [https://www.ieee-jas.net/article/doi/10.1109/JAS.2025.125111]
• 56. Top 5 Drug Discovery Trends 2025 Driving Breakthroughs [https://www.pelagobio.com/cetsa-drug-discovery-resources/blog/drug-discovery-trends-2025/]
• 57. Advancing drug development with “Fit-for-Purpose” modeling ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12436579/]
• 58. Mitigate Negative Transfer with Similarity Heuristic Lifelong ... [https://arxiv.org/html/2406.12251v1]
• 59. A Proof of Faster Convergence [https://pubmed.ncbi.nlm.nih.gov/33705329/]
• 60. Applying Evolutionary Multitasking for Process Parameter ... [https://www.mdpi.com/2076-3417/12/18/9378]
• 61. PC-SSRDE: A paradigm crossover-based differential ... [https://www.sciencedirect.com/science/article/abs/pii/S0020025524011022]
• 62. ECC 2025 Program | Friday June 27, 2025 [https://controls.papercept.net/conferences/conferences/ECC25/program/ECC25_ContentListWeb_3.html]
• 63. Adaptive AI-enhanced computation offloading with ... [https://www.nature.com/articles/s41598-025-00409-4]
• 64. Beyond Neural Incompatibility: Easing Cross-Scale ... [https://arxiv.org/html/2510.24208v1]
• 65. Strategic Multimodal Representation Alignment for Optimal ... [https://arxiv.org/html/2511.12121v2]
• 66. ECTTLNER: An Effective Cross-Task Transferring Learning ... [https://link.springer.com/article/10.1007/s11063-025-11729-x]
• 67. Adaptive evolutionary algorithms with linear average ... [https://www.sciencedirect.com/science/article/abs/pii/S1568494625009469]
• 68. Accelerating Convergence through Uncommon Region ... [https://arxiv.org/html/2505.05661v1]
• 69. Optimization of One-Dimensional Functions Using the ... [https://kujnsr.com/JNSR/article/view/234]
• 70. Search for Global Maxima in Multimodal Functions by ... [https://www.mdpi.com/2079-3197/7/3/43]
• 71. Enhancing evolutionary multitasking for high-dimensional ... [https://www.sciencedirect.com/science/article/abs/pii/S0950705125011219]
• 72. Hybrid genetic algorithm and deep learning techniques for ... [https://www.nature.com/articles/s41598-025-06375-1]
• 73. Chaotic golden ratio guided local search for big data ... [https://www.sciencedirect.com/science/article/pii/S2215098623000654]
• 74. A dynamic multitask evolutionary algorithm for high ... [https://www.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2025.1667167/full]
• 75. Multi-task benchmarking of spatially resolved gene expression ... [https://genomebiology.biomedcentral.com/articles/10.1186/s13059-025-03505-w]
• 76. Multi-task benchmarking of spatially resolved gene ... [https://pubmed.ncbi.nlm.nih.gov/40098171/]
• 77. Evaluating the performance of meta-heuristic algorithms on ... [https://link.springer.com/article/10.1007/s00521-022-07788-z]
• 78. Enhancing differential evolution algorithm for CEC 2014 ... [https://link.springer.com/article/10.1007/s00521-025-11678-5]
• 79. Choice of benchmark optimization problems does matter [https://www.sciencedirect.com/science/article/abs/pii/S2210650223001517]
• 80. GitHub - dmolina/cec2017real: Repository with source ... [https://github.com/dmolina/cec2017real]
• 81. Evolutionary multitasking with evolutionary trend alignment ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417424031889]
• 82. Adaptive evolutionary multitask optimization based on ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417425012217]
• 83. Learning Where, What and How to Transfer [https://arxiv.org/html/2511.15199v1]
• 84. An adaptive multitasking optimization algorithm based on ... [http://www.aimspress.com/article/doi/10.3934/mbe.2024107?viewType=HTML]
• 85. Multimodal multiobjective optimization with structural network ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11747759/]
• 86. An Evolutionary Multitasking Method for Positive and ... [https://www.sciencedirect.com/science/article/abs/pii/S0950705125017125]
• 87. AI-driven drug discovery using a context-aware hybrid ... [https://www.nature.com/articles/s41598-025-19593-4]
• 88. Chaos-enhanced metaheuristics: classification, ... [https://link.springer.com/article/10.1007/s40747-025-01791-2]
• 89. Examining Spatial (Grid) Convergence [https://www.grc.nasa.gov/www/wind/valid/tutorial/spatconv.html]
• 90. Knowledge Transfer and Networks: A Bibliometric ... [https://link.springer.com/article/10.1007/s13132-025-02814-6]
• 91. How to Display Complex Network Data with Information ... [https://www.interaction-design.org/literature/article/how-to-display-complex-network-data-with-information-visualization?srsltid=AfmBOoo02KP_2h4myZzB0SIFKnSgB293MUjar0a1WDN3A_Y4Kmeb36b_]
• 92. Heterogeneous network location, digitalization, and patent ... [https://www.nature.com/articles/s41598-025-24258-3]
• 93. A Two-Level Transfer Learning Algorithm for Evolutionary ... [https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2019.01408/full]
• 94. Knowledge Transfer Between Network Reconstruction and ... [https://www.sciencedirect.com/science/article/abs/pii/S0925231225019356]
• 95. Optimizing Biomedical Health Efficiency: Unlocking the Full ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12579706/]
• 96. An evolutionary multitasking algorithm for multi-objective ... [https://www.sciencedirect.com/science/article/abs/pii/S095219762500764X]
• 97. Highlights from the 2025 AWS Life Sciences Symposium's ... [https://aws.amazon.com/blogs/industries/highlights-from-the-2025-aws-life-sciences-symposiums-clinical-trials-track/]
• 98. Accelerating antibody discovery and optimization with high ... [https://jbiomedsci.biomedcentral.com/articles/10.1186/s12929-025-01141-x]
• 99. CRISPR Clinical Trials: A 2025 Update [https://innovativegenomics.org/news/crispr-clinical-trials-2025/]