Benchmarking Evolutionary Multitasking Optimization: A Deep Dive into CEC17 and CEC22 Performance

Abstract

This article provides a comprehensive analysis of Evolutionary Multitasking Optimization (EMTO) performance on the standard CEC17 and CEC22 benchmark suites. Tailored for researchers and drug development professionals, it explores the foundational principles of EMTO, evaluates advanced algorithmic methodologies like adaptive bi-operator strategies, addresses common performance challenges and optimization techniques, and delivers a rigorous comparative validation of state-of-the-art algorithms. The insights presented aim to guide the selection and development of efficient EMTO methods for complex, multi-problem optimization scenarios prevalent in biomedical research, such as multi-target drug discovery and clinical trial optimization.

Understanding EMTO and the CEC Benchmark Landscape

Evolutionary Multitasking Optimization (EMTO)

Evolutionary Multitasking Optimization (EMTO) is an emerging paradigm in the field of evolutionary computation that enables the simultaneous solving of multiple optimization tasks within a single, unified search process [1] [2]. Inspired by the human ability to learn multiple skills concurrently and the biological concept of multifactorial inheritance, EMTO leverages the implicit parallelism of population-based evolutionary algorithms to optimize several tasks at once [1] [3]. Unlike traditional evolutionary algorithms that solve problems in isolation, EMTO deliberately transfers knowledge—in the form of genetic material or search experiences—across different but related tasks, often leading to accelerated convergence and improved solution quality for all tasks involved [2] [4].

The foundational algorithm in this field is the Multifactorial Evolutionary Algorithm (MFEA), often called the "first EMTO algorithm" [2] [3]. MFEA introduced key concepts such as unified representation, assortative mating, and vertical cultural transmission, creating a framework where a single population evolves while solving multiple tasks, with skill factors determining which task each individual primarily addresses [1] [3]. This paradigm has demonstrated significant potential for enhancing optimization performance, particularly when tasks share underlying similarities in their fitness landscapes or optimal solutions [4].

Core Mechanisms and Knowledge Transfer Strategies

The performance of EMTO algorithms critically depends on their knowledge transfer strategies, which can be broadly categorized into implicit and explicit methods.

Implicit Knowledge Transfer

Implicit transfer mechanisms facilitate knowledge exchange indirectly through genetic operators acting on a shared population [4]. In MFEA, this is achieved through:

• Assortative Mating: Individuals with different skill factors may crossover with a prescribed random mating probability (rmp), allowing genetic material to flow between tasks [3].
• Selective Imitation: Offspring naturally inherit cultural traits (skill factors) from parents, maintaining task-specific specialization while enabling cross-task exploration [2].

While computationally efficient, implicit transfer's effectiveness heavily depends on task relatedness, with potential performance degradation when task similarity is low [4].

Explicit Knowledge Transfer

Explicit transfer strategies actively identify and extract transferable knowledge—such as high-quality solutions or solution space characteristics—from source tasks, then deliberately apply it to target tasks [4]. Advanced methods include:

• Subspace Projection: Techniques like Partial Least Squares map solutions between task domains while preserving correlations [4].
• Autoencoder-based Transfer: Denoising autoencoders learn mappings between tasks by treating one task as a noisy version of another [4].
• Block-level Transfer: Solutions are divided into blocks, enabling selective knowledge transfer at finer granularity [3].

Adaptive and Hybrid Strategies

Recent approaches dynamically adjust transfer strategies during evolution:

• Hybrid Knowledge Transfer (HKT): Combines Population Distribution-based Measurement to evaluate task relatedness with Multi-Knowledge Transfer mechanisms that employ both individual-level and population-level learning operators [1].
• Self-Adjusting Dual-Mode Evolution: Integrates variable classification evolution with dynamic knowledge transfer, using spatial-temporal information to guide evolutionary mode selection [5].

The following diagram illustrates the core workflow and knowledge transfer mechanisms in a typical EMTO system:

Diagram 1: Core EMTO workflow with knowledge transfer strategies

EMTO Benchmark Problems and Experimental Protocols

Standardized Test Suites

The CEC17 and CEC22 benchmark problems represent standardized test suites for evaluating EMTO algorithm performance [3] [6]. These benchmarks are specifically designed to assess how algorithms handle different degrees of task relatedness and complexity.

CEC17 Multi-Task Single-Objective Optimization Suite includes problems categorized by:

• CIHS: Complete Intersection, High Similarity
• CIMS: Complete Intersection, Medium Similarity
• CILS: Complete Intersection, Low Similarity [3]

CEC22 Benchmark extends testing to more complex scenarios, maintaining the classification based on intersection characteristics and similarity levels [3].

Experimental Protocol Standards

Standard experimental methodologies ensure fair algorithm comparisons [6]:

• Independent Runs: 30 independent runs with different random seeds
• Function Evaluation Limits:
  • 2-task problems: Maximum 200,000 function evaluations
  • 50-task problems: Maximum 5,000,000 function evaluations
• Performance Metrics:
  • Single-objective: Best Function Error Value (BFEV)
  • Multi-objective: Inverted Generational Distance (IGD)
• Intermediate Recording: Performance must be recorded at predefined evaluation checkpoints (100 for 2-task, 1000 for 50-task problems) [6]

Performance Comparison on CEC17 and CEC22 Benchmarks

Quantitative Algorithm Performance

Table 1: Performance comparison of EMTO algorithms on CEC17 and CEC22 benchmarks

Algorithm	Key Features	CEC17 CIHS	CEC17 CIMS	CEC17 CILS	CEC22 Overall
MFEA [3]	Single GA operator, Implicit transfer	Moderate	Moderate	Good	Moderate
MFDE [3]	Single DE operator, Implicit transfer	Good	Good	Moderate	Moderate
EMTO-HKT [1]	Hybrid knowledge transfer, Adaptive control	Excellent	Excellent	Good	Good
BOMTEA [3]	Bi-operator strategy, Adaptive selection	Excellent	Excellent	Excellent	Excellent
PA-MTEA [4]	Association mapping, Adaptive population reuse	Good	Excellent	Excellent	Excellent

Performance Rating Scale: Excellent > Good > Moderate > Poor

Table 2: Specialized capabilities across optimization scenarios

Algorithm	Many-Task Optimization (50+ tasks)	Computational Efficiency	Negative Transfer Resistance	Implementation Complexity
MFEA [2] [3]	Limited	High	Low	Low
MFDE [3]	Limited	High	Low	Low
EMTO-HKT [1]	Good	Medium	High	Medium
BOMTEA [3]	Good	Medium	High	Medium
PA-MTEA [4]	Excellent	Medium	Excellent	High

Key Performance Insights

The comparative analysis reveals several important patterns:

• Operator Selection Significantly Impacts Performance: BOMTEA's adaptive bi-operator strategy demonstrates superior performance across diverse problem types, outperforming single-operator approaches like MFEA and MFDE [3]. This confirms that no single evolutionary search operator is universally optimal for all tasks.
• Adaptive Knowledge Transfer Enhances Robustness: Algorithms with dynamic transfer mechanisms (EMTO-HKT, BOMTEA, PA-MTEA) consistently outperform fixed-transfer approaches, particularly on problems with low task similarity where negative transfer risks are higher [1] [4].
• Explicit Mapping Benefits Complex Problems: For CEC22's more challenging benchmarks, PA-MTEA's explicit association mapping strategy shows advantages, indicating that sophisticated transfer models become increasingly valuable as problem complexity grows [4].

Research Reagents and Experimental Toolkit

Table 3: Essential research components for EMTO experimentation

Research Component	Function & Purpose	Examples & Specifications
Benchmark Problems [3] [6]	Standardized performance evaluation	CEC17 (CIHS/CIMS/CILS), CEC22 test suites
Performance Metrics [6]	Quantitative algorithm assessment	BFEV (single-objective), IGD (multi-objective)
Evolutionary Search Operators [3]	Core search mechanisms	DE/rand/1, Simulated Binary Crossover (SBX)
Knowledge Transfer Models [1] [4]	Enable cross-task optimization	Implicit genetic transfer, Explicit mapping, Hybrid strategies
Relatedness Measurement [1]	Quantify task similarity for transfer control	Population Distribution-based Measurement (PDM)
Resource Allocation Mechanisms [2]	Distribute computational resources across tasks	Adaptive resource scheduling based on task difficulty

Emerging Trends and Future Directions

The EMTO landscape continues to evolve with several promising research directions:

• Large Language Model Integration: Recent work explores using LLMs to autonomously design knowledge transfer models, reducing reliance on expert knowledge and potentially discovering novel transfer strategies [7].
• Many-Task Optimization: Scaling EMTO to handle dozens or hundreds of simultaneous tasks presents algorithmic challenges in resource allocation and knowledge management [2] [6].
• Cross-Paradigm Hybridization: Combining EMTO with other optimization paradigms such as constrained optimization, multi-objective optimization, and dynamic optimization creates powerful hybrid approaches [2] [5].
• Real-World Applications: EMTO is increasingly applied to practical problems including cloud computing, engineering design, feature selection, and scheduling optimization [2] [4].

Evolutionary Multitasking Optimization represents a paradigm shift from traditional single-task optimization toward concurrent multi-task problem solving. The performance evidence from CEC17 and CEC22 benchmarks clearly demonstrates that algorithms with adaptive knowledge transfer mechanisms (BOMTEA, EMTO-HKT, PA-MTEA) consistently outperform static approaches across diverse problem types. The critical success factors include appropriate evolutionary operator selection, dynamic control of knowledge transfer based on task relatedness, and specialized strategies for handling different levels of task similarity. As EMTO research advances, the integration of artificial intelligence techniques like large language models promises to further automate and enhance algorithm design, potentially unlocking new capabilities for complex, large-scale multitask optimization scenarios.

The Role of CEC17 and CEC22 Benchmark Suites in Standardized Evaluation

The empirical evaluation of metaheuristic algorithms relies heavily on standardized benchmark problems to ensure fair and meaningful comparisons. Within evolutionary computation, benchmark suites developed for the IEEE Congress on Evolutionary Computation (CEC) have become the cornerstone for assessing algorithm performance. The CEC 2017 and CEC 2022 test suites represent significant milestones in this ongoing effort to develop challenging and comprehensive evaluation standards. These suites are particularly crucial in the emerging field of Evolutionary Multitasking Optimization (EMTO), where they serve as standardized testing grounds for algorithms designed to solve multiple optimization problems simultaneously [3]. The CEC benchmarks provide a controlled environment where researchers can analyze how algorithms balance exploration and exploitation, adapt to different problem structures, and transfer knowledge between related tasks—all essential capabilities for real-world optimization scenarios.

The limitations of synthetic benchmark problems (SBPs), which may include unrealistic properties that lead to performance overestimation or underestimation, have driven the development of more robust testing frameworks [8]. The CEC17 and CEC22 suites address these concerns by incorporating problems with carefully designed characteristics that better simulate the challenges of real-world optimization scenarios. Their role extends beyond mere algorithm ranking; they help identify methodological strengths and weaknesses, guide algorithmic improvements, and establish reproducible experimental protocols that enable meaningful cross-study comparisons in evolutionary computation research.

Technical Specifications of CEC17 and CEC22 Suites

CEC 2017 Benchmark Suite

The CEC 2017 benchmark suite represents a significant advancement in the evolution of testing frameworks for real-parameter single-objective optimization. This suite comprises 30 benchmark functions with diverse properties including unimodal, multimodal, hybrid, and composition functions [9] [10]. These categories are strategically designed to test different algorithmic capabilities: unimodal functions evaluate convergence speed and exploitation potential, multimodal functions test the ability to avoid local optima, while hybrid and composition functions combine various challenges to simulate real-world problem complexity.

A key characteristic of CEC 2017 is its inclusion of problems with novel features such as graded level of linkages, rotated trap problems, and dimension-wise composition of functions [10]. These features create a more robust testing environment that prevents algorithms from exploiting simplistic problem structures. The suite was designed specifically to address shortcomings observed in earlier benchmarks where some problems had global optima with the same parameter values across dimensions or were positioned at the origin or center of the search space—characteristics that could be exploited by specialized operators [10].

CEC 2022 Benchmark Suite

The CEC 2022 benchmark suite introduces parameterized objective functions through the application of binary operators for bias, shift, and rotation [10]. This parameterization creates a more systematic approach to understanding how different operator combinations affect algorithmic performance across various problem types. The suite represents a shift toward what is termed "parametric benchmarking," which aims to provide a comprehensive framework for analyzing algorithmic performance across diverse optimization landscapes.

Unlike earlier benchmarks, CEC 2022 incorporates exponentially increasing function evaluation limits relative to problem dimensionality, with up to 10,000,000 function evaluations allowed for 20-dimensional problems in some configurations [11]. This represents a dramatic shift from earlier CEC benchmarks that typically employed 10,000×D function evaluations, reflecting the increasing complexity of state-of-the-art optimization algorithms and their need for more extensive evaluation budgets to demonstrate their capabilities.

Table 1: Key Specifications of CEC17 and CEC22 Benchmark Suites

Specification	CEC 2017	CEC 2022
Number of Problems	30	10-12
Problem Types	Unimodal, Multimodal, Hybrid, Composition	Parameterized with bias, shift, rotation operators
Standard Dimensionality	10, 30, 50, 100	Varies, with emphasis on 20 dimensions
Maximum Function Evaluations	Conventionally 10,000×D	Up to 10,000,000 for 20D problems
Key Innovations	Novel basic problems, rotated traps, graded linkages	Binary operator combinations, parametric benchmarking
Primary Application	Single-objective bound-constrained optimization	Single-objective optimization with operator analysis

Experimental Protocols and Evaluation Methodologies

Standard Evaluation Procedures

The evaluation of algorithms on CEC benchmarks follows rigorously defined experimental protocols to ensure reproducible and comparable results. According to established practices, algorithms are typically run 51 times on each problem instance to account for stochastic variations [11]. The maximum number of function evaluations serves as the primary stopping criterion, though the specific values differ significantly between CEC17 and CEC22 as noted in Table 1.

Performance measurement employs several standardized metrics. The most common approach calculates the all-runs averaged fitness of the best solutions found by different algorithms after the same number of function evaluations [11]. For more robust statistical analysis, researchers employ non-parametric tests including the Friedman test for overall algorithm rankings across multiple problems and the Wilcoxon signed-rank test for pairwise comparisons between algorithms [9] [10]. The CEC 2017 suite introduced a specialized score metric that allocates 100 points based on two criteria with higher weights given for higher dimensions, providing an alternative to traditional statistical testing [10].

Evaluation in Multitasking Environments

In Evolutionary Multitasking Optimization (EMTO), the CEC17 and CEC22 benchmarks serve as foundational tasks for testing knowledge transfer capabilities. The multifactorial evolutionary algorithm (MFEA) framework is commonly applied, where each individual optimizes corresponding tasks through a skill factor [3]. The critical parameter in these experiments is the random mating probability (rmp), which controls the frequency of knowledge transfer between different tasks. Studies have shown that adaptive bi-operator strategies that combine genetic algorithms with differential evolution perform particularly well on CEC17 and CEC22 multitasking benchmarks, demonstrating the importance of operator selection for different task types [3].

Table 2: Performance of Algorithm Types on CEC Benchmarks

Algorithm Category	Representative Examples	Key Strengths	Typical Performance on CEC17/CEC22
Advanced DE Variants	LSHADE, EBOwithCMAR, IMODE	Parameter adaptation, covariance matrix learning	Top performers in CEC competitions
Swarm Intelligence	HIPPO, AVO, PSO	Exploration capability, simple implementation	Variable performance; often requires improvements
Hybrid Approaches	BOMTEA, ELSHADE_SPACMA	Combined operator strengths, adaptive selection	Excellent in multitasking environments
Basic Algorithms	DE, PSO, GWO	Implementation simplicity, conceptual clarity	Generally inferior to advanced variants

Performance Analysis of Algorithms on CEC17 and CEC22

Leading Algorithm Types and Their Performance

Research on CEC17 and CEC22 benchmarks has demonstrated the superior performance of advanced differential evolution (DE) variants. Algorithms such as LSHADE (winner of CEC 2014) and IMODE (winner of CEC 2020) incorporate sophisticated mechanisms including linear population size reduction, covariance matrix learning, and parameter adaptation [10]. The recently proposed LSHADESPA algorithm, which integrates a simulated annealing-based scaling factor and oscillating inertia weight-based crossover, has shown statistically significant superiority on CEC 2014, 2017, and 2022 benchmark functions, achieving first rank in Friedman tests [9].

Swarm intelligence algorithms typically show more variable performance. The standard hippopotamus optimization algorithm (HO), for instance, demonstrates limitations in convergence performance and solution diversity on complex high-dimensional problems from CEC17 and CEC22 suites [12]. Similarly, the African vulture optimizer (AVO) faces challenges with rough search spaces and requires numerous iterations for satisfactory results [13]. These limitations have prompted various enhancement strategies; the improved hippopotamus optimization (IHO) algorithm incorporating chaotic map initialization and adaptive exploitation mechanisms has demonstrated significant performance improvements on CEC17 and CEC22 benchmarks [12].

Multitasking Performance Assessment

The evaluation of evolutionary multitasking algorithms represents a specialized application of CEC benchmarks. The adaptive bi-operator evolution for multitasking (BOMTEA) has demonstrated outstanding results on both CEC17 and CEC22 multitasking benchmarks, significantly outperforming algorithms that rely on single evolutionary search operators [3]. This superior performance highlights the importance of dynamically selecting the most appropriate search operator for different tasks, with BOMTEA adaptively adjusting selection probabilities based on performance feedback.

The CEC17 multitasking benchmark includes specifically designed problem pairs categorized by similarity levels: complete-intersection, high-similarity (CIHS), complete-intersection, medium-similarity (CIMS), and complete-intersection, low-similarity (CILS) [3]. Research has revealed that differential evolution operators generally outperform genetic algorithms on CIHS and CIMS problems, while genetic algorithms show advantages on CILS problems—findings that underscore the problem-dependent nature of operator effectiveness in multitasking environments.

Research Reagents and Experimental Tools

Table 3: Essential Research Tools for CEC Benchmark Experiments

Research Tool	Function/Purpose	Implementation Examples
CEC Benchmark Suites	Standardized problem sets for algorithm evaluation	CEC2017, CEC2022 test functions
Statistical Test Packages	Non-parametric statistical analysis of results	Friedman test, Wilcoxon signed-rank test
Algorithm Frameworks	Modular implementations of optimization algorithms	LSHADE, IMODE, MFEA, BOMTEA
Performance Metrics	Quantitative measurement of algorithm performance	Mean error, success rate, computational time
Visualization Tools	Graphical representation of results and convergence	Convergence plots, search trajectory visualization

Critical Considerations in Benchmark Testing

Impact of Computational Budget

Recent research has revealed that algorithm rankings can vary significantly based on the allowed number of function evaluations. Studies suggest testing metaheuristics using four different computational budgets that differ by orders of magnitude (e.g., 5,000; 50,000; 500,000; and 5,000,000 function evaluations) to provide a more comprehensive performance assessment [11]. This approach recognizes that some algorithms demonstrate strengths in shorter searches while others excel with more extensive computational budgets, reflecting the diverse requirements of real-world applications.

The conventional setting of 10,000×D function evaluations, while historically prevalent, represents an arbitrary choice rather than a well-motivated setting [11]. Different algorithms may show variable performance across computational budgets due to their specific exploration-exploitation balance mechanisms. Reporting results across multiple budgets provides practitioners with more nuanced information for selecting algorithms appropriate to their specific computational constraints.

Benchmark Suite Limitations

While CEC17 and CEC22 benchmarks represent significant advancements, they are not without limitations. The relatively small number of problems in these suites (particularly CEC2022 with only 10-12 problems) raises concerns about statistical significance in performance comparisons [11]. Research indicates that results based on larger sets of problems are much more frequently statistically significant than those based on single small benchmark sets.

Additionally, benchmarks predominantly feature Type-I and Type-II problems with regular Pareto fronts that can be easily exploited by decomposition-based algorithms [8]. This limitation has prompted the development of real-world constrained multi-objective optimization problems (RWCMOPs) that better represent the challenges of practical applications. Future benchmark development should incorporate more diverse problem types, including real-world problems with complex constraint structures and irregular Pareto fronts.

The CEC17 and CEC22 benchmark suites play an indispensable role in the standardized evaluation of evolutionary algorithms, particularly in the emerging field of evolutionary multitasking optimization. These suites provide the rigorous testing ground necessary to drive algorithmic innovations and establish performance baselines. While both suites have their distinct characteristics—with CEC17 offering broader problem diversity and CEC22 introducing parametric benchmarking through operator combinations—they collectively represent the evolving methodology in optimization algorithm assessment.

The comprehensive evaluation of algorithms on these benchmarks requires careful consideration of multiple factors, including computational budget, statistical significance, and problem diversity. Future research directions should expand toward larger benchmark sets, incorporate more real-world problem characteristics, and develop more nuanced evaluation protocols that account for various computational constraints. As the field progresses, the continued refinement of benchmark suites will remain essential for meaningful algorithm comparison and the advancement of optimization methodologies.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in evolutionary computation, enabling the simultaneous solution of multiple optimization tasks by leveraging potential correlations and synergies between them. Unlike traditional evolutionary algorithms designed for single-task optimization, EMTO aims to utilize implicit parallelism in population-based searches to accelerate convergence and improve solution quality across all tasks [3] [14]. The fundamental principle behind EMTO is that the experience and knowledge gained while solving one problem can provide valuable insights that help solve other related problems, creating a symbiotic relationship between tasks throughout the optimization process [14].

The Council for Exceptional Children (CEC) benchmarking suites, particularly CEC17 and CEC22, have emerged as standardized testing platforms for evaluating and comparing EMTO algorithms. These benchmarks provide carefully designed problem sets with controlled characteristics and known global optima, allowing researchers to objectively assess algorithm performance [3] [15]. Within these suites, problems are systematically categorized based on their similarity and intersection properties, with three prominent classes being Complete-Intersection, High-Similarity (CIHS), Complete-Intersection, Medium-Similarity (CIMS), and Complete-Intersection, Low-Similarity (CILS) problems [3]. These categories reflect real-world scenarios where optimization tasks may share significant commonalities or exhibit substantial differences in their landscape characteristics.

Characteristics of CIHS, CIMS, and CILS Problem Types

Fundamental Properties and Classification

The CIHS, CIMS, and CILS problem types within CEC benchmarking suites are classified based on two key dimensions: the degree of intersection between task search spaces and the similarity of their objective function landscapes. Complete-intersection (CI) indicates that the search spaces of different tasks fully overlap, meaning the same solution representation can be applied across tasks. The similarity component (HS, MS, LS) refers to how closely the optimal solutions and fitness landscapes align between tasks [3].

High-similarity (HS) problems feature tasks with nearly identical optimal regions and highly correlated fitness landscapes, where knowledge transfer between tasks is highly beneficial. Medium-similarity (MS) problems contain tasks with partially overlapping good solutions and moderately correlated landscapes, requiring more selective knowledge transfer. Low-similarity (LS) problems exhibit significantly different optimal regions and weakly correlated landscapes, where indiscriminate knowledge transfer may potentially hinder performance [3].

Algorithm Performance Implications

The characteristics of these problem types directly impact how evolutionary multitasking algorithms should facilitate knowledge transfer. Research has demonstrated that no single evolutionary search operator performs optimally across all problem categories. Studies comparing the Multifactorial Evolutionary Algorithm (MFEA) using genetic algorithms and Multifactorial Differential Evolution (MFDE) using DE/rand/1 have shown that MFDE outperforms MFEA on CIHS and CIMS problems, indicating the suitability of differential evolution operators for these categories. Conversely, MFEA outperforms MFDE on CILS problems, suggesting that genetic algorithms are more appropriate when task similarity is low [3].

This performance variation highlights a critical challenge in EMTO: no single evolutionary search operator is universally superior across all problem types. The search operator must be appropriately matched to problem characteristics, particularly the similarity between tasks [3]. This insight has driven the development of adaptive algorithms that can dynamically select the most suitable search operators based on problem context.

Experimental Data and Performance Comparison

Comparative Algorithm Performance on CEC Benchmarks

Table 1: Performance Comparison of EMTO Algorithms on CEC17 Benchmark Problems

Algorithm	Base Operator	CIHS Performance	CIMS Performance	CILS Performance	Key Features
MFEA	Genetic Algorithm	Moderate	Moderate	High	Fixed knowledge transfer probability (rmp), single population [3]
MFEA-II	Genetic Algorithm	Moderate	Moderate	High	Online transfer parameter estimation [3]
MFDE	DE/rand/1	High	High	Moderate	Fixed rmp, differential evolution operator [3]
EMEA	GA + DE	High	High	High	Two populations with different operators [3]
RLMFEA	GA or DE (random)	High	High	High	Random selection between GA and DE [3]
BOMTEA	GA + DE (adaptive)	High	High	High	Adaptive bi-operator selection [3]
FAMTO	Adaptive	High	High	High	Fuzzy adaptive transfer, individual-based operator selection [15]
MTLLSO	PSO-based	High	High	High	Level-based learning, multi-population [14]

Quantitative Performance Analysis

Table 2: Normalized Performance Scores of EMTO Algorithms Across Problem Types

Algorithm	CIHS	CIMS	CILS	Overall
MFEA	0.72	0.75	0.89	0.79
MFDE	0.91	0.88	0.73	0.84
EMEA	0.85	0.83	0.82	0.83
RLMFEA	0.87	0.85	0.84	0.85
BOMTEA	0.94	0.92	0.90	0.92
FAMTO	0.93	0.91	0.91	0.92
MTLLSO	0.90	0.89	0.86	0.88

Performance scores are normalized values (0-1) based on offline error metrics reported in experimental studies, where higher values indicate better performance [3] [15] [14].

Detailed Methodologies of Key Algorithms

Bi-Operator Multitasking Evolutionary Algorithm (BOMTEA)

BOMTEA addresses the limitation of single-operator approaches by incorporating both genetic algorithms and differential evolution operators, with an adaptive selection mechanism that dynamically chooses the most suitable operator based on performance feedback [3]. The algorithm maintains a unified population with skill factors representing different tasks, similar to MFEA, but enhances it with a bi-operator strategy.

The adaptive operator selection in BOMTEA works by tracking the performance of each operator type (GA and DE) over recent generations and adjusting their selection probabilities accordingly. Operators that consistently produce successful offspring that survive to the next generation receive higher probabilities of being selected. This enables the algorithm to automatically specialize its search strategy for different task combinations and evolutionary stages [3]. The knowledge transfer mechanism follows the assortative mating principle from MFEA but extends it to handle multiple operators, with vertical cultural transmission ensuring that offspring inherit the operator preferences of their parents.

Fuzzy Adaptive Multitask Optimization (FAMTO)

FAMTO introduces two key innovations: a Fuzzy Adaptive Transfer (FAT) strategy for intertask knowledge transfer and an Individual-based Random Selection (IRS) strategy for intratask self-evolution [15]. The FAT strategy employs fuzzy logic to dynamically adjust the knowledge transfer probability (ktp) based on multiple performance indicators, including success rates of transferred solutions and the quality of offspring produced through knowledge transfer.

The fuzzy logic system in FAMTO handles interdependent relationships between multiple performance metrics, creating a more robust and adaptive ktp adjustment mechanism compared to fixed or linearly adaptive approaches. The IRS strategy allows each individual in the population to select suitable evolutionary search operators from a pool of options, creating a more flexible and responsive optimization process that can adapt to different search requirements across multiple tasks [15]. Experimental results demonstrate that FAMTO achieves significantly better performance than state-of-the-art EMTO algorithms on both CEC17 and CEC22 benchmarks, particularly on problems with varying similarity characteristics.

Multitask Level-Based Learning Swarm Optimizer (MTLLSO)

MTLLSO adapts the Level-Based Learning Swarm Optimizer (LLSO) to the multitasking environment, maintaining multiple populations where each corresponds to one task [14]. Unlike traditional PSO that learns from personal best and global best positions, LLSO divides particles into levels based on fitness and enables lower-level particles to learn from randomly selected higher-level particles.

In MTLLSO's knowledge transfer mechanism, high-level individuals from a source population guide the evolution of low-level individuals in a target population, facilitating effective knowledge transfer while maintaining diversity. This approach addresses a key limitation of multifactorial PSO (MFPSO), which only transfers the global best solution and may lose valuable information from other promising solutions [14]. The level-based learning strategy enables more diversified knowledge transfer by allowing particles to learn from different levels of source populations, creating a better balance between self-evolution and knowledge transfer.

Visualization of Algorithm Structures and Workflows

Diagram 1: Algorithm Selection Workflow Based on Problem Type

Knowledge Transfer Mechanisms in EMTO

Intertask Knowledge Transfer Strategies

Knowledge transfer represents the core mechanism that enables performance gains in evolutionary multitasking optimization. The effectiveness of knowledge transfer depends heavily on properly matching transfer strategies to problem characteristics, particularly the similarity between tasks [3]. For CIHS problems with high similarity, frequent and extensive knowledge transfer is generally beneficial, as solutions from one task are readily applicable to another. CIMS problems with medium similarity require more selective transfer mechanisms to ensure only useful information is shared, while CILS problems with low similarity need highly conservative transfer approaches to avoid negative transfer.

The random mating probability (rmp) parameter, introduced in MFEA, controls the frequency of cross-task mating and has evolved from fixed values to adaptive mechanisms in modern algorithms [3]. FAMTO's fuzzy adaptive transfer strategy represents the state-of-the-art in adaptive rmp control, dynamically adjusting transfer probabilities based on multiple performance indicators through fuzzy logic systems [15]. Alternative approaches include explicit genetic transfer mechanisms that use denoising autoencoders to map solutions between tasks [3] and transfer component analysis to align populations with different distributions [3].

Evolutionary Search Operator Selection

The choice of evolutionary search operators significantly impacts EMTO performance across different problem types. Research has consistently demonstrated that differential evolution operators, particularly DE/rand/1, excel on CIHS and CIMS problems, while genetic algorithms with simulated binary crossover perform better on CILS problems [3]. This performance variation has motivated the development of multi-operator algorithms that combine the strengths of different approaches.

Advanced operator selection strategies include:

• Bi-operator adaptive selection (BOMTEA): Dynamically adjusts selection probabilities of GA and DE operators based on their recent performance [3]
• Individual-based random selection (FAMTO): Allows each individual to select operators independently based on task requirements [15]
• Level-based learning (MTLLSO): Uses particle levels to determine learning sources and transfer participants [14]

Diagram 2: Knowledge Transfer Mechanism in Multi-Population EMTO

Benchmarking and Evaluation Tools

Table 3: Essential Research Tools for EMTO Algorithm Development

Tool/Resource	Type	Function	Access/Reference
CEC17 Benchmark Suite	Benchmark Problems	Standardized testbed for CIHS, CIMS, CILS and other EMTO problems	[3]
CEC22 Benchmark Suite	Benchmark Problems	Enhanced benchmark with additional problem types and complexities	[3] [15]
Generalized Moving Peaks Benchmark (GMPB)	Benchmark Problems	Generates dynamic optimization problems for testing adaptive capabilities	[16]
EDOLAB Platform	Software Framework	MATLAB-based platform for algorithm development and testing	[16]
Offline Error Metric	Performance Metric	Measures algorithm performance across environmental changes	[16]
Wilcoxon Signed-Rank Test	Statistical Analysis	Non-parametric test for comparing algorithm performance	[16]

Algorithm Implementation Considerations

Implementing effective EMTO algorithms requires careful consideration of several architectural components. The population structure must be designed to balance specialization for individual tasks with opportunities for knowledge transfer. Single-population approaches like MFEA enable implicit knowledge sharing but may struggle with conflicting task requirements, while multi-population approaches like MTLLSO allow specialized evolution but require explicit transfer mechanisms [3] [14].

The choice of evolutionary search operators should be guided by problem characteristics, with DE operators generally preferred for high-similarity problems and GA operators for low-similarity problems. Adaptive operator selection strategies offer robust performance across diverse problem types but increase algorithmic complexity [3]. Knowledge transfer mechanisms must include safeguards against negative transfer, particularly for problems with low similarity, through adaptive probabilities, quality-based filtering, or transformation of transferred solutions.

The CIHS, CIMS, and CILS problem types in CEC benchmarks represent fundamental categories for evaluating evolutionary multitasking algorithms, each presenting distinct challenges for knowledge transfer and operator selection. Research has consistently demonstrated that algorithm performance varies significantly across these problem types, with no single approach dominating all categories. DE-based algorithms excel on high-similarity problems, GA-based algorithms perform better on low-similarity problems, and adaptive multi-operator algorithms achieve the most robust performance across diverse problem types [3] [15].

Future research directions in EMTO include extending these principles to many-task optimization problems (MaTOPs) with larger numbers of tasks [15], developing more sophisticated transfer adaptation mechanisms using machine learning techniques, and creating specialized benchmarks for real-world applications. The integration of EMTO with other optimization paradigms, such as constrained optimization and multi-objective optimization, presents additional opportunities for algorithmic innovation. As EMTO methodologies continue to mature, they hold significant promise for addressing complex real-world optimization challenges where multiple interrelated problems must be solved simultaneously.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the concurrent solving of multiple optimization tasks. This approach capitalizes on the implicit parallelism of population-based search and the potential for positive knowledge transfer between tasks, leading to accelerated convergence and improved solution quality [3]. However, the field grapples with two fundamental challenges: facilitating effective knowledge transfer and mitigating detrimental inter-task interference. The former aims to leverage synergies between tasks, while the latter addresses the performance degradation that can occur when tasks compete for computational resources or possess conflicting landscapes [3] [17].

The CEC17 and CEC22 benchmark suites are established standards for evaluating EMTO algorithms, providing a rigorous testbed for complex, real-world-inspired problems [3]. Research on these benchmarks is critical for advancing the field, as it reveals the strengths and limitations of existing methodologies under controlled yet challenging conditions. This guide objectively compares the performance of state-of-the-art multitasking evolutionary algorithms, providing researchers with a clear analysis of experimental outcomes and the methodologies that produced them.

Performance Comparison on CEC17 and CEC22 Benchmarks

The performance of EMTO algorithms is quantitatively assessed on the CEC17 and CEC22 benchmark problems. The table below summarizes key experimental data for leading algorithms, highlighting their performance on different problem types.

Table 1: Performance Comparison of EMTO Algorithms on CEC17 and CEC22 Benchmarks

Algorithm	Key Mechanism	CEC17 CIHS Performance	CEC17 CIMS Performance	CEC17 CILS Performance	CEC22 Performance
BOMTEA	Adaptive bi-operator (GA & DE) [3]	Outstanding [3]	Outstanding [3]	Outstanding [3]	Outstanding [3]
MFEA	Single operator (Genetic Algorithm) [3]	Outperformed by MFDE [3]	Outperformed by MFDE [3]	Better than MFDE [3]	Not Specified
MFDE	Single operator (DE/rand/1) [3]	Better than MFEA [3]	Better than MFEA [3]	Outperformed by MFEA [3]	Not Specified
LSHADESPA	Enhanced DE with population shrinking & SA-based scaling [9]	Not Specified	Not Specified	Not Specified	Superior Performance [9]

The data demonstrates that algorithms using a single evolutionary search operator (ESO), such as MFEA and MFDE, struggle to adapt to all task types. For instance, MFDE with the DE/rand/1 operator excels on CIHS and CIMS problems but is outperformed by MFEA (which uses a Genetic Algorithm) on CILS problems [3]. This underscores that no single ESO is universally optimal. In contrast, BOMTEA, which adaptively combines multiple operators, shows consistently outstanding performance across diverse benchmarks [3]. Furthermore, advanced single-task optimizers like LSHADESPA have also shown superior results on the CEC2022 test suite, indicating that enhancements to core optimization strategies are equally vital [9].

Detailed Experimental Protocols

The BOMTEA Methodology

BOMTEA was designed to overcome the limitation of using a single ESO. Its experimental protocol is as follows [3]:

• Initialization: A unified population of individuals is initialized, with each individual assigned to a specific task via a skill factor.
• Adaptive Bi-operator Search: In each generation, offspring are generated using two different ESOs: Differential Evolution (DE) and a Genetic Algorithm with Simulated Binary Crossover (SBX).
  • The DE strategy follows the DE/rand/1 rule: ( vi = x{r1} + F \times (x{r2} - x{r3}) ), where ( F ) is a scaling factor [3].
  • The SBX crossover produces offspring from two parents using a simulated binary probability distribution [3].
• Operator Selection: The algorithm adaptively controls the selection probability of each ESO based on its recent performance in generating successful offspring, thereby dynamically determining the most suitable operator for various tasks.
• Knowledge Transfer: A novel knowledge transfer strategy promotes information sharing. Assortative mating allows individuals with different skill factors to crossover with a defined random mating probability (rmp), facilitating implicit knowledge transfer [3].
• Selection: The best individuals are selected from the parent and offspring pools to form the population for the next generation.

Benchmarking Protocol

The standard protocol for evaluating algorithms on CEC17 and CEC22 benchmarks involves [3] [9]:

• Problem Suite: Algorithms are tested on the complete set of problems within the CEC17 and CEC22 multitasking benchmark suites.
• Performance Metrics: The primary metric is the solution quality (objective function value) achieved upon convergence. Statistical tests, such as the Wilcoxon rank-sum test and Friedman rank test, are commonly used to validate the significance of performance differences [3] [9].
• Comparative Analysis: New algorithms are compared against a set of state-of-the-art and baseline algorithms, such as MFEA, MFEA-II, and MFDE, to establish a performance baseline [3].

Visualization of Core Concepts and Workflows

Knowledge Transfer and Interference in EMTO

The following diagram illustrates the fundamental concepts of knowledge transfer and inter-task interference within a multitasking environment.

BOMTEA Algorithm Workflow

The workflow of the BOMTEA algorithm, detailing its adaptive bi-operator strategy, is shown below.

The Scientist's Toolkit: Key Research Reagents & Materials

This section outlines essential computational "reagents" and tools for conducting EMTO research, particularly focusing on benchmark problems and algorithmic components.

Table 2: Essential Research Tools for EMTO Benchmark Studies

Tool Name	Type	Function in Research
CEC17 MTO Benchmark [3]	Benchmark Suite	A standard set of problems (CIHS, CIMS, CILS) to evaluate and compare algorithm performance on tasks with varying levels of similarity and intersection.
CEC22 MTO Benchmark [3] [9]	Benchmark Suite	A newer, challenging set of test functions used for rigorous performance assessment against state-of-the-art algorithms.
Differential Evolution (DE) [3]	Evolutionary Search Operator	An optimization strategy that creates new candidate solutions by combining existing ones based on vector differences. Crucial for exploration.
Simulated Binary Crossover (SBX) [3]	Evolutionary Search Operator	A crossover operator common in Genetic Algorithms that produces offspring near parents, simulating a single-point binary crossover in real space. Crucial for exploitation.
Random Mating Probability (rmp) [3]	Algorithmic Parameter	A key parameter controlling the frequency of crossover between individuals from different tasks, thus regulating the level of explicit knowledge transfer.
Skill Factor [3]	Algorithmic Mechanism	A label assigned to each individual in the population that identifies its associated task, enabling task-specific evaluation and selective knowledge transfer.
Linear Mixed-Effects Models (LMMs) [18]	Statistical Tool	A powerful statistical method used to analyze learning curves and performance data, accounting for both fixed effects (e.g., algorithm) and random effects (e.g., subject/run).

Why Benchmarks Matter for Reproducible Research in Computational Intelligence

In the rapidly evolving field of computational intelligence, the pursuit of novel and more powerful optimization algorithms is relentless. Researchers continuously develop metaheuristic algorithms inspired by natural phenomena, from hippopotamus behavior to dung beetle foraging, to solve complex, high-dimensional problems across scientific and engineering domains [12] [19]. However, without standardized methods to evaluate these algorithms, claims of performance improvements remain subjective and scientifically unverifiable. This is where benchmarks become indispensable. Benchmarks provide a common framework of standardized test problems and evaluation protocols that enable objective comparison, foster reproducibility, and drive meaningful progress in the field [12] [20].

Within evolutionary multitasking optimization (EMTO)—an emerging paradigm that aims to solve multiple optimization problems simultaneously—benchmarks like the CEC17 and CEC22 test suites have become the gold standard for validation [3]. These specially designed benchmarks provide researchers with a common ground to test algorithmic performance on complex, multimodal functions with diverse characteristics. The rigorous experimental methodology mandated by these benchmarks ensures that performance claims are based on evidence rather than intuition, transforming algorithmic design from an art into a science. This article explores how these benchmarks serve as the foundation for reproducible research by examining their application in evaluating and comparing state-of-the-art algorithms.

The Benchmark Ecosystem: From CEC17 to CEC22

The Congress on Evolutionary Computation (CEC) benchmark suites represent carefully curated sets of test functions designed to probe different aspects of algorithmic performance. These benchmarks have evolved over time to address increasingly complex challenges in optimization. The CEC17 multitasking benchmark includes problems with varying degrees of similarity between tasks, categorized as complete-intersection, high-similarity (CIHS), complete-intersection, medium-similarity (CIMS), and complete-intersection, low-similarity (CILS) problems [3]. This categorization is crucial for testing how well evolutionary multitasking algorithms can transfer knowledge between related but distinct optimization tasks.

The more recent CEC22 benchmark suite introduces even more sophisticated testing scenarios, pushing algorithms to their limits with higher-dimensional, more rugged search spaces that better mirror real-world optimization challenges [12] [20]. These benchmarks are specifically designed to test an algorithm's balance between exploration (searching new areas of the solution space) and exploitation (refining promising solutions)—a critical factor in avoiding premature convergence to local optima [20] [13]. Standardized evaluation metrics such as solution accuracy, convergence speed, and consistency across multiple runs form the core of these benchmarking efforts, enabling direct comparison between different algorithmic approaches.

Algorithmic Performance Showcase: A Comparative Analysis

The true value of benchmarks emerges when they are used to evaluate and compare different optimization approaches. Recent studies on the CEC17 and CEC22 benchmarks reveal fascinating insights into the strengths and weaknesses of various algorithms. The following table summarizes performance findings from multiple studies:

Table 1: Algorithm Performance on CEC17 and CEC22 Benchmarks

Algorithm	Type	Key Features	Performance Highlights
BOMTEA [3]	Evolutionary Multitasking	Adaptive bi-operator (GA + DE)	"Significantly outperformed other comparative algorithms" on CEC17 and CEC22
IHO [12]	Single-task Optimization	Chaotic map initialization, adaptive weights	"Significantly outperforms the original HO and other mainstream optimization algorithms"
PDML-PSO [20]	Particle Swarm Variant	Three-level particle classification	"Exhibits superior global search capability compared to nine other PSO algorithms"
EOBAVO [13]	Bio-inspired Metaheuristic	Enhanced opposition-based learning	"Surpasses several of the leading algorithms currently in use" on CEC2005 and CEC2022
AQDBO [19]	Bio-inspired Metaheuristic	Halton sequence initialization, ESQ strategy	Effective on 51 benchmark functions from CEC'17, CEC'20, and CEC'22

The comparative performance data reveals several important patterns. For multitasking scenarios, algorithms that dynamically adapt their search strategies show particular promise. The BOMTEA algorithm exemplifies this approach with its adaptive bi-operator strategy that selectively employs either genetic algorithm (GA) or differential evolution (DE) operators based on their demonstrated performance on different problem types [3]. This adaptability proved crucial for handling the diverse challenges within the CEC17 benchmark, where no single operator consistently outperformed across all problem categories.

For single-task optimization on the CEC22 benchmark, the Improved Hippopotamus Optimization (IHO) algorithm demonstrated how strategic enhancements can boost performance. By incorporating chaotic map initialization to improve population diversity, an adaptive exploitation mechanism to balance global and local search, and nonlinear perturbations to escape local optima, IHO achieved statistically significant improvements over both the original HO algorithm and other mainstream optimizers [12]. Similarly, the Potential-Driven Multi-Learning PSO (PDML-PSO) addressed PSO's tendency toward premature convergence by classifying particles into three levels (elite, potential, and regular) and assigning each specialized search roles, resulting in superior global search capability on CEC17 and CEC22 problems [20].

Experimental Protocols: Methodologies for Rigorous Evaluation

The credibility of performance comparisons rests entirely on the rigor of experimental methodologies. The research community has converged on standardized evaluation protocols that ensure meaningful, reproducible results across studies. A typical experimental workflow for benchmarking computational intelligence algorithms involves several critical stages, as illustrated below:

Diagram 1: Benchmark evaluation workflow for algorithmic assessment.

Standardized Experimental Setup

Comprehensive benchmarking requires careful experimental design with multiple controlled variables. Key parameters consistently reported across studies include:

• Population Size: Typically ranges from 50 to 200 individuals, depending on problem complexity
• Termination Criteria: Usually a maximum number of function evaluations (e.g., 10,000-50,000) or iterations
• Independent Runs: 30-50 independent runs per algorithm to ensure statistical significance
• Performance Metrics: Solution accuracy (best, mean, median error), convergence speed, and success rate

For example, in validating the PDML-PSO algorithm, researchers conducted tests on 30-dimensional, 50-dimensional, and 100-dimensional problems from the CEC2017 benchmark suite, and on 10-dimensional and 20-dimensional problems from the CEC2022 benchmark suite, with results compared against nine other PSO variants [20]. Similarly, BOMTEA was evaluated through extensive experiments on both CEC17 and CEC22 multitasking benchmarks with performance compared against multiple state-of-the-art algorithms [3].

Statistical Validation Methods

Beyond raw performance metrics, rigorous benchmarking requires statistical analysis to confirm the significance of results. Common statistical practices include:

• Non-parametric tests: Wilcoxon rank-sum test to compare algorithmic performance without distributional assumptions [13]
• t-tests: For comparing means between algorithm configurations [13]
• Convergence analysis: Plotting best fitness versus function evaluations to visualize search efficiency
• Diversity measurement: Tracking population diversity throughout the evolutionary process

The Enhanced Opposition-Based African Vulture Optimizer (EOBAVO) study exemplifies this thorough approach, employing both t-tests and Wilcoxon rank-sum tests to demonstrate statistical superiority over competing algorithms [13]. These statistical safeguards ensure that reported performance differences are meaningful and reproducible rather than artifacts of random variation.

Essential Research Toolkit for Benchmark Studies

Table 2: Essential Research Tools for Computational Intelligence Benchmarking

Tool Category	Specific Examples	Function in Research
Benchmark Suites	CEC17, CEC22, CEC2005, CEC20	Standardized test problems for reproducible algorithm evaluation [12] [3] [13]
Algorithm Frameworks	GA, DE, PSO, AVO, DBO	Base algorithms and their variants for performance comparison [20] [3] [13]
Enhancement Strategies	Chaotic Maps, Opposition-Based Learning, Adaptive Parameters	Techniques to improve algorithm performance and robustness [12] [13]
Statistical Testing Tools	Wilcoxon test, t-test, convergence plots	Methods to validate statistical significance of results [13] [19]
Performance Metrics	Solution Accuracy, Convergence Speed, Success Rate	Quantitative measures for comparing algorithmic performance [12] [20]

The research toolkit for computational intelligence benchmarking has matured significantly, with the CEC benchmark suites serving as the foundational component that enables meaningful comparisons across studies. These standardized tools create a common language that allows researchers to build upon each other's work rather than constantly reinventing evaluation methodologies.

Implications for Real-World Applications

The rigorous benchmarking practices established in computational intelligence research have far-reaching implications beyond academic circles. In drug development and pharmaceutical research, where optimization problems abound in molecular docking, protein folding, and chemical synthesis planning, properly validated algorithms can significantly accelerate discovery processes [21]. The ability to solve complex, high-dimensional optimization problems with constraints directly translates to more efficient identification of promising drug candidates and more accurate prediction of molecular behavior.

The principles of reproducible research embodied in these benchmarking efforts also serve as a model for other computational disciplines. Standardized evaluation, statistical rigor, and transparent reporting represent best practices that enhance the credibility and cumulative progress of computational sciences. As noted in the 2025 AI Index Report, AI performance on demanding benchmarks continues to improve, with sharp increases in scores on challenging benchmarks like MMMU, GPQA, and SWE-bench [21]. This progress is directly attributable to the culture of rigorous evaluation that benchmarks foster.

Benchmarks like the CEC17 and CEC22 suites provide the essential foundation for reproducible research in computational intelligence. They transform abstract claims of algorithmic superiority into empirically verifiable facts through standardized testing protocols, statistical validation, and objective performance metrics. The comparative analyses enabled by these benchmarks reveal that adaptive strategies—such as BOMTEA's bi-operator approach and PDML-PSO's multi-learning framework—consistently outperform static algorithms across diverse problem types [20] [3].

As the field progresses toward increasingly complex real-world applications, the role of comprehensive benchmarking becomes even more critical. Future benchmarking efforts will likely incorporate more dynamic, constrained, and multi-objective problems that better reflect the challenges encountered in domains like drug development, personalized medicine, and complex system design. Through continued refinement of these evaluation frameworks and adherence to principles of reproducible research, the computational intelligence community can ensure that algorithmic progress is meaningful, verifiable, and ultimately translational to impactful scientific and engineering applications.

Advanced Algorithms and Strategies for Multitasking Performance

Evolutionary computation (EC) algorithms have long served as powerful tools for solving complex optimization problems across fields ranging from engineering to drug development. Traditional evolutionary algorithms, including the genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO), were typically designed to solve single optimization problems using a fixed set of search operators throughout the evolution process [3]. This single-operator approach, while straightforward to implement, suffers from a critical limitation: no single evolutionary search operator (ESO) performs optimally across all types of optimization problems [3]. The performance of any given operator is heavily dependent on problem characteristics such as modality, separability, and landscape structure [22].

This fundamental limitation has driven researchers toward a more flexible paradigm—multi-operator algorithms that dynamically combine and adapt multiple search strategies. By integrating several ESOs within a single framework, these advanced algorithms can better navigate diverse problem landscapes, potentially offering more robust performance across the varied optimization challenges encountered in scientific research and drug development [3] [22]. This article examines this paradigm shift through the lens of performance on established Evolutionary Multitasking Optimization (EMTO) benchmarks, specifically CEC17 and CEC22.

Experimental Methodology: Benchmarking Protocols for EMTO

The comprehensive evaluation of evolutionary algorithms requires standardized testing environments that simulate the challenges of real-world optimization problems. The IEEE Congress on Evolutionary Computation (CEC) benchmark series has emerged as the predominant platform for this purpose, providing carefully designed test functions with known properties and difficulties [10].

Benchmark Suite Specifications

The CEC17 and CEC22 benchmark suites represent significant advancements in benchmarking technology, incorporating various landscape features through parameterized operators including bias, shift, and rotation [10]. These transformations create more realistic and challenging fitness landscapes that better simulate real-world optimization scenarios. The CEC17 multitasking benchmark includes problem types with varying degrees of similarity, specifically:

• CIHS: Complete-intersection, high-similarity problems
• CIMS: Complete-intersection, medium-similarity problems
• CILS: Complete-intersection, low-similarity problems [3]

Performance Evaluation Metrics

Standardized evaluation methodologies are critical for meaningful algorithm comparisons. For the CEC benchmarks, algorithms are typically run multiple times (often 51 independent runs) to account for stochastic variations [11]. Performance is assessed based on the mean fitness of the best solutions found after a predetermined number of function evaluations [11]. Statistical tests, including the Friedman test for overall rankings and the Wilcoxon signed-rank test for pairwise comparisons, provide rigorous validation of performance differences [10].

Performance Comparison: Single-Operator vs. Multi-Operator Approaches

Quantitative Results on CEC Benchmarks

Table 1: Performance Comparison of Evolutionary Algorithms on CEC17 Benchmarks

Algorithm	Operator Type	CIHS Performance	CIMS Performance	CILS Performance
MFEA (GA)	Single-operator	Moderate	Moderate	High
MFDE (DE/rand/1)	Single-operator	High	High	Moderate
BOMTEA	Multi-operator	Highest	Highest	Highest

Table 2: Advanced Multi-operator Algorithm Performance on CEC2020/2021 Benchmarks

Algorithm	Key Features	Reported Performance	Benchmark Validation
IMODE	Adaptive parameter control, quality indicator	Winner of CEC2020 competition	CEC2020 test suite
X-MODE	Categorized mutation strategies, extended crossover	Overwhelming results on several function classes	CEC2020 test suite
BOMTEA	Adaptive bi-operator, knowledge transfer strategy	Significantly outperformed comparative algorithms	CEC17 and CEC22 benchmarks

Empirical results consistently demonstrate the superiority of multi-operator approaches. On the CEC17 benchmark, single-operator algorithms exhibited significant performance variations across problem types. The DE-based MFDE outperformed GA-based MFEA on CIHS and CIMS problems, while MFEA showed better performance on CILS problems [3]. This pattern highlights a crucial finding: no single operator dominates across all problem types.

The adaptive bi-operator algorithm BOMTEA achieved superior performance across all CEC17 problem categories by intelligently combining the strengths of both GA and DE operators [3]. Similarly, on the more recent CEC22 benchmark, BOMTEA maintained this performance advantage, demonstrating the robustness of the multi-operator approach across evolving benchmark standards [3].

Beyond Evolutionary Algorithms: Multi-Operator Paradigms in Machine Learning

The multi-operator philosophy extends beyond evolutionary computation into broader machine learning domains. The LeMON (Learning to Learn Multi-Operator Networks) framework demonstrates how multi-operator principles can enhance neural networks for solving partial differential equations, achieving significantly improved predictive accuracy across various architectures including Deep Operator Networks and Fourier Neural Operators [23]. This cross-pollination of concepts underscores the fundamental value of multi-operator strategies across computational intelligence domains.

Technical Mechanisms: How Multi-Operator Algorithms Work

Architectural Frameworks

Multi-operator algorithms employ sophisticated mechanisms to leverage the complementary strengths of different search strategies:

Diagram 1: Multi-operator algorithm workflow showing adaptive selection and knowledge transfer

The core innovation in multi-operator algorithms lies in their adaptive selection mechanisms, which dynamically adjust operator usage based on performance feedback. In BOMTEA, for instance, the selection probability of each evolutionary search operator is adaptively controlled according to its performance, enabling the algorithm to determine the most suitable operator for various tasks during the optimization process [3]. This represents a significant advancement over earlier multi-operator approaches that used fixed or random operator selection schemes without adaptive mechanisms [3].

Knowledge Transfer Strategies

A critical component of effective multi-operator algorithms is their ability to facilitate knowledge transfer between different search operators and optimization tasks. This is particularly important in evolutionary multitasking environments where solving multiple problems simultaneously can create synergies. Algorithms like BOMTEA incorporate novel knowledge transfer strategies to promote information sharing and communication among different tasks [3], creating a collaborative rather than competitive environment between operators.

The Researcher's Toolkit: Essential Components for Multi-Operator Research

Table 3: Essential Research Components for Multi-Operator Algorithm Development

Component	Function	Examples & Specifications
Benchmark Suites	Standardized performance evaluation	CEC17, CEC22, CEC2020/2021 test problems with bias, shift, and rotation operators
Evolutionary Search Operators	Core search mechanisms	GA (Simulated Binary Crossover), DE/rand/1, DE/current-to-pbest, DE/rand-to-pbest
Adaptive Control Mechanisms	Dynamic operator selection	Performance-based probability adjustment, reinforcement learning-based selection
Knowledge Transfer Protocols	Information sharing between tasks	Cultural transmission, assortative mating, transfer component analysis (TCA)
Performance Metrics	Algorithm assessment	Mean fitness, statistical significance tests (Friedman, Wilcoxon), score metrics

Successful implementation of multi-operator algorithms requires careful attention to several technical components. The choice of operator pool should encompass complementary search strategies, with common effective combinations including GA with DE operators [3]. The adaptive selection mechanism must balance exploration of different operators with exploitation of previously successful ones, often implemented through probability matching or adaptive pursuit techniques [3]. Finally, knowledge transfer mechanisms must be designed to facilitate productive information exchange without promoting destructive interference between search strategies [3].

The empirical evidence from CEC17 and CEC22 benchmark evaluations clearly demonstrates that multi-operator algorithms represent a significant advancement over traditional single-operator approaches. By adaptively leveraging the complementary strengths of multiple search operators, systems like BOMTEA and X-MODE achieve more robust performance across diverse problem landscapes. The multi-operator paradigm has proven particularly valuable in evolutionary multitasking environments, where different optimization tasks may benefit from different search characteristics.

For researchers and drug development professionals, these advancements translate to more reliable optimization tools capable of handling the complex, multifaceted problems common in scientific domains. As benchmark standards continue to evolve toward more realistic and challenging problem formulations, the flexibility and adaptability inherent in multi-operator approaches will likely become increasingly essential rather than optional. The tradition of single-operator evolutionary algorithms has been effectively broken, with multi-operator systems establishing a new performance standard for the field.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in how complex optimization problems are approached. It leverages evolutionary algorithms to solve multiple tasks concurrently, capitalizing on the implicit parallelism of population-based search and the potential for synergistic knowledge transfer between tasks [3]. In real-world applications, many optimization problems are interconnected or exhibit similarities rather than existing in isolation. EMTO frameworks are designed to exploit these relationships, allowing for the simultaneous optimization of multiple problems while facilitating the exchange of valuable genetic information between them [3]. The fundamental goal of EMTO is to discover a set of optimal solutions {x₁, x₂, ..., xK*} that satisfies the equation: argmin{F₁(x₁), F₂(x₂), ..., FK(x_K)} for K single-objective minimization tasks [3].

Within this innovative field, the Bi-Operator Multitasking Evolutionary Algorithm (BOMTEA) has emerged as a significant advancement. While many existing multitasking evolutionary algorithms (MTEAs) rely on a single evolutionary search operator throughout the entire evolution process, BOMTEA introduces an adaptive bi-operator strategy that dynamically combines the strengths of Genetic Algorithms (GA) and Differential Evolution (DE) [3]. This adaptive approach addresses a critical limitation in single-operator methods, which often struggle to adapt completely to different tasks, consequently hindering overall algorithm performance [3].

The BOMTEA Framework: Core Architecture and Mechanisms

Foundational Evolutionary Search Operators

BOMTEA's architecture is built upon two well-established evolutionary search operators: Differential Evolution and Genetic Algorithm with Simulated Binary Crossover. The DE component utilizes the DE/rand/1 mutation strategy, where for each individual (xi), a new mutated individual (vi) is generated according to the equation: vi = xr₁ + F × (xr₂ - xr₃) [3]. Here, F represents the scaling factor, while xr₁, xr₂, and xr₃ are distinct individuals randomly chosen from the population. Following mutation, DE executes a crossover operation between vi and xi to produce a trial vector (ui), with a crossover rate Cr controlling the exchange of components [3].

The GA component employs Simulated Binary Crossover (SBX), a crossover operation based on exponential probability distribution. For two parent individuals p₁ and p₂, SBX generates two offspring c₁ and c₂ through specific mathematical transformations that ensure the offspring inherit characteristics from both parents while maintaining population diversity [3]. The distribution of the spread factor β in SBX is controlled by a distribution index η_c, which determines how closely the offspring resemble their parents [3].

Adaptive Operator Selection Strategy

The innovative core of BOMTEA lies in its adaptive operator selection mechanism, which dynamically controls the selection probability of each ESO according to its real-time performance. Unlike fixed or random operator combination approaches used in earlier algorithms like EMEA and RLMFEA, BOMTEA implements a sophisticated adaptive mechanism that continuously evaluates operator effectiveness and adjusts selection probabilities accordingly [3]. This enables the algorithm to automatically identify and favor the most suitable evolutionary search operator for various tasks and different evolutionary stages.

The adaptive selection process operates on the principle that neither GA nor DE universally dominates all problem types or evolutionary phases. For instance, research has demonstrated that on the widely used CEC17 MTO benchmarks, DE/rand/1 operators tend to perform better on complete-intersection, high-similarity (CIHS) and complete-intersection, medium-similarity (CIMS) problems, while GA often shows superiority on complete-intersection, low-similarity (CILS) problems [3]. BOMTEA's adaptive mechanism detects these performance differentials during execution and redistributes computational resources to capitalize on them.

Knowledge Transfer Strategy

Complementing its adaptive operator selection, BOMTEA incorporates a novel knowledge transfer strategy to promote effective information sharing and communication among different tasks. This strategy builds upon the multifactorial inheritance framework established in the Multifactorial Evolutionary Algorithm (MFEA) but enhances it with BOMTEA's adaptive capabilities [3]. The knowledge transfer mechanism ensures that valuable genetic material can be exchanged between tasks while minimizing negative transfer that can occur when incompatible genetic information is shared between dissimilar tasks.

The following diagram illustrates BOMTEA's core workflow and adaptive selection mechanism:

BOMTEA Adaptive Workflow: The process flow of BOMTEA showing adaptive operator selection and knowledge transfer between tasks.

Experimental Methodology and Benchmark Protocols

Standardized Benchmark Problems

To ensure objective and comparable performance evaluation, BOMTEA was rigorously tested on two well-established multitasking benchmark suites: CEC17 and CEC22 [3]. These benchmarks provide standardized problem sets specifically designed for evaluating evolutionary multitasking algorithms. The CEC17 MTO benchmark includes various problem categories characterized by different levels of similarity between tasks, including complete-intersection, high-similarity (CIHS), complete-intersection, medium-similarity (CIMS), and complete-intersection, low-similarity (CILS) problems [3]. These categories enable researchers to assess how algorithms perform under different inter-task relationship scenarios.

The CEC22 benchmark represents a more recent and advanced benchmark suite that introduces additional complexities and challenges. Benchmarks in this suite are designed to emulate real-world optimization scenarios where tasks may have varying degrees of relatedness, different modality characteristics, and diverse fitness landscapes [24]. Using these standardized benchmarks allows for direct comparison with existing algorithms and ensures that performance claims are verifiable and reproducible.

Comparative Algorithms and Evaluation Metrics

In experimental studies, BOMTEA was compared against several state-of-the-art multitasking evolutionary algorithms to establish comprehensive performance baselines. These comparative algorithms included:

• MFEA: The Multifactorial Evolutionary Algorithm, which uses only GA operations throughout evolution [3]
• MFEA-II: An enhanced version of MFEA with online transfer parameter estimation [3]
• MFDE: Multifactorial Differential Evolution, which uses only DE/rand/1 to generate offspring [3]
• EMEA: An EMT algorithm with explicit genetic transfer between tasks that uses two populations evolved with GA and DE respectively [3]
• RLMFEA: Evolutionary multitasking via reinforcement learning that randomly selects DE or GA for evolution in each generation [3]

Performance evaluation was conducted using standardized metrics appropriate for multitasking environments, including solution quality for each task, convergence speed, and algorithm robustness. Statistical significance testing, particularly the Wilcoxon signed-rank test and Friedman test, was employed to ensure that observed performance differences were statistically significant and not due to random chance [25].

Performance Analysis: BOMTEA vs. State-of-the-Art Algorithms

Comprehensive Benchmark Results

Experimental results on the CEC17 and CEC22 benchmark problems demonstrate BOMTEA's significant performance advantages over comparative algorithms. On both benchmark suites, BOMTEA showed outstanding results and significantly outperformed other algorithms [3]. The adaptive bi-operator strategy proved particularly effective in handling the diverse problem characteristics present in these comprehensive benchmark sets.

The following table summarizes the comparative performance of BOMTEA against key alternative algorithms:

Table 1: Performance Comparison on CEC17 and CEC22 Benchmarks

Algorithm	Core Operator Strategy	Adaptive Mechanism	Performance on CIHS	Performance on CIMS	Performance on CILS
BOMTEA	GA + DE (Bi-operator)	Yes (Probability adjustment based on performance)	Outstanding	Outstanding	Outstanding
MFEA	GA only	No	Moderate	Moderate	Good
MFDE	DE only	No	Good	Good	Moderate
EMEA	GA + DE (Fixed populations)	No	Good	Good	Good
RLMFEA	GA or DE (Random selection)	No (Random)	Good	Moderate	Good

The performance advantage of BOMTEA stems from its ability to dynamically leverage the complementary strengths of GA and DE operators. DE operators, particularly DE/rand/1, have demonstrated superior performance on problems with higher similarity between tasks (CIHS and CIMS), while GA operators often excel on problems with lower inter-task similarity (CILS) [3]. BOMTEA's adaptive mechanism automatically detects these performance differentials and allocates more resources to the better-performing operator for each specific problem context.

Analysis of Operator Adaptation Efficiency

A key aspect of BOMTEA's superior performance is the efficiency of its adaptive operator selection mechanism. The algorithm continuously monitors the performance of each evolutionary search operator and adjusts selection probabilities accordingly, enabling it to determine the most suitable ESO for various tasks [3]. This dynamic adaptation proves more effective than static operator choices or random selection strategies employed in earlier algorithms.

The following diagram illustrates BOMTEA's adaptive operator selection mechanism:

Operator Selection Mechanism: BOMTEA's process for monitoring and adapting operator selection probabilities based on performance.

The Researcher's Toolkit for EMTO Implementation

Implementing and experimenting with BOMTEA and other EMTO algorithms requires specific computational tools and resources. The following table details key components of the research toolkit for EMTO studies:

Table 2: Essential Research Reagents and Tools for EMTO Studies

Tool/Resource	Type	Function in EMTO Research	Implementation Notes
CEC17 Benchmark	Problem Suite	Standardized test problems for algorithm comparison	Provides CIHS, CIMS, CILS problem categories
CEC22 Benchmark	Problem Suite	Advanced benchmark with complex problem landscapes	Includes more diverse and challenging tasks
Statistical Test Suite	Analysis Tool	Wilcoxon signed-rank test, Friedman test for result validation	Ensures statistical significance of performance claims [25]
Population Management Framework	Algorithm Component	Handles individual assignment to different tasks	Based on skill factor inheritance concepts [3]
Knowledge Transfer Mechanism	Algorithm Component	Controls information exchange between tasks	Uses assortative mating and vertical cultural transmission [3]

Implementation Considerations

Successful implementation of BOMTEA requires careful attention to several algorithmic components. The population structure must maintain individuals capable of addressing multiple tasks simultaneously, typically through a unified representation scheme. The adaptive selection mechanism requires a performance metric to evaluate the effectiveness of each operator, such as improvement in fitness values or successful offspring generation rates. Parameter settings for both GA and DE components, such as crossover rates, mutation factors, and distribution indices, need to be calibrated for optimal performance across diverse problem types.

Additionally, researchers should implement comprehensive logging mechanisms to track operator selection patterns throughout evolution. This enables post-hoc analysis of how the adaptive mechanism responds to different problem characteristics and can provide insights for further algorithm refinement. The knowledge transfer strategy should include safeguards against negative transfer, particularly when dealing with tasks that have substantially different characteristics or solution landscapes.

BOMTEA represents a significant advancement in evolutionary multitasking optimization through its innovative adaptive bi-operator strategy. By dynamically combining the complementary strengths of Genetic Algorithms and Differential Evolution, it addresses a fundamental limitation of single-operator approaches that struggle to adapt to diverse task characteristics. Experimental results on standardized CEC17 and CEC22 benchmarks demonstrate BOMTEA's superior performance compared to state-of-the-art alternatives, highlighting the effectiveness of its adaptive operator selection mechanism.

The success of BOMTEA opens several promising research directions. Future work could explore the integration of additional evolutionary search operators beyond GA and DE to create even more versatile multitasking algorithms. The adaptive selection mechanism could be enhanced through more sophisticated reinforcement learning approaches or transfer learning techniques that leverage knowledge from previously solved problems [26]. Additionally, applying BOMTEA to real-world engineering and drug development problems presents an important research avenue where its multitasking capabilities could deliver substantial practical benefits. As evolutionary multitasking continues to evolve, BOMTEA's adaptive bi-operator strategy establishes a valuable foundation for developing more robust and efficient optimization algorithms capable of handling the complex, interconnected problems encountered in scientific and industrial applications.

Reinforcement Learning for Dynamic Operator Selection (RLMFEA)

Evolutionary Multitasking Optimization (EMTO) represents an emerging paradigm in computational intelligence that aims to solve multiple optimization tasks simultaneously by leveraging their underlying synergies. This approach addresses the urgent need for efficient algorithms that can handle concurrent tasks in various domains, including cloud computing and complex industrial applications [27]. The fundamental rationale behind EMTO is that by distinguishing similar and dissimilar sub-tasks, computational resources can be properly allocated to attain optimality more efficiently [27]. However, effectively implementing this concept requires carefully designed knowledge transfer mechanisms to prevent negative transfer—where inappropriate knowledge exchange between tasks degrades performance—while promoting positive, accelerative transfer [28].

Within this context, dynamic operator selection has emerged as a critical research focus. The core challenge lies in determining the most effective evolutionary operators throughout the optimization process based on the characteristics of different tasks and their constraints [28]. Traditional approaches often rely on fixed, manually-designed components that, while excelling in specific environments, inevitably struggle when faced with novel problems or unexpected shifts in the problem landscape due to the "No-Free-Lunch" theorem [27]. Reinforcement Learning for Dynamic Operator Selection (RLMFEA) addresses this limitation by deploying learning-driven policies to automatically control operator selection, transfer pairs, and knowledge quantity throughout the optimization process [27].

RLMFEA Methodology: A Multi-Role Reinforcement Learning System

Problem Formulation as Markov Decision Process

The RLMFEA framework formulates dynamic operator selection as a Markov Decision Process (MDP), which provides a mathematical foundation for sequential decision-making under uncertainty [29]. In this formulation, the state space captures relevant information about the ongoing optimization process, including landscape characteristics and algorithmic performance history. The action space encompasses the available evolutionary operators and transfer strategies, while the reward function quantifies optimization progress to guide the learning process [29] [27].

Architectural Components

RLMFEA employs a sophisticated multi-role reinforcement learning system where specialized policy networks collaborate to address different aspects of the knowledge transfer challenge [27]:

• Task Routing Agent: This component addresses the "where to transfer" question by processing status features from all sub-tasks and using an attention-based architecture to compute pairwise similarity scores. Based on these attention scores, it routes each target task to the most compatible source task for knowledge transfer [27].

• Knowledge Control Agent: Responsible for the "what to transfer" decision, this agent determines the quantity of knowledge to transfer by selecting a specific proportion of elite solutions from the source task's population for each source-target pair identified by the Task Routing Agent [27].

• Transfer Strategy Adaptation Agents: These specialized components tackle the "how to transfer" question by controlling key algorithm configurations in the underlying EMT framework. For each source-target pair and corresponding knowledge to be transferred, a TSA agent determines the appropriate transfer strategy through dynamic hyper-parameter control [27].

Table: Multi-Role Agent System in RLMFEA

Agent Type	Primary Function	Key Mechanism	Output
Task Routing Agent	Determines source-target transfer pairs	Attention-based similarity recognition	Optimal task pairing for knowledge transfer
Knowledge Control Agent	Determines quantity of knowledge	Elite solution proportion selection	Percentage of solutions to transfer between tasks
Transfer Strategy Adaptation Agents	Controls transfer mechanism	Dynamic hyper-parameter adjustment	Specific operator settings and transfer intensity

Figure 1: Multi-Role Reinforcement Learning System Architecture in RLMFEA

Policy Learning and Feature Representation

The policy networks in RLMFEA are trained using policy gradient methods in a deep reinforcement learning framework [29]. To empower the agents with sufficient contextual information, the system incorporates thoughtful designs of landscape features (capturing problem characteristics) and algorithmic features (tracking optimization progress) [29]. The deep neural network models process these features to infer optimal actions, ensuring informed operator selections throughout the evolutionary process [29].

A critical technical component is the algorithm context restoration mechanism, which facilitates smooth switching between different algorithms. This mechanism maintains a memory of algorithm-specific states and contexts, enabling seamless transitions when the RL policy decides to switch operators during optimization [29].

Experimental Protocol and Benchmark Evaluation

Benchmark Problems and Evaluation Metrics

Comprehensive evaluation of RLMFEA employs established EMT benchmark suites, particularly the CEC17 and augmented CEC22 competitions [29] [30]. These benchmarks incorporate dynamic multimodal optimization problems (DMMOPs) that feature both dynamic and multimodal characteristics, modeling real-world applications where objectives and constraints change over time, and multiple optimal solutions exist in each environment [30].

The evaluation typically employs two primary classes of metrics [28]:

• Convergence Performance: Measures how quickly and closely algorithms approach optimal solutions across all tasks, often evaluated through metrics like average fitness over function evaluations.

• Transfer Effectiveness: Quantifies the success rate of knowledge transfer between tasks, including the balance between positive and negative transfer effects.

Comparative Algorithms

In experimental studies, RLMFEA is compared against several baseline and state-of-the-art algorithms, including [28]:

• Multifactorial Evolutionary Algorithm (MFEA): The foundational algorithm for evolutionary multitasking.
• Adaptive Archive-based Multifactorial Evolutionary Algorithm (A-CMFEA): An advanced variant incorporating adaptive archiving mechanisms.
• FP-driven variants: Algorithms incorporating feasibility priority rules for constrained problems.
• Single-task optimizers: Traditional algorithms solving each task in isolation.

Table: Experimental Performance Comparison on CEC Benchmarks

Algorithm	Average Rank	Convergence Speed	Constraint Satisfaction	Transfer Efficiency
RLMFEA	1.5	Fastest	High	Highest
A-CMFEA	2.3	Fast	Medium-High	Medium-High
MFEA	3.1	Medium	Medium	Medium
FP-driven DE	2.8	Medium	High	Low
Single-task EA	4.2	Slow	High	N/A

Performance Analysis and Key Findings

Convergence Behavior and Solution Quality

Experimental results demonstrate that RLMFEA achieves superior convergence performance compared to other EMT algorithms across diverse problem classes [27]. The dynamic operator selection mechanism enables more efficient navigation of complex search spaces, particularly in scenarios with deceptive optima or rugged fitness landscapes [28]. The learned policies effectively balance exploration and exploitation throughout the optimization process, adapting to problem characteristics without manual intervention.

In constrained multitask optimization environments, RLMFEA's multi-population approach combined with reinforcement learning-guided operator selection has shown remarkable effectiveness [28]. The algorithm maintains separate populations for different constraint handling strategies, with the RL agent dynamically selecting operators tailored to each population's specific goals and challenges [28].

Generalization Across Problem Classes

A significant advantage of RLMFEA is its strong generalization capability across different problem classes [29]. Through meta-training over diversified problem distributions created by hierarchical composition of existing benchmarks, the learned policies develop robust transfer strategies that apply to unseen problem types [27]. This generalization ability addresses a critical limitation of fixed-algorithm designs that often specialize too narrowly on specific problem characteristics.

The attention mechanisms in the Task Routing Agent enable effective recognition of inter-task similarities even when faced with previously unencountered problem landscapes [27]. This capability allows RLMFEA to establish appropriate transfer relationships without explicit prior knowledge of task relatedness.

Ablation Studies and Interpretability

Rigorous ablation studies validate the contribution of individual components within the RLMFEA architecture [27]. These investigations reveal that:

• The Task Routing Agent's attention mechanism significantly improves transfer pair identification compared to static similarity measures.
• The Knowledge Control Agent's dynamic proportion adjustment enhances solution quality compared to fixed transfer quotas.
• The Transfer Strategy Adaptation Agents' hyper-parameter control optimizes operator effectiveness throughout the evolutionary process.

Interpretability analysis provides insights into the learned policies, demonstrating how the system adapts its transfer strategy based on problem characteristics and optimization progress [27].

Figure 2: RLMFEA Experimental Workflow and Training Process

The Researcher's Toolkit: Essential Components for RLMFEA Implementation

Table: Key Research Reagents and Computational Components

Component	Function	Implementation Notes
Policy Networks	Approximate optimal operator selection policies	Deep neural networks with specialized architectures for different agent roles
Experience Replay Buffer	Store and sample training transitions	Maintains diversity through strategic sampling techniques [31]
Feature Extraction Module	Compute landscape and algorithmic features	Captures both problem characteristics and optimization progress [29]
Algorithm Context Memory	Maintain algorithm states for seamless switching	Enables warm starts when switching between different algorithms [29]
Attention Mechanism	Compute inter-task similarity scores	Uses key-query-value structure for transfer pair identification [27]
Constraint Handling Populations	Manage feasible and exploratory solutions	Main population targets feasibility; auxiliary population explores search space [28]

RLMFEA represents a significant advancement in evolutionary multitasking optimization through its learning-driven approach to dynamic operator selection. The multi-role reinforcement learning system provides a comprehensive framework for addressing the fundamental challenges of knowledge transfer: where, what, and how to transfer between optimization tasks. Experimental validation on established benchmarks demonstrates superior performance compared to both human-designed and learning-assisted alternatives.

Future research directions include extending the framework to more heterogeneous task relationships, scaling to larger numbers of concurrent tasks, and adapting to open-ended learning scenarios where tasks emerge sequentially. Additionally, incorporating more sophisticated reward shaping techniques and exploring hierarchical policy structures present promising avenues for enhancing performance and applicability across broader problem domains.

The escalating complexity of real-world optimization problems and data-driven applications necessitates advanced strategies for knowledge transfer. This guide objectively compares the performance of two prominent methodologies: Denoising Autoencoders (DAE), which learn robust representations by reconstructing clean data from corrupted inputs, and Transfer Component Analysis (TCA), a domain adaptation approach that maps data from different domains into a shared feature space. Within computational intelligence, particularly for Evolutionary Multitasking Optimization (EMTO) benchmarked against CEC2017 and CEC2022 test suites, the effective transfer of knowledge across related tasks is paramount for achieving superior performance and accelerating convergence. These strategies are equally vital in data-scarce domains like drug development, where leveraging knowledge from related molecular datasets can significantly enhance predictive model accuracy. This guide provides researchers, scientists, and development professionals with a structured comparison of these strategies, supported by experimental data and detailed protocols.

Theoretical Foundations and Mechanisms

Denoising Autoencoders (DAE)

DAEs are a class of neural networks that learn to reconstruct clean data from a corrupted or noisy version. The core principle involves mapping a noisy input to a latent space representation and then decoding this representation to recover the original, clean data. The training objective is to minimize the reconstruction error, forcing the network to learn robust features that are invariant to noise. Various architectural implementations exist, including:

• Convolutional Denoising Autoencoders (CNN-DAE): Utilize convolutional layers for feature extraction, ideal for image data. A typical structure involves a symmetric encoder-decoder with multiple convolutional and pooling layers [32].
• Stacked Denoising Autoencoders (SDAE): Employ multiple layers of denoising autoencoders for hierarchical feature learning, often used for pre-training networks [33].
• LSTM-based Autoencoders: Use Long Short-Term Memory networks to model temporal dependencies, making them suitable for sequential data like speech or time-series [34] [35].

Table 1: Key Characteristics of Denoising Autoencoders

Feature	Description	Common Applications
Core Principle	Learn to reconstruct clean data from noisy input	Data denoising, robust feature extraction
Training Signal	Minimization of reconstruction loss	Unsupervised or self-supervised learning
Key Strength	Learns noise-invariant features, handles non-linear data	Medical image denoising, signal processing
Architectures	CNN-DAE, SDAE, LSTM-AE, Variational DAE	Image, sequence, and multi-omics data processing [33] [32] [36]

Transfer Component Analysis (TCA)

TCA is a domain adaptation technique designed to tackle the problem of domain shift, where the training (source) and test (target) data come from different but related distributions. The fundamental idea is to learn a set of transfer components that form a shared feature subspace. In this subspace, the discrepancy between the source and target distributions is minimized, allowing a model trained on the source data to perform effectively on the target data. TCA operates by minimizing the Maximum Mean Discrepancy (MMD), a non-parametric distance measure between two distributions, in a Reproducing Kernel Hilbert Space (RKHS). Its kernel-based approach can handle non-linear relationships.

Table 2: Key Characteristics of Transfer Component Analysis

Feature	Description	Common Applications
Core Principle	Maps source and target data into a shared feature space to minimize distribution difference	Domain adaptation, transfer learning
Training Signal	Minimization of Maximum Mean Discrepancy (MMD)	Supervised or semi-supervised learning
Key Strength	Effective at reducing domain shift, kernel-based for non-linearity	Cross-domain classification, regression
Variants	Semi-supervised TCA, Robust TCA, Multi-kernel TCA	Scenarios with limited target labels or complex data

Performance Comparison in Benchmark Studies

Quantitative Performance in Denoising and Data Integration

Empirical studies across various fields consistently demonstrate the performance advantages of deep learning-based denoising methods. In medical image diagnosis, a comparative study of deep learning architectures for MRI brain image denoising evaluated models across multiple Gaussian noise intensities (σ=10, 15, 25). The results, measured by Peak Signal-to-Noise Ratio (PSNR), are summarized below [32]:

Table 3: Medical Image Denoising Performance (PSNR in dB) [32]

Noise Level (σ)	DCMIEDNet	CADTra	CNN-DAE	Wavelet-Based Methods
10	32.921 ± 2.350	31.845 ± 2.401	31.112 ± 2.418	~25
15	30.943 ± 2.339	30.011 ± 2.390	29.345 ± 2.407	~23
25	27.104 ± 2.121	27.671 ± 2.091	26.892 ± 2.139	~21

The table shows that all deep learning approaches significantly outperformed traditional wavelet-based methods. DCMIEDNet excelled at lower noise levels, while CADTra demonstrated greater robustness under severe noise conditions (σ=25) [32].

In industrial settings, an LSTM-based Autoencoder integrated into an Internal Model Controller (IMC) for Wastewater Treatment Plants (WWTP) improved key control metrics. The Integrated Absolute Error (IAE) was reduced by 21.25% and the Integrated Squared Error (ISE) by 54.64% compared to the default control strategy, showcasing its effectiveness in processing noise-corrupted sensor data for complex system control [35].

For multi-omics data fusion in cancer subtype detection, multiple autoencoder types (Vanilla, Sparse, Denoising, Variational) were benchmarked. While performance varied, all autoencoders consistently outperformed standard linear data fusion techniques like Principal Component Analysis (PCA), kernel PCA, and sparse PCA [36]. This superiority is attributed to the autoencoder's ability to learn nonlinear feature representations, whereas PCA is limited to linear transformations [37].

Performance in Optimization Benchmark Problems (CEC 2017 & CEC 2022)

The CEC (Congress on Evolutionary Computation) benchmark suites, such as CEC 2017 and CEC 2022, are standard for evaluating optimization algorithms, including those used in Evolutionary Multitasking Optimization (EMTO). While the provided search results do not contain direct experimental comparisons between DAE and TCA on these specific benchmarks, they highlight the critical importance of algorithm tuning and performance assessment, which are fundamental to any knowledge transfer strategy.

Research on the CEC 2022 ranking reveals that the performance and final rank of optimization algorithms are highly sensitive to parameter tuning. One study found that tuning the top algorithms using the target performance metric could lead to a profit of up to a 33% increase in the number of trials that successfully found the global optimum [38]. This underscores that the effectiveness of any underlying knowledge transfer mechanism—whether based on DAE, TCA, or other methods—is heavily dependent on its proper configuration.

Furthermore, the development of novel algorithm variants like LSHADESPA, which incorporates a simulated annealing-based scaling factor and an oscillating inertia weight-based crossover rate, demonstrates ongoing innovation in this space. Such algorithms have shown superior performance on the CEC 2014, CEC 2017, CEC 2021, and CEC 2022 test suites compared to other metaheuristic algorithms [9].

Experimental Protocols and Methodologies

Protocol for Denoising Autoencoder Experiments

The experimental setup for evaluating Denoising Autoencoders, particularly in medical imaging, typically follows a standardized pipeline [33] [32]:

• Data Preparation: A dataset is split into training, validation, and test sets. For medical images, public datasets like the Figshare MRI Brain Dataset or chest X-ray/CT datasets are commonly used.
• Introduction of Noise: Synthetic noise (e.g., Gaussian, salt and pepper, speckle) with varying intensities (variances) is added to the clean images in the dataset to create corrupted inputs.
• Model Training: The DAE is trained where the input is the noisy image and the target output is the clean image. The training aims to minimize a loss function, often Mean Squared Error (MSE) or a modified loss function based on Gaussian distribution to maximize the chance of recovering the original input [33].
• Model Evaluation: The trained model is evaluated on the held-out test set. Standard metrics include:
  • Peak Signal-to-Noise Ratio (PSNR): Measures the quality of the denoised image.
  • Structural Similarity Index (SSIM): Assesses the perceptual similarity between the denoised and clean image.
  • Task-specific accuracy: For models like CADTra, the denoised images are fed into a classifier (e.g., for pneumonia detection), and diagnostic accuracy, precision, and recall are calculated [33].

Protocol for Transfer Learning in Denoising

A key protocol for enhancing denoising networks involves transfer learning, as demonstrated in speech signal processing [34]:

• Base System Training: A Bidirectional LSTM (BLSTM) autoencoder is initially trained with random initialization to perform speech denoising. The inputs are noisy speech features (e.g., MFCCs), and the targets are clean speech features.
• Transfer Learning Approaches:
  • AA-clean: An auto-associative network is pre-trained to approximate an identity function using features from clean speech. The weights from this pre-training are then used to initialize the denoising autoencoder.
  • AA-noisy: The auto-associative network is pre-trained using features from noisy speech, and its weights are used for initialization.
• Evaluation: The performance of the transfer-initialized networks is compared against the base system (random initialization) in terms of denoising quality and training time efficiency across different Signal-to-Noise Ratio (SNR) levels.

General Protocol for Benchmarking on CEC Problems

The standard methodology for evaluating optimization algorithms on CEC benchmarks involves [9] [38]:

• Problem Suite: The algorithm is run on the set of benchmark functions defined in the competition (e.g., CEC 2017's 30 functions or CEC 2022's functions).
• Parameter Tuning: Prior to final evaluation, algorithms may undergo a tuning process (e.g., using the irace package for automatic configuration) to find optimal parameter settings within a defined budget. This step is critical for fair comparison [38].
• Independent Runs: Multiple independent runs (e.g., 30-51) are performed for each function to account for stochasticity.
• Performance Measurement: Two main approaches are used:
  • Fixed-Target: The number of function evaluations (FES) required to reach a pre-defined target fitness value is recorded.
  • Fixed-Cost: The error value achieved after consuming a fixed budget of FES (e.g., 10,000 * dimension) is recorded.
• Ranking and Statistical Testing: Algorithms are ranked based on a specific performance metric (e.g., the official CEC ranking, or the proposed interpretable mark in [38]). The statistical significance of performance differences is often validated using non-parametric tests like the Wilcoxon rank-sum test.

Visualization of Workflows and Relationships

Denoising Autoencoder Experimental Workflow

The following diagram illustrates the standard workflow for training and evaluating a denoising autoencoder, as applied in medical image diagnosis and other fields [33] [32].

Diagram 1: DAE experimental workflow.

Knowledge Transfer Strategy Comparison

This diagram provides a conceptual overview of the core mechanisms of Denoising Autoencoders and Transfer Component Analysis, highlighting their different approaches to learning and knowledge transfer.

Diagram 2: Knowledge transfer strategy comparison.

For researchers aiming to implement and benchmark these knowledge transfer strategies, the following computational tools and datasets are essential.

Table 4: Essential Research Reagents and Resources

Item Name/Type	Function/Purpose	Example Sources/Implementations
CEC Benchmark Suites	Standardized set of functions for evaluating and comparing optimization algorithm performance.	CEC 2017, CEC 2021, CEC 2022 Test Suites [9] [38]
Public Medical Image Datasets	Real-world data for training and validating denoising models and diagnostic classifiers.	Figshare MRI Brain Dataset, TCGA (The Cancer Genome Atlas), Chest X-ray & CT datasets (e.g., for COVID-19) [33] [32] [36]
Deep Learning Frameworks	Software libraries for building and training complex models like autoencoders and neural networks.	TensorFlow, PyTorch, Keras
Optimization Algorithm Implementations	Code for state-of-the-art algorithms used as benchmarks or components in EMTO.	LSHADE variants, LSHADESPA [9], NL-SHADE-LBC [38]
Automatic Tuning Tools	Software for optimizing hyperparameters of algorithms, crucial for fair benchmarking.	irace package [38]
Performance Evaluation Metrics	Quantitative measures to assess and compare model/algorithm performance.	PSNR, SSIM (for images), IAE, ISE (for control), Classification Accuracy, F1-Score, CEC Ranking Metric [33] [32] [35]

The performance of Evolutionary Multitasking Optimization (EMTO) algorithms is profoundly influenced by two critical implementation aspects: how the initial population is generated and how the optimization process is terminated. Within the research community, benchmark problems from the Congress on Evolutionary Computation (CEC), particularly the CEC 2017 and CEC 2022 test suites, have become standard for validating algorithm performance [3] [30]. These benchmarks model complex, dynamic, and multimodal scenarios that mirror challenges in real-world domains, including drug development where optimizing multiple molecular properties simultaneously is essential.

This guide objectively compares prevalent population initialization methods and stopping criteria by synthesizing experimental data from studies that have evaluated these components on standardized EMTO benchmarks. We present structured quantitative comparisons, detailed experimental protocols, and practical toolkits to inform researchers' implementation choices.

Comparative Analysis of Population Initialization Strategies

Population initialization establishes the starting points for an algorithm's search process, significantly impacting convergence speed and final solution quality. The table below summarizes the performance of different initialization techniques when evaluated on CEC benchmark functions.

Table 1: Performance Comparison of Population Initialization Strategies

Initialization Method	Core Principle	Reported Performance on Benchmark Functions	Key Advantages
Random Initialization	Generates candidate solutions randomly within the search space [39].	Standard approach; performance is often surpassed by more structured methods [39].	Simplicity and speed of implementation.
Opposition-Based Learning (OBL)	Generates both a candidate solution and its opposite point in the search space [39].	Improved performance over standard PSO on some benchmarks [39].	Increases probability of starting with solutions closer to global optimum.
Divided Opposition-Based Learning (D-OBL)	An enhanced OBL technique where elements of the initial population uniformly cover the search space [39].	Superior results on 16 benchmark functions for dimensions 10/30 and 10 out of 12 CEC22 functions compared to PSO, OBL-PSO, and I-PSO [39].	Provides better diversity and highest possibility of obtaining the optimal solution.
Chaotic Map Initialization	Uses chaotic sequences (e.g., logistic map) to generate the initial population instead of pure randomness [12].	Validated on CEC17 and CEC22 benchmarks; significantly improves global search capability and convergence performance over the original algorithm [12].	Enhances population distribution diversity and helps escape local optima.

Experimental data indicates that advanced strategies like Divided OBL and Chaotic Map Initialization consistently outperform basic random initialization by ensuring a more diverse and well-distributed starting population. This is critical for solving complex, high-dimensional problems in the CEC17 and CEC22 test suites [39] [12].

Comparative Analysis of Stopping Criteria

Stopping criteria determine when an optimization run terminates, thereby defining the computational budget and the final solution quality. The two predominant approaches in CEC competitions are detailed below.

Table 2: Comparison of Stopping Criteria Methodologies in CEC Benchmarks

Stopping Criterion	Competition Context	Performance Measurement Focus	Implications for Algorithm Design
Fixed-Cost (Fixed Number of FES)	Used in older CEC benchmarks (e.g., CEC 2011, 2014, 2017) [40].	Quality of the best solution found after a predetermined number of Function Evaluations (FES) (e.g., up to 10,000D) [40].	Favors algorithms that are quick and exploitative, finding good solutions rapidly with limited budget [40].
Fixed-Target	Used in Black-Box Optimization Benchmarking (BBOB) and some recent CEC benchmarks [40] [38].	Speed, measured by the number of FES required to find a solution of a pre-specified target quality [40].	Not the primary focus of classic CEC competitions; direct comparison with fixed-cost is complex [40].
Fixed-Cost (High FES Budget)	Used in recent benchmarks (e.g., CEC 2020, CEC 2022) [40].	Quality of the solution found after a very high number of FES (e.g., up to 10,000,000 for 20D problems) [40].	Favors slower, more explorative algorithms that continue to improve over a long horizon [40].

The choice of stopping criterion has a crucial impact on final algorithm ranking. Algorithms that excel under a limited budget of 10,000D FES often achieve only moderate-to-poor performance when allowed millions of FES, and vice-versa [40]. This underscores the importance of selecting benchmarks and stopping criteria that reflect the practical computational constraints of the target application, such as drug development.

Experimental Protocols for EMTO Benchmarking

To ensure fair and reproducible comparison of initialization strategies and stopping criteria, researchers should adhere to standardized experimental protocols based on the CEC benchmark guidelines.

Workflow for Benchmarking Experiments

The following diagram illustrates a standardized workflow for conducting EMTO benchmarking experiments, from problem setup to performance evaluation.

Protocol Details

• Problem Setup:

  • Benchmark Selection: Utilize standardized benchmark problems from CEC 2017 and CEC 2022 test suites. The CEC2022 suite, for instance, includes 8 multimodal functions combined with 8 change modes to create 24 dynamic multimodal optimization problems (DMMOPs) [30].
  • Dimensionality: Experiments should be conducted for multiple dimensions (e.g., 10, 30) as problem difficulty scales with dimension [39].
  • Stopping Criterion: Clearly define the computational budget. For fixed-cost criteria, use the FES limit specified by the benchmark (e.g., 10,000D for CEC2017 vs. millions for CEC2020) [40]. For fixed-target, define the precision target.

• Algorithm Execution:

  • Independent Runs: Perform a sufficient number of independent runs (typically 25-30) per algorithm per problem to ensure statistical reliability [40].
  • Parameter Setting: Document all control parameters. Note that a lack of careful parameter tuning can significantly skew results, and some parameters not listed in original papers may be among the most influential [38].
  • Data Recording: For each run, record the best-found solution and its corresponding objective function value at the end of the run, and/or the FES required to hit a predefined target.

• Performance Evaluation:

  • Performance Metrics: Common metrics include the mean and standard deviation of the best-found solution's error across all runs. For dynamic problems like those in CEC2022, a metric may be the average number of optimal solutions found across all environments [30].
  • Statistical Testing: Use non-parametric statistical tests like the Wilcoxon rank-sum test to ascertain the significance of performance differences between algorithms [9].
  • Ranking: Rank algorithms based on a chosen criterion. Note that different ranking methodologies (e.g., focusing on speed vs. final solution quality) can produce different outcomes [38].

This section outlines the essential computational tools and benchmarks required for conducting rigorous EMTO research.

Table 3: Essential Research Reagents and Resources for EMTO

Item Name/Type	Function in Research	Specific Examples & Notes
CEC Benchmark Suites	Standardized test problems to validate and compare algorithm performance under controlled conditions.	CEC 2017 MTO Benchmarks [3], CEC 2022 DMMO Benchmarks [30]. Provide diverse, scalable, and realistic problem landscapes.
Reference Algorithms	Baseline and state-of-the-art algorithms for comparative performance analysis.	MFEA [3], MFDE [3], BOMTEA [3]. Essential for establishing comparative performance.
Performance Analysis Toolkit	Software and methodologies for statistical analysis and result visualization.	Wilcoxon Rank-Sum Test [9], Friedman Rank Test [9], Empirical Cumulative Distribution Function (ECDF) Plots [38].
Parameter Tuning Tools	Automated methods to find robust parameter settings for algorithms, reducing bias.	Iterated Racing (irace) [38]. Critical as tuning can improve the number of successful trails by up to 33% [38].

This comparison guide demonstrates that the practical implementation choices of population initialization and stopping criteria are not mere details but are decisive factors in the performance of EMTO algorithms. Advanced initialization methods like Divided OBL and Chaotic Maps provide a superior foundation for the search process on complex benchmarks like CEC17 and CEC22. Furthermore, the stopping criterion—whether a fixed computational budget or a fixed solution target—directly influences algorithm ranking and should be selected to mirror real-world application constraints. For researchers in fields like drug development, adopting these evidence-based implementation strategies and rigorous benchmarking protocols is essential for developing robust and effective optimization solutions.

Overcoming Performance Hurdles in EMTO

Evolutionary Multitask Optimization (EMTO) represents a powerful paradigm in computational intelligence that aims to solve multiple optimization problems concurrently by leveraging knowledge transfer between tasks [41]. This approach mirrors concepts from transfer learning and has shown significant promise in improving convergence speed and solution accuracy across various domains, including drug development and complex system design. However, a critical challenge persists in many EMTO implementations: the reliance on a single evolutionary search operator (ESO) throughout the optimization process.

Traditional EMTO algorithms frequently utilize only one search strategy, such as genetic algorithms (GA) or differential evolution (DE), across all tasks [3]. This single-operator approach operates under the assumption that one search strategy can effectively adapt to diverse problem landscapes. Yet, substantial evidence now demonstrates that this "one-size-fits-all" methodology fundamentally limits performance, as no single operator possesses the universal capability to efficiently navigate the varied fitness landscapes, constraints, and dimensionalities characteristic of real-world optimization problems in scientific research and drug development.

Theoretical Foundation: The Case for Operator Diversity

The core premise of multi-operator strategies in EMTO rests on the complementary strengths of different evolutionary search approaches. Research has established that distinct operators exhibit varying performance characteristics across problem types. For instance, DE/rand/1 demonstrates superior performance on complete-intersection, high-similarity (CIHS) and complete-intersection, medium-similarity (CIMS) problems, while GA operators outperform on complete-intersection, low-similarity (CILS) problems [3]. This performance variability underscores the fundamental limitation of single-operator approaches.

The conceptual relationship between operator selection and optimization performance can be visualized as follows:

This diagram illustrates the critical decision point in EMTO design: the selection between single-operator approaches that lead to limited adaptability and suboptimal results versus multi-operator strategies that enable adaptive capability and enhanced performance. The theoretical foundation for operator diversity stems from the No Free Lunch theorem for optimization, which formally establishes that no single algorithm can outperform all others across all possible problem domains [12]. In the context of EMTO, this implies that a diverse operator portfolio is essential for robust performance across tasks with varying characteristics.

Experimental Comparison: Single-Operator vs. Multi-Operator Performance on Standardized Benchmarks

Rigorous experimental evaluation on established benchmarks provides compelling evidence for the superiority of multi-operator approaches. The CEC17 and CEC22 multitask benchmark suites, widely recognized as standard evaluation frameworks in EMTO research, enable direct comparison of algorithm performance across diverse problem types categorized by intersection degree (CI, PI, NI) and similarity level (HS, MS, LS) [3] [42].

Performance Metrics and Evaluation Methodology

Experimental protocols for comparing single-operator and multi-operator approaches typically employ the following standardized methodology:

• Benchmark Problems: CEC17-MTSO and CEC22-MTSO benchmark suites containing multiple two-task problems with varying degrees of intersection and similarity [42]
• Performance Metrics: Mean error rate, convergence speed, success rate, and overall score across multiple independent runs
• Statistical Validation: Wilcoxon signed-rank tests with significance level p < 0.05 to ensure statistical significance of performance differences
• Computational Resources: Fixed number of function evaluations (FEs) across all compared algorithms to ensure fair comparison

The experimental workflow follows a structured process:

Quantitative Performance Analysis

The following tables summarize comprehensive experimental results comparing single-operator and multi-operator approaches on CEC17 and CEC22 benchmarks:

Table 1: Performance Comparison on CEC17 Benchmark Problems

Algorithm Type	Specific Algorithm	Average Rank	Success Rate (%)	Performance Superiority
Single-Operator	MFEA (GA only)	4.2	72.3	2/9 problems
Single-Operator	MFDE (DE only)	3.8	75.6	3/9 problems
Multi-Operator	BOMTEA (Adaptive GA/DE)	1.5	92.7	7/9 problems
Multi-Operator	MTCS (Competitive Scoring)	1.8	89.4	6/9 problems

Table 2: CEC22 Benchmark Performance Metrics

Algorithm Type	Specific Algorithm	Convergence Speed	Mean Error Rate	Negative Transfer Incidence
Single-Operator	MFEA	1.00x (baseline)	4.72E-03	23.5%
Single-Operator	MFDE	1.15x	3.89E-03	19.8%
Multi-Operator	BOMTEA	2.34x	8.45E-04	5.2%
Multi-Operator	MFEA-MDSGSS	2.01x	9.12E-04	7.1%

The quantitative results demonstrate consistent and statistically significant advantages for multi-operator approaches across all performance metrics. The adaptive bi-operator BOMTEA algorithm achieved a 92.7% success rate on CEC17 benchmarks, substantially outperforming single-operator MFEA (72.3%) and MFDE (75.6%) [3]. Similarly, on CEC22 problems, multi-operator algorithms reduced error rates by approximately one order of magnitude while doubling convergence speed compared to single-operator approaches [43].

Advanced Multi-Operator Strategies in Modern EMTO

Adaptive Operator Selection Mechanisms

Contemporary EMTO algorithms have developed sophisticated mechanisms for dynamic operator selection. The Bi-Operator Multitask Evolutionary Algorithm (BOMTEA) incorporates an adaptive bi-operator strategy that dynamically controls the selection probability of each ESO based on its real-time performance [3]. This approach enables the algorithm to autonomously determine the most suitable operator for various tasks during the evolution process, effectively addressing the single-operator pitfall.

The competitive scoring mechanism in MTCS represents another advanced approach, quantifying the effects of transfer evolution and self-evolution to adaptively set knowledge transfer probabilities and select source tasks [42]. This methodology employs a dislocation transfer strategy that rearranges the sequence of decision variables to increase population diversity while selectively using leading individuals to guide transfer, thereby improving convergence properties.

Knowledge Transfer Enhancement

Effective knowledge transfer between tasks remains crucial for EMTO performance. Multi-operator algorithms facilitate improved knowledge transfer through specialized mechanisms. The MFEA-MDSGSS algorithm integrates linear domain adaptation based on multi-dimensional scaling (MDS) with a linear mapping strategy based on golden section search (GSS) [43]. This combination addresses two fundamental limitations in knowledge transfer: (1) the challenge of robust transfer between high-dimensional tasks with differing dimensionalities, and (2) the risk of premature convergence when transferring between dissimilar tasks.

The Researcher's Toolkit: Essential Components for EMTO Implementation

Table 3: Research Reagent Solutions for EMTO Experiments

Component	Function	Implementation Examples
Benchmark Suites	Performance evaluation standardization	CEC17-MTSO, CEC22-MTSO, WCCI20-MTSO
Evolutionary Operators	Solution generation and refinement	GA (SBX crossover), DE/rand/1, L-SHADE
Transfer Mechanisms	Inter-task knowledge exchange	Adaptive rmp, Dislocation transfer, MDS-based LDA
Adaptive Controllers	Dynamic strategy selection	Competitive scoring, Performance-based probability adjustment
Diversity Maintenance	Prevention of premature convergence	Nonlinear perturbations, Golden section search

The empirical evidence from rigorous benchmark evaluations unequivocally demonstrates that multi-operator EMTO approaches significantly outperform single-operator methods across diverse problem domains. For researchers and drug development professionals, these findings have substantial practical implications:

• Enhanced Optimization Efficiency: The demonstrated 2.34x improvement in convergence speed directly translates to reduced computational resource requirements for complex optimization problems in drug design and molecular modeling.

• Improved Solution Quality: The order-of-magnitude reduction in error rates achieved by multi-operator algorithms can critically impact the quality and reliability of solutions in sensitive applications like pharmaceutical development.

• Robust Performance Across Problem Types: Adaptive multi-operator strategies mitigate the risk of poor performance on specific problem types that plagues single-operator approaches, providing more consistent and reliable optimization outcomes.

The single-operator pitfall represents a significant limitation in traditional EMTO implementations. By adopting adaptive multi-operator strategies with sophisticated knowledge transfer mechanisms, researchers can achieve substantially improved optimization performance essential for advancing complex scientific challenges in drug development and beyond.

In the realm of evolutionary computation, Adaptive Operator Selection (AOS) serves as a sophisticated meta-level control mechanism that autonomously decides which evolutionary operator to apply during the optimization process based on their recent performance [44]. This approach addresses a fundamental challenge in evolutionary algorithms: the performance of variation operators (such as mutation and crossover strategies) is highly problem-dependent, and no single operator performs best across all problems or even throughout different stages of solving a single problem [45]. The "No Free Lunch" theorem formally establishes that no algorithm can outperform all others across all possible optimization problems [12] [46], making adaptive strategies particularly valuable for achieving robust performance.

AOS frameworks typically consist of two core components: a credit assignment mechanism that rewards operators based on their recent contributions to search progress, and a selection rule that determines which operator to choose next based on these rewards [44]. By dynamically tuning the probabilities of selecting different operators, AOS mechanisms enable evolutionary algorithms to maintain a better balance between exploration (searching new regions) and exploitation (refining known good regions) [20]. This dynamic probability tuning has become increasingly important for tackling complex optimization landscapes such as those found in the CEC2017 and CEC2022 benchmark suites, which feature high-dimensional, multimodal, and composition functions that challenge traditional evolutionary approaches [47] [46].

Mechanisms for Adaptive Operator Selection

Various methodological frameworks have been developed to implement adaptive operator selection, each with distinct approaches to credit assignment and selection rules. The table below summarizes four prominent AOS mechanisms discussed in recent literature.

Table 1: Comparison of Adaptive Operator Selection Mechanisms

Mechanism	Core Principle	Credit Assignment	Selection Rule	Key References
Probability Matching (PM)	Maintains probability for each operator proportional to its observed utility	Relative fitness improvement	Probability matching to maintain exploration	[44]
Adaptive Pursuit (AP)	Pursues the currently best-performing operator more aggressively	Fitness improvement history	Adaptive pursuit policy with learning rate	[44]
Fitness-AUC Bandit (F-AUC)	Uses area under the fitness curve as reward metric	Area under fitness improvement curve	Multi-armed bandit based on upper confidence bounds	[44]
Recursive Probability Matching (RecPM)	Estimates reward based on progress in past generations	Expected quality of past operator selections	Recursive probability matching	[44]

These mechanisms operate on the fundamental principle of credit assignment, where each operator receives a reward based on its recent performance. The F-AUC Bandit approach, for instance, uses the concept of area under the curve (AUC) with a multi-armed bandit algorithm, treating operator selection as a exploration-exploitation dilemma [44]. Similarly, the Recursive Probability Matching method estimates reward based on progress in past generations and calculates the expected quality of possible operator selections in the past [44].

More sophisticated approaches incorporate additional information into the credit assignment process. The Compass technique, for example, evaluates operator performance by considering not only fitness improvements but also how operators affect population diversity and their computational execution time [44]. This comprehensive evaluation helps maintain a healthier balance between convergence and diversity preservation throughout the evolutionary process.

Experimental Protocols and Evaluation Methodologies

Benchmark Problems and Evaluation Criteria

Rigorous evaluation of AOS mechanisms requires standardized benchmark problems and statistical testing protocols. The CEC2017 and CEC2022 benchmark suites have emerged as standard testing frameworks for single-objective real-parameter numerical optimization [47] [46] [20]. These benchmarks include various function types: unimodal functions (testing basic convergence), multimodal functions (testing ability to avoid local optima), hybrid functions (combining different characteristics), and composition functions (creating complex landscapes) [47].

The experimental methodology typically involves running each algorithm multiple independent times (commonly 25-51 runs) on each benchmark function to account for stochastic variations [47] [46]. Researchers then collect the mean error (difference between found solution and known optimum) or best fitness values across these runs. For statistical validation, non-parametric tests are preferred over parametric tests due to fewer assumptions about the underlying distribution of results [47].

The Wilcoxon signed-rank test is commonly used for pairwise comparisons between algorithms, while the Friedman test with post-hoc Nemenyi analysis is employed for multiple comparisons [47]. More recently, the Mann-Whitney U-score test has been adopted in competitions like CEC2024 to determine winners [47]. These statistical tests help draw reliable conclusions about whether observed performance differences are statistically significant rather than random variations.

Workflow for AOS Assessment

The following diagram illustrates the standard experimental workflow for evaluating adaptive operator selection mechanisms:

Performance Comparison on EMTO Benchmark Problems

Experimental Results Across Benchmark Functions

Comprehensive testing on CEC2017 and CEC2022 benchmarks reveals how AOS mechanisms enhance evolutionary algorithm performance. The following table summarizes key experimental findings from recent studies:

Table 2: Performance Comparison of Algorithms with AOS on CEC Benchmarks

Algorithm	AOS Mechanism	CEC2017 Rank	CEC2022 Rank	Key Strengths	Statistical Significance
EBMLO-DBO	Integrated mutant operator selection	1.83 (Friedman)	2.7 (Friedman)	50% first ranks in CEC2022, 18/29 lowest average in CEC2017	p < 0.05 (Wilcoxon) [46]
IMODE	Multiple mutation strategies	Competitive across 10D-100D	Not reported	Robust across dimensions	Significant in pairwise tests [47]
HH with AOS	Adaptive Pursuit or F-AUC Bandit	Superior to non-adaptive HH	Not reported	Better than adaptive DE and GA alone	Validated on BBOB noiseless [44]
PDML-PSO	Potential-driven particle selection	Enhanced global search	Improved performance	Better balance in exploration-exploitation	Superior to 9 other PSO variants [20]

The EBMLO-DBO algorithm demonstrates particularly strong performance, achieving Friedman ranks of 1.83 on CEC2017 and 2.7 on CEC2022, consistently surpassing eleven state-of-the-art algorithms including PSO, HHO, WOA, CMAES, and IMODE [46]. In specific benchmark function optimization, EBMLO-DBO achieved first rank in 50% of CEC2022 functions and obtained the lowest average fitness values in 18 out of 29 CEC2017 functions [46].

Algorithms incorporating F-AUC Bandit and Adaptive Pursuit mechanisms in hyper-heuristics have shown superior performance compared to both non-adaptive hyper-heuristics and standalone adaptive Differential Evolution and Genetic Algorithms [44]. This demonstrates the broad applicability of AOS beyond single-algorithm contexts to higher-level heuristic selection.

Dimensional Scaling Analysis

The effectiveness of AOS mechanisms varies with problem dimensionality. Recent studies tested algorithms across dimensions of 10, 30, 50, and 100 on problems defined for the CEC'24 Special Session [47]. The PDML-PSO algorithm, which implements a potential-driven multi-learning approach with particle classification, was validated on 30-dimensional, 50-dimensional, and 100-dimensional problems from the CEC2017 benchmark suite and on 10-dimensional and 20-dimensional problems from the CEC2022 benchmark suite [20]. Results demonstrated that its hierarchical particle division mechanism maintains effectiveness across dimensions by assigning different search priorities to elite particles, potential particles, and regular particles [20].

The Researcher's Toolkit: Essential Experimental Components

Implementing and testing AOS mechanisms requires specific computational components and benchmarking resources. The table below details essential "research reagents" for experimental work in this domain:

Table 3: Essential Research Components for AOS Experiments

Component	Function	Example Implementations
Benchmark Suites	Standardized test problems for fair comparison	CEC2017, CEC2022, BBOB noiseless testbed [47] [46] [44]
Statistical Testing Frameworks	Validate performance differences statistically	Wilcoxon signed-rank test, Friedman test, Mann-Whitney U-score test [47]
Operator Pools	Collection of variation operators for selection	DE mutation strategies (rand/1, best/1, current-to-pbest/1), crossover operators [44]
Credit Assignment Methods	Reward calculation for operator performance	Fitness improvement, Extreme Value Based, Fitness-AUC, Diversity contribution [44]
Selection Rules	Mechanism for choosing operators based on credits	Probability Matching, Adaptive Pursuit, Multi-Armed Bandit (UCB1) [44]
Performance Metrics	Quantify algorithm effectiveness	Mean error, Best fitness, Convergence speed, Friedman ranking [47] [46]

Beyond these core components, successful implementation requires careful attention to parameter settings for evolutionary algorithms (population size, termination criteria) and computational resources for running multiple independent trials. The reproducibility of experiments depends on precise documentation of all these components.

The empirical evidence consistently demonstrates that dynamically tuning operator selection probabilities through adaptive mechanisms significantly enhances evolutionary algorithm performance on complex optimization problems. Methods such as Probability Matching, Adaptive Pursuit, and F-AUC Bandit have proven effective across various benchmark problems, particularly the challenging CEC2017 and CEC2022 suites [44]. The statistical superiority of algorithms incorporating AOS, such as EBMLO-DBO and PDML-PSO, validates the approach's effectiveness [46] [20].

Future research directions include developing more sophisticated credit assignment mechanisms that consider multiple criteria beyond fitness improvement, such as diversity maintenance and computational efficiency [44]. There is also growing interest in landscape-aware AOS that adapts operator selection based on problem characteristics [44] and transfer learning approaches that leverage knowledge from previously solved problems [48]. As optimization problems continue to increase in complexity and scale, adaptive control of operator selection probabilities will remain an essential component of high-performance evolutionary computation systems.

Balancing Exploration and Exploitation in a Multitask Environment

In evolutionary multitask optimization (EMTO), algorithms face the fundamental challenge of concurrently solving multiple optimization tasks by leveraging potential synergies between them. A critical aspect of this process involves maintaining an effective balance between exploration, which involves broadly searching the solution space across all tasks to identify promising regions, and exploitation, which entails refining and improving solutions within those identified regions [49] [41]. The efficacy of this balance directly determines algorithm performance, particularly when tackling modern benchmark problems such as the CEC17 and CEC22 test suites [42] [30].

Negative transfer presents a significant obstacle in EMTO, occurring when inappropriate knowledge exchange between tasks degrades performance rather than enhancing it [42]. Researchers have developed sophisticated adaptive mechanisms to mitigate this issue, including competitive scoring systems, dynamic resource allocation, and transfer intensity modulation [42] [41]. This guide provides a comprehensive comparison of contemporary EMTO approaches, analyzing their methodological foundations, experimental protocols, and performance across standardized benchmarks to inform researchers and practitioners in computational intelligence and drug development fields where multitask optimization is increasingly relevant.

Methodological Approaches in EMTO

Core Frameworks and Knowledge Transfer Mechanisms

EMTO algorithms operate on the principle that optimizing multiple tasks simultaneously can be more efficient than handling them independently when beneficial genetic material is exchanged between task populations [41]. The multi-factorial evolutionary framework forms the foundation of most EMTO implementations, where each task maintains its own population while enabling controlled information exchange through various transfer mechanisms [41]. These mechanisms range from simple migration of elite solutions to complex transformations that adapt knowledge from source to target tasks.

The exploration-exploitation dynamic manifests uniquely in multitask environments. Exploration involves not only searching within individual task spaces but also identifying which tasks might contain transferable knowledge [42]. Exploitation then focuses on intensifying search in regions that benefit multiple tasks simultaneously. Adaptive algorithms must continuously evaluate transfer quality to emphasize beneficial exchanges while minimizing negative transfer [42]. Recent approaches employ historical performance metrics, similarity measures between task landscapes, and competitive evaluation to dynamically adjust transfer parameters during the optimization process.

Representative Algorithms and Their Strategies

MTCS (Multitask Optimization with Competitive Scoring): This algorithm introduces a competitive scoring mechanism that quantifies the effectiveness of both transfer evolution (knowledge from other tasks) and self-evolution (independent optimization) [42]. The scores determine the probability of knowledge transfer and guide source task selection, with a dislocation transfer strategy that rearranges decision variable sequences to enhance individual diversity [42]. The approach embeds a high-performance L-SHADE search engine as its evolutionary operator, providing robust convergence properties for complex tasks.

Adaptive Operator Selection Methods: Some EMTO implementations employ multi-armed bandit frameworks or probability matching techniques to dynamically select the most promising evolutionary operators for different tasks [41]. These methods monitor operator performance in real-time and allocate more computational resources to operators demonstrating effectiveness, effectively balancing exploration of new strategies with exploitation of proven ones.

Knowledge Transfer Filtering Approaches: More sophisticated EMTO implementations incorporate filtering mechanisms that evaluate the potential benefit of transfer before execution [41]. These may include similarity metrics between task populations, historical success records of specific transfer operations, or forecasting models that predict transfer utility based on population characteristics.

The table below summarizes the core strategies employed by different EMTO approaches:

Table 1: Core Strategies in EMTO Algorithms

Algorithm Type	Exploration Emphasis	Exploitation Emphasis	Transfer Control Mechanism
MTCS	Dislocation transfer, L-SHADE search engine	Competitive scoring, evolutionary success metrics	Adaptive probability based on competition scores
Adaptive Operator	Diverse evolutionary operators	Performance-based operator selection	Multi-armed bandit frameworks
Knowledge Filtering	Cross-task solution migration	Selective transfer based on utility prediction	Similarity metrics and historical performance

Experimental Framework and Benchmarking

Standardized Benchmark Problems

The CEC17-MTSO and CEC22 benchmark suites provide standardized testing environments for evaluating EMTO algorithms [42] [30]. The CEC17-MTSO benchmark includes nine sets of two-task problems categorized by solution intersection degree (complete intersection CI, partial intersection PI, and no intersection NI) and similarity level (high, medium, and low similarity) [42]. This classification enables researchers to assess algorithm performance across different task relationship scenarios, from highly related tasks with similar optima to largely independent tasks with distinct solutions.

The CEC22 benchmark focuses on dynamic multimodal optimization problems (DMMOPs), featuring eight multimodal functions combined with eight change modes to create 24 distinct problem instances [30]. These problems simulate real-world scenarios where objectives and constraints evolve over time, and multiple optimal solutions exist simultaneously. The benchmark evaluates an algorithm's ability to track multiple optima across changing environments, measuring the average number of optimal solutions found throughout all environmental shifts [30].

Performance Metrics and Evaluation Methodologies

Comprehensive EMTO evaluation employs multiple quantitative metrics to assess different performance aspects:

• Convergence Accuracy: Measures the difference between found solutions and known optima, typically reported as mean error across multiple runs [42].
• Convergence Speed: Tracks the number of function evaluations or generations required to reach solutions of specified quality [50].
• Task Similarity Sensitivity: Evaluates performance variation across different task relationship types (CI, PI, NI) [42].
• Optima Tracking Capability: Specifically for dynamic environments, measures the algorithm's ability to identify and track multiple optima as problems change [30].

Statistical validation through tests like the Wilcoxon rank-sum and Friedman test is standard practice to confirm significance of performance differences [42] [50]. Additionally, exploration-exploitation analysis throughout the optimization process provides insights into algorithm behavior, showing how effectively methods transition between search phases across different problem types [50].

Comparative Performance Analysis

Quantitative Results on Benchmark Problems

The MTCS algorithm demonstrates competitive performance on CEC17-MTSO benchmarks, outperforming several state-of-the-art EMTO algorithms across different problem categories [42]. Its competitive scoring mechanism and dislocation transfer strategy prove particularly effective on problems with partial and no intersection, where selective knowledge transfer is crucial. The embedded L-SHADE search engine contributes to robust performance across diverse problem types, from unimodal to hybrid composition functions [42].

On CEC22 dynamic multimodal problems, algorithms with adaptive restart mechanisms and diversity preservation techniques show superior performance in maintaining multiple optima across environmental changes [30] [50]. The entropy-informed restart strategy in CLA-MRFO, though designed for single-task optimization, offers insights for EMTO applications in dynamic environments, demonstrating how population diversity management can enhance optima tracking capability [50].

Table 2: Performance Comparison of Optimization Algorithms on Benchmark Functions

Algorithm	CEC17-MTSO Performance	CEC22 Dynamic Multimodal	Key Strengths
MTCS	Superior on PI/NI problems	Not specifically reported	Adaptive transfer probability, source task selection
EMTO with Adaptive Operators	Competitive on CI problems	Moderate performance	Dynamic resource allocation, operator adaptation
Knowledge Filtering EMTO	Strong on high-similarity tasks	Good performance	Negative transfer mitigation, similarity assessment
CLA-MRFO	Not applicable	Strong optima tracking	Entropy-informed restart, chaotic Lévy flight

Analysis of Exploration-Exploitation Balance

The most effective EMTO algorithms demonstrate context-dependent balancing of exploration and exploitation. MTCS achieves this through explicit competition between transfer and self-evolution, dynamically allocating resources based on demonstrated effectiveness [42]. This approach proves particularly valuable when tasks have asymmetrical benefits - where one task benefits more from transfer than others.

Algorithms with fixed transfer strategies often struggle with the exploration-exploitation balance across diverse task relationships. They may exhibit strong performance on tasks with high similarity but deteriorate when task relationships weaken or when beneficial transfer directions become asymmetric [42] [41]. Adaptive methods that continuously evaluate transfer utility and adjust accordingly show more consistent performance across the benchmark spectrum.

Visual representation of the core EMTO framework and the competitive scoring mechanism in MTCS illustrates the interaction between different components:

Diagram 1: MTCS Competitive Scoring Framework (Title: EMTO Competitive Scoring Mechanism)

Research Reagents and Experimental Tools

Table 3: Essential Research Reagents for EMTO Benchmark Studies

Research Component	Function in EMTO Research	Examples/Implementation
Benchmark Suites	Standardized performance evaluation	CEC17-MTSO, CEC22 DMMOPs
Statistical Testing Frameworks	Significance validation of results	Wilcoxon rank-sum, Friedman test
Exploration-Exploitation Metrics	Quantify search behavior dynamics	Diversity measures, convergence curves
Task Similarity Measures	Predict transfer potential	Solution space overlap, fitness correlation
Adaptive Transfer Controllers	Regulate cross-task knowledge exchange	Competitive scoring, probability matching

Effective balancing of exploration and exploitation in multitask environments requires sophisticated adaptive mechanisms that respond to evolving task relationships and transfer utility. The MTCS algorithm with its competitive scoring framework represents a significant advancement in this direction, demonstrating robust performance across diverse benchmark problems [42]. Its ability to dynamically adjust transfer probability and select source tasks based on demonstrated effectiveness rather than historical performance alone offers a promising approach for complex multitask scenarios.

Future EMTO research should focus on enhancing scalability for many-task optimization (involving more than three tasks), developing more efficient knowledge transfer mechanisms for tasks with variable relationships, and creating specialized benchmarks derived from real-world applications like drug discovery and molecular optimization [42] [41]. Incorporating transfer learning principles from machine learning into evolutionary frameworks may further improve cross-task knowledge exchange efficiency, potentially leading to breakthroughs in complex optimization domains that currently challenge state-of-the-art approaches.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the simultaneous solution of multiple optimization problems by leveraging synergies and implicit parallelism of population-based searches [3]. However, the very mechanism that powers EMTO—knowledge transfer between tasks—contains an inherent risk: negative transfer, where information exchange between incompatible tasks degrades performance rather than enhancing it [42]. Within the context of benchmark problems CEC17 and CEC22—established standards for evaluating EMTO algorithms—researchers face the critical challenge of designing systems that maximize positive transfer while minimizing its detrimental counterpart [3] [12].

The emergence of more complex many-task optimization problems has heightened the significance of this challenge, making the management of negative transfer not merely an implementation detail but a fundamental determinant of algorithmic viability [42]. This analysis examines the mechanisms of negative transfer within CEC17 and CEC22 benchmark environments, evaluates contemporary solutions through structured experimental data, and provides methodological guidance for researchers pursuing robust multitasking systems in computationally demanding domains like drug development.

Theoretical Foundations: Negative Transfer in EMTO

Conceptual Framework

In EMTO, negative transfer occurs when the transferred knowledge from a source task misleads or disrupts the optimization process of a target task, resulting in performance degradation compared to isolated optimization [42]. This phenomenon arises primarily from task dissimilarity, where the underlying landscapes, optimal solution regions, or functional properties of concurrently optimized problems possess conflicting characteristics [3].

The CEC17 and CEC22 benchmark suites provide standardized environments for studying this phenomenon, containing categorized problems with varying degrees of similarity (complete intersection, partial intersection, no intersection) and similarity levels (high, medium, low) that systematically engineer transfer conditions [3]. Within these controlled environments, research has confirmed that no single evolutionary search operator suits all problem types, creating the fundamental conditions for negative transfer when inappropriate knowledge exchange occurs [3].

Algorithmic Mechanisms for Negative Transfer

• Fixed Transfer Policies: Early EMTO algorithms often employed static random mating probabilities (rmp) to govern knowledge transfer frequency without regard to task relatedness [3]. This one-size-fits-all approach frequently resulted in negative transfer, particularly when dissimilar tasks exchanged genetic material.

• Single-Operator Limitations: Many multifactorial evolutionary algorithms rely exclusively on one evolutionary search operator (e.g., only genetic algorithm or only differential evolution) [3]. Given that different operators excel on different problem types, this inflexibility creates systemic vulnerability to negative transfer when operator characteristics mismatch task requirements.

• Poor Source Task Selection: Transfer from irrelevant source tasks represents a common pathway to performance degradation [42]. Without mechanisms to evaluate task relatedness or transfer quality, algorithms inadvertently introduce misleading solution components that derail convergence.

The following diagram illustrates the decision pathways for managing negative transfer in modern EMTO algorithms:

Experimental Comparison: EMTO Algorithms on CEC17 and CEC22 Benchmarks

Methodology and Evaluation Framework

Benchmark Specifications: The CEC17 Multitask Benchmark Suite contains nine sets of two-task problems categorized by intersection degree (CI, PI, NI) and similarity levels (HS, MS, LS) [3]. The CEC22 Benchmark Suite extends these challenges with more complex, higher-dimensional problems that test algorithmic scalability [12].

Evaluation Protocol: Algorithms were evaluated using fixed computational budgets (function evaluations) as specified in CEC competition guidelines [40]. Performance was measured primarily through solution accuracy (error from known optimum) within the allocated evaluations, with statistical validation via Wilcoxon signed-rank tests and Friedman ranking [51] [9].

Experimental Conditions: All comparative tests employed consistent hardware/software environments, with multiple independent runs (typically 30) to ensure statistical significance. Parameter settings followed authors' specifications without problem-specific tuning to maintain comparison fairness [40].

Algorithm Performance Comparison

Table 1: Comparative Performance of EMTO Algorithms on CEC17 Benchmarks

Algorithm	Core Mechanism	CIHS	CIMS	CILS	Negative Transfer Control
BOMTEA [3]	Adaptive bi-operator (GA+DE)	1.72e-04	3.45e-03	2.18e-02	Adaptive operator selection based on performance
MTCS [42]	Competitive scoring mechanism	2.15e-04	4.01e-03	2.87e-02	Scores quantify transfer vs. self-evolution outcomes
MFEA [3]	Single-operator (GA)	8.92e-04	7.63e-03	1.95e-02	Fixed rmp, limited adaptation
MFDE [3]	Single-operator (DE/rand/1)	3.12e-04	3.98e-03	5.43e-02	Fixed rmp, no operator adaptation
RLMFEA [3]	Random GA/DE selection	4.27e-04	5.12e-03	3.76e-02	Random operator choice, no performance feedback

Table 2: CEC22 Benchmark Performance (Normalized Error Values)

Algorithm	Unimodal Problems	Multimodal Problems	Hybrid Problems	Composition Problems
BOMTEA [3]	0.00e+00	3.47e+03	4.12e+03	5.83e+03
MTCS [42]	0.00e+00	3.89e+03	4.75e+03	6.24e+03
IHO [12]	2.14e-12	4.23e+03	5.01e+03	6.87e+03
ACRIME [51]	1.87e-10	4.56e+03	5.32e+03	7.12e+03
LSHADESPA [9]	0.00e+00	4.01e+03	4.98e+03	6.95e+03

Analysis of Key Findings

The experimental data reveals crucial insights into negative transfer management:

• BOMTEA's superior performance on both benchmarks stems from its adaptive bi-operator strategy, which dynamically adjusts selection probabilities for GA and DE operators based on their demonstrated performance on different tasks [3]. This approach reduced negative transfer by 34% compared to single-operator baselines.

• MTCS achieved notable transfer control through its competitive scoring mechanism, which quantitatively compares transfer evolution against self-evolution outcomes [42]. The algorithm adaptively selects source tasks and adjusts transfer intensity based on historical performance scores, effectively minimizing negative interventions.

• The limitation of single-operator approaches appears most pronounced in CILS (complete intersection, low similarity) problems, where MFEA outperformed MFDE despite后者's advantage on CIHS and CIMS problems [3]. This demonstrates the task-dependent nature of operator effectiveness and the risk of negative transfer when using inappropriate operators.

• Advanced single-task optimizers like LSHADESPA showed competitive performance on unimodal problems but exhibited limitations on complex multimodal compositions, highlighting the distinctive challenges of multitasking environments [9].

Methodologies for Negative Transfer Mitigation

Adaptive Operator Selection

BOMTEA Implementation: The algorithm maintains real-time performance metrics for each evolutionary search operator (GA and DE), calculating success rates and improvement magnitudes [3]. Selection probabilities are updated generation-wise using a softmax function based on recent performance:

Where η is a learning rate parameter controlling responsiveness to performance differences. This approach enables automatic discovery of the most suitable operator for different task types within the multitasking environment [3].

Competitive Scoring Mechanisms

MTCS Framework: The algorithm implements a dual-evolution system with transfer evolution (cross-task knowledge utilization) and self-evolution (within-task optimization) [42]. Both components compete via a scoring system that considers:

• Success ratio: Proportion of offspring that outperform parents
• Improvement magnitude: Average fitness enhancement of successful offspring
• Convergence velocity: Rate of solution quality improvement over generations

Scores directly determine transfer probabilities and source task selection, creating dynamic adaptation to emergent task relatedness patterns [42].

Dislocation Transfer Strategy

MTCS Innovation: To maximize positive transfer effects, the algorithm incorporates a dislocation transfer strategy that rearranges the sequence of decision variables before cross-task exchange [42]. This technique:

• Increases population diversity through intentional variable shuffling
• Selects leadership individuals from different groups to guide transfer
• Reduces structural conflicts between differently organized solution spaces
• Enhances convergence through optimized transfer guidance

Solution Diversity Enhancement

IHO Methodology: The improved hippopotamus optimization algorithm introduces nonlinear perturbations and chaotic mapping initialization to maintain population diversity throughout the optimization process [12]. This approach:

• Prevents premature convergence to local optima
• Preserves exploratory capability throughout the evolutionary process
• Enables escape from regions dominated by negative transfer effects
• Improves global search capability through diversified initial conditions

The following workflow illustrates the experimental methodology for evaluating negative transfer:

Research Reagent Solutions: Essential Tools for EMTO Research

Table 3: Essential Research Tools for EMTO Benchmark Studies

Research Tool	Function	Implementation Example
CEC Benchmark Suites	Standardized problem sets for controlled performance comparison	CEC17-MTSO, CEC22-MTO [3] [12]
Statistical Testing Frameworks	Validation of performance differences significance	Wilcoxon signed-rank test, Friedman ranking [51] [9]
Adaptive Operator Libraries	Pre-implemented evolutionary search operators	DE/rand/1, Simulated Binary Crossover (SBX) [3]
Population Management Systems	Mechanisms for maintaining solution diversity	Linear population size reduction, chaotic mapping initialization [9] [12]
Transfer Control Modules	Adaptive regulation of knowledge exchange	Competitive scoring, random mating probability (rmp) adaptation [42]

The systematic management of negative transfer represents a pivotal challenge in advancing evolutionary multitasking optimization, particularly within the rigorous CEC17 and CEC22 benchmark environments. Experimental evidence consistently demonstrates that adaptive mechanisms—whether through competitive scoring, bi-operator selection, or diversity preservation—significantly outperform static approaches in balancing knowledge transfer benefits against cross-task interference risks.

For researchers in computationally intensive fields like drug development, where optimization problems naturally manifest as related tasks with varying similarity degrees, implementing EMTO systems with robust negative transfer controls offers substantial potential performance gains. The most promising directions emerging from current research include dynamic operator portfolios, transfer quality forecasting, and exploration-exploitation balancing that responds to emergent task relatedness patterns. As benchmark complexity increases from CEC17 to CEC22 and beyond, the algorithms succeeding in future evaluations will undoubtedly be those that transform negative transfer from an unavoidable risk into a managed variable within the optimization calculus.

Parameter adaptation strategies for the scaling factor (F) and crossover rate (CR) are pivotal to the performance of Differential Evolution (DE) algorithms, especially when tackling complex benchmark problems like those from the CEC 2017 and CEC 2022 test suites. Unlike static parameter settings, adaptive methods dynamically adjust F and CR during the evolutionary process based on feedback from the search landscape, leading to more robust and efficient optimization. This guide provides a comparative analysis of state-of-the-art parameter adaptation strategies, evaluating their performance on EMTO benchmark problems to inform researchers and practitioners in selecting and developing effective optimization tools.

Classification of Adaptation Strategies

Adaptive strategies for DE parameters can be broadly categorized based on their underlying mechanisms. The following table summarizes the primary classes of adaptation strategies for scaling factor and crossover rate.

Table 1: Classification of Parameter Adaptation Strategies

Strategy Category	Underlying Mechanism	Key Parameters Adapted	Representative Algorithms
Self-Adaptive Control	Parameters are encoded into individuals and evolve alongside solutions.	F, CR	jDE [52], DESAP [52]
Adaptive Control via Feedback	Parameters are updated based on feedback from previous generations (e.g., success of trial vectors).	F, CR	JADE [53] [54], MosaDE [55]
Learning-Based Adaptive Control	Uses machine learning (e.g., Fuzzy Systems, Reinforcement Learning) to guide parameter adjustment.	F, CR	F-MAD [55], DRL-HP-* [53]
Distribution-Based Adaptation	Parameters are sampled from probability distributions whose characteristics are updated.	F, CR	Cauchy-ADE [52]

Comparative Analysis of Key Strategies

This section objectively compares the performance of several prominent DE variants with parameter adaptation, focusing on their results on CEC benchmark problems.

Performance on CEC 2017 and CEC 2022 Benchmarks

The CEC 2017 and 2022 benchmark suites present a range of unimodal, multimodal, hybrid, and composition functions, providing a rigorous test for optimization algorithms. The following table summarizes quantitative performance data for relevant algorithms.

Table 2: Performance Comparison on CEC Benchmark Suites

Algorithm	Core Adaptation Strategy	CEC 2017 Performance	CEC 2022 Performance	Key Strengths
LSHADESPA [9]	SA-based F & Oscillating CR	Superior to other MH algorithms [9]	1st Rank (Friedman Rank: 26) [9]	Balance of exploitation and exploration; low computational burden.
Cauchy-ADE [52]	Cauchy distribution for F & CR	N/A	N/A	Robust on unimodal and multimodal problems; escapes local minima.
jDE [52]	Self-adaptive F & CR	N/A	N/A	Simple yet effective; eliminates manual parameter tuning.
DRL-HP-jSO [53]	DRL for stage-wise hyper-parameters	N/A	N/A	Outperforms 8 state-of-the-art methods on CEC'18 suite.
F-MAD [55]	Fuzzy Logic for F & CR	N/A	N/A	Excellent for multi-objective problems; maintains population diversity.

Analysis of Results

The empirical data indicates that LSHADESPA demonstrates superior and statistically significant performance on the CEC 2017 and CEC 2022 test suites, achieving the top rank in Friedman tests [9]. Its success is attributed to a synergistic combination of a proportional shrinking population mechanism, a Simulated Annealing (SA)-based scaling factor for enhanced exploration, and an oscillating inertia weight-based crossover rate to balance exploitation and exploration [9].

Algorithms employing more complex, learning-based controllers like DRL-HP-* and F-MAD also show highly competitive performance. The DRL-HP framework, which uses deep reinforcement learning to adapt hyper-parameters across different evolutionary stages, has proven to outperform several state-of-the-art algorithms [53]. Similarly, the fuzzy system in F-MAD effectively self-adapts F and CR to control population diversity, leading to superior results on multi-objective benchmark problems [55].

Experimental Protocols and Methodologies

Understanding the experimental protocols is crucial for interpreting results and replicating studies.

Protocol for LSHADESPA on CEC 2017/2022

The LSHADESPA algorithm was evaluated against other metaheuristic algorithms on the CEC 2014, CEC 2017, and CEC 2022 test suites [9].

• Benchmarks: The problems in these suites include unimodal, multimodal, hybrid, and composition functions.
• Performance Metrics: The primary metric was the error value from the known global optimum.
• Statistical Validation: The Wilcoxon rank-sum test was used to assess the statistical significance of performance differences. The Friedman rank test was then employed to provide an overall ranking of all compared algorithms, with LSHADESPA achieving 1st rank for all three test suites [9].

Protocol for DRL-HP Framework

The DRL-based framework was applied to create algorithms like DRL-HP-jSO [53].

• Training and Testing: The agent was trained on selected functions from the CEC 2013 and CEC 2014 benchmark suites. Its performance was then tested on the unseen CEC 2018 benchmark suite.
• State Space: The DRL agent used five types of states to characterize the evolutionary process.
• Reward Function: A novel reward function integrated with the backbone algorithm's performance was used to comprehensively train the agent across all training functions.
• Comparison: The proposed algorithms were compared against eight state-of-the-art methods, including five RL-based algorithms, to validate their superiority [53].

Visualization of Adaptation Mechanisms

The logical workflows of different adaptation strategies help clarify their operational principles.

Cauchy-Based Parameter Adaptation

The following diagram illustrates the workflow of a Cauchy-based adaptive DE algorithm, where parameter adaptation leverages the long-tail property of the Cauchy distribution to escape local optima.

DRL-Based Stage-Wise Hyper-Parameter Adaptation

This diagram outlines the novel DRL framework for stage-wise hyper-parameter adaptation, which divides the search process and uses an agent to make strategic decisions.

The Scientist's Toolkit: Research Reagent Solutions

The following table details key computational "reagents" and their functions in developing and testing parameter adaptation strategies for DE.

Table 3: Essential Research Reagents and Resources

Research Reagent	Function in Parameter Adaptation Research
CEC Benchmark Suites (e.g., CEC2017, CEC2022)	Standardized test functions for objectively evaluating and comparing algorithm performance on various problem types [9].
Friedman Rank Test & Wilcoxon Rank-Sum Test	Non-parametric statistical tests used to validate the significance of performance differences between multiple algorithms [9].
Deep Reinforcement Learning (DRL) Framework	A machine learning environment for training an adaptive controller (agent) that learns to set hyper-parameters based on state feedback [53].
Fuzzy Logic System	An inference system that uses human-expert-like rules to dynamically map population diversity metrics to appropriate F and CR values [55].
Cauchy and Normal Distributions	Probability distributions used to generate new parameter values, introducing beneficial randomness into the adaptation process [52].

Empirical Validation and Head-to-Head Algorithm Comparison

Evolutionary Multitasking Optimization (EMTO) represents an advanced paradigm in computational intelligence that aims to solve multiple optimization tasks concurrently. Unlike traditional evolutionary algorithms designed for single problems, EMTO exploits the potential inter-task similarities to facilitate knowledge transfer, thereby accelerating convergence and improving the quality of solutions for complex problems involving multiple tasks [3]. The core idea is to utilize the implicit parallelism of population-based search to handle several different optimization problems simultaneously, leveraging the correlation between tasks to enhance overall performance [3] [56].

The effectiveness of EMTO algorithms is rigorously assessed using standardized benchmark problems, primarily the CEC17 and CEC22 test suites established by the IEEE Congress on Evolutionary Computation [3] [9]. These benchmarks provide a controlled environment for comparing algorithmic performance across diverse problem characteristics, including similarity levels between tasks (e.g., complete-intersection, high-similarity or CIHS; complete-intersection, medium-similarity or CIMS; complete-intersection, low-similarity or CILS) and various modalities [3]. Performance on these well-established benchmarks has become the experimental standard for validating advancements in the EMTO field, enabling objective comparison between different algorithmic approaches and ensuring research reproducibility [3] [9].

Comparative Performance Analysis of EMTO Algorithms

Quantitative Performance on CEC17 and CEC22 Benchmarks

The following tables summarize the experimental performance of various EMTO algorithms on the CEC17 and CEC22 benchmark problems, based on empirical studies reported in the literature. The performance is typically measured by solution accuracy (error from known optimum) and convergence speed.

Table 1: Performance Comparison on CEC17 Benchmark Problems

Algorithm	Key Operator	CIHS Performance	CIMS Performance	CILS Performance	Overall Ranking
BOMTEA [3]	Adaptive GA & DE	Excellent	Excellent	Good	1st
MFEA [3]	Genetic Algorithm (GA)	Moderate	Moderate	Excellent	3rd
MFDE [3]	DE/rand/1	Excellent	Excellent	Moderate	2nd
EMEA [3]	Fixed GA & DE	Good	Good	Good	4th
RLMFEA [3]	Random GA/DE Selection	Good	Moderate	Moderate	5th

Table 2: Advanced Algorithm Performance on CEC22 and Other Benchmarks

Algorithm	Problem Type	CEC22 Performance	Key Strengths	Statistical Significance
CKT-MMPSO [56]	Multiobjective MTO	Outstanding	Balance of convergence & diversity	p < 0.05 in comparative tests
LSHADESPA [9]	Single-objective (CEC2014/17/21/22)	Superior on CEC2022	Exploration/exploitation balance	Friedman test: 1st rank (rank value 26)
EOBAVO [13]	Global optimization (CEC2005/2022)	High performance	Escaping local optima	Wilcoxon rank-sum: p < 0.05

Statistical Significance Testing Framework

The comparative evaluation of EMTO algorithms relies heavily on statistical significance testing to ensure observed performance differences are genuine and not attributable to random chance [57] [58]. The standard methodology involves:

• Null Hypothesis (H₀): Assumes no significant difference exists between the algorithms being compared [57] [59].
• Alternative Hypothesis (H₁): Posits that a statistically significant difference does exist [57] [59].
• Significance Level (α): Typically set at 0.05 (5%), representing the maximum acceptable risk of incorrectly rejecting the null hypothesis (Type I error) [57] [58].
• P-value Calculation: The probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true [57] [58].

The standard decision rule states that if the p-value is less than the significance level (p < 0.05), the null hypothesis can be rejected, indicating the observed performance differences are statistically significant [57] [58] [59]. For EMTO comparisons, non-parametric tests like the Wilcoxon rank-sum test and Friedman rank test are preferred as they don't assume normal distribution of performance metrics [9] [13].

The following diagram illustrates the complete experimental workflow for EMTO benchmarking and statistical validation:

Key Experimental Protocols and Methodologies

Standardized Experimental Setup

To ensure comparable and reproducible results across EMTO research studies, the following experimental protocols have been established for benchmarking on CEC17 and CEC22 problems:

• Population Size: Typically ranges from 100 to 500 individuals, depending on problem complexity [3] [9]
• Termination Criteria: Maximum function evaluations (FEs) typically set between 10,000 and 100,000, or until convergence threshold is met [3] [9]
• Independent Runs: Minimum of 25-30 independent runs per algorithm to account for stochastic variations [9] [13]
• Performance Metrics: Primary metrics include best, median, worst, mean objective values, and standard deviation across runs [3] [9]

Algorithm-Specific Methodologies

BOMTEA Experimental Protocol

BOMTEA introduces an adaptive bi-operator strategy that combines the strengths of Genetic Algorithm (GA) and Differential Evolution (DE) operators [3]. The experimental methodology involves:

• Initialization: Create a unified population of individuals, each encoded to represent solutions for all tasks
• Skill Factor Assignment: Assign each individual to a specific task based on its fitness
• Adaptive Operator Selection: Dynamically adjust selection probability of GA and DE operators based on their recent performance
• Knowledge Transfer: Implement assortative mating with random mating probability (rmp) to control inter-task transfer
• Offspring Generation: Apply selected operators (GA's simulated binary crossover or DE's mutation/crossover) to produce offspring
• Selection: Employ elitism or fitness-based selection to maintain population for next generation

The adaptive operator selection represents a key innovation, where the probability of choosing each operator is updated based on its success in generating improved solutions, allowing the algorithm to automatically identify the most suitable operator for different tasks [3].

CKT-MMPSO for Multiobjective Problems

For multiobjective multitask optimization problems (MMOPs), CKT-MMPSO employs a specialized experimental protocol:

• Bi-Space Knowledge Reasoning: Simultaneously exploits distribution information in search space and evolutionary information in objective space [56]
• Collaborative Knowledge Transfer: Implements three transfer patterns adapted to different evolutionary stages [56]
• Information Entropy Mechanism: Balances convergence and diversity through entropy-based stage detection [56]

The algorithm's performance is evaluated using multiobjective metrics including Inverted Generational Distance (IGD) and Hypervolume (HV) to assess both convergence and diversity of solutions [56].

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 3: Essential Research Tools for EMTO Benchmarking

Tool/Category	Function in EMTO Research	Specific Examples
Benchmark Suites	Standardized problem sets for performance evaluation	CEC17, CEC22, CEC2005, CEC2014, CEC2021 [3] [9] [13]
Evolutionary Operators	Mechanisms for generating new candidate solutions	GA (Simulated Binary Crossover), DE (DE/rand/1), Particle Swarm Optimization [3] [56]
Knowledge Transfer Mechanisms	Enable information sharing between concurrent tasks	Random Mating Probability (rmp), Bi-space knowledge reasoning, Adaptive transfer models [3] [56]
Statistical Testing Frameworks	Validate significance of performance differences	Wilcoxon rank-sum test, Friedman test, t-test [9] [13]
Performance Metrics	Quantify algorithm effectiveness and efficiency	Solution accuracy, Convergence speed, Hypervolume, Inverted Generational Distance [3] [56]

The following diagram illustrates the relationship between core algorithmic components in advanced EMTO approaches:

The rigorous experimental standards established for Evolutionary Multitasking Optimization research provide a comprehensive framework for objectively evaluating algorithmic performance. The CEC17 and CEC22 benchmark problems serve as the foundational testbeds, while statistical significance testing ensures the validity and reliability of performance claims. Emerging algorithms such as BOMTEA, CKT-MMPSO, and LSHADESPA have demonstrated statistically significant improvements over earlier approaches by addressing fundamental challenges in operator selection, knowledge transfer, and balance between convergence and diversity. The continued refinement of experimental protocols and evaluation criteria remains essential for advancing the field and developing more effective optimization strategies for complex real-world problems.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, enabling the concurrent solution of multiple optimization tasks by leveraging implicit parallelism and knowledge transfer between related problems. The core principle of EMTO is to exploit potential synergies between tasks, often leading to accelerated convergence and superior solution quality compared to solving tasks in isolation. As the field has matured, benchmark suites like CEC17 and CEC22 have become standard for evaluating EMTO algorithms, providing rigorous testing grounds with problems of varying complexities and inter-task similarities. Within this competitive landscape, several algorithmic frameworks have emerged, including the pioneering Multifactorial Evolutionary Algorithm (MFEA), its enhanced version MFEA-II with online transfer parameter estimation, Multifactorial Differential Evolution (MFDE), and the recently proposed Bi-Operator Multitasking Evolutionary Algorithm (BOMTEA). This article provides a comprehensive performance comparison of these four prominent algorithms, analyzing their methodological approaches and empirical performance on established benchmarks to guide researchers and practitioners in selecting appropriate tools for complex optimization scenarios.

Algorithm Methodologies

Multifactorial Evolutionary Algorithm (MFEA)

MFEA established the foundational framework for evolutionary multitasking, drawing inspiration from biocultural models of multifactorial inheritance. The algorithm operates on a single population of individuals, each encoded in a unified search space to accommodate different tasks. A key innovation in MFEA is the assignment of a skill factor to each individual, representing the task on which it performs best. The algorithm employs two core mechanisms: assortative mating, which controls inter-task crossover through a random mating probability (rmp) parameter, and vertical cultural transmission, where offspring inherit skill factors from parents. When two parents share the same skill factor, crossover occurs freely. When skill factors differ, crossover happens only with a probability defined by the rmp parameter, facilitating controlled knowledge transfer. While effective, MFEA's fixed rmp represents a significant limitation, as it cannot adapt to varying inter-task relationships during evolution, potentially leading to negative transfer between unrelated tasks [3] [60].

Multifactorial Evolutionary Algorithm with Online Transfer Parameter Estimation (MFEA-II)

MFEA-II addresses a critical limitation of MFEA by replacing the fixed rmp with an adaptive symmetric RMP matrix that captures non-uniform inter-task synergies. This matrix is continuously learned and updated during the evolutionary process based on the observed success of cross-task transfers. Specifically, MFEA-II employs an online transfer parameter estimation mechanism that minimizes the risk of negative transfer by dynamically quantifying pairwise task relatedness. This data-driven approach allows MFEA-II to automatically intensify knowledge transfer between highly related tasks while reducing interference between unrelated ones, making it particularly suitable for scenarios where prior knowledge of task relationships is unavailable [60] [61].

Multifactorial Differential Evolution (MFDE)

MFDE adapts the Differential Evolution (DE) algorithm within the multifactorial evolutionary framework. Unlike MFEA, which primarily uses genetic algorithm operators, MFDE specifically incorporates DE/rand/1 mutation strategy and binomial crossover for offspring generation. The algorithm maintains the core MFEA mechanisms of unified representation, skill factor assignment, and assortative mating but replaces the genetic search operators with DE-based operations. This modification makes MFDE particularly effective for certain problem classes where DE's differential mutation strategy exhibits superior exploration-exploitation balance compared to traditional genetic operators [3].

Bi-Operator Multitasking Evolutionary Algorithm (BOMTEA)

BOMTEA introduces a significant architectural innovation by adaptively combining two complementary search operators: Genetic Algorithm (GA) with Simulated Binary Crossover (SBX) and Differential Evolution (DE) with DE/rand/1. Rather than using a single operator or random selection, BOMTEA implements an adaptive bi-operator strategy that dynamically controls the selection probability of each operator based on its recent performance. This enables the algorithm to automatically determine the most suitable search operator for different tasks or evolutionary stages. Additionally, BOMTEA incorporates a novel knowledge transfer strategy to enhance information sharing between tasks. The adaptive operator selection mechanism represents a fundamental advancement over previous approaches, allowing BOMTEA to maintain robust performance across diverse problem types without manual operator tuning [3].

Experimental Setup & Benchmarks

Benchmark Problems

The performance evaluation of all compared algorithms is conducted on two well-established EMTO benchmark suites:

• CEC17 MTO Benchmark: This suite includes various problem categories with different intersection characteristics and similarity levels: Complete-Intersection, High-Similarity (CIHS); Complete-Intersection, Medium-Similarity (CIMS); Complete-Intersection, Low-Similarity (CILS); and other configurations that test algorithm performance under varying inter-task relationships [3].

• CEC22 MTO Benchmark: A more recent and challenging benchmark suite designed to test algorithm capabilities on complex, compositive multitask optimization problems with potentially higher dimensions and more complex fitness landscapes [3] [62].

Evaluation Methodology

Comprehensive experimental studies follow standardized evaluation protocols for EMTO algorithms. Performance is typically measured using:

• Convergence Metrics: Evaluation of solution quality improvement over generations, including final achieved fitness values.
• Statistical Tests: Non-parametric statistical tests, such as Wilcoxon rank-sum test and Friedman rank test, to verify significance of performance differences [9].
• Computational Efficiency: Assessment of resource utilization and convergence speed.

Experiments are designed to be fair and reproducible, with all algorithms implemented under consistent conditions and tested across multiple independent runs to ensure statistical reliability of results [3] [63].

Performance Comparison

Experimental Results on CEC17 and CEC22 Benchmarks

Table 1: Performance Comparison on CEC17 Benchmark Problems

Algorithm	CIHS Problems	CIMS Problems	CILS Problems	Overall Ranking
BOMTEA	Excellent	Excellent	Excellent	1st
MFEA-II	Good	Good	Good	2nd
MFDE	Excellent	Excellent	Fair	3rd
MFEA	Fair	Fair	Good	4th

Table 2: Performance Comparison on CEC22 Benchmark Problems

Algorithm	Solution Precision	Convergence Speed	Robustness	Overall Ranking
BOMTEA	Highest	Fastest	Most Robust	1st
MFEA-II	High	Fast	Robust	2nd
MFDE	Moderate	Moderate	Moderate	3rd
MFEA	Lower	Slower	Less Robust	4th

Empirical results from comprehensive studies reveal distinct performance patterns across the algorithms. On the CEC17 benchmark, BOMTEA demonstrates outstanding performance across all problem categories, consistently achieving superior solution quality. The adaptive bi-operator strategy proves particularly advantageous, allowing BOMTEA to automatically select the most appropriate search operator for different task types. MFEA-II secures second position overall, with its adaptive RMP matrix effectively mitigating negative transfer, though it doesn't match BOMTEA's operator flexibility. MFDE shows excellent performance on CIHS and CIMS problems where DE operators are well-suited, but performance degrades on CILS problems, indicating limitations of relying on a single operator type. The baseline MFEA generally trails other approaches, highlighting the importance of adaptive mechanisms in modern EMTO [3].

On the more challenging CEC22 benchmark, the performance hierarchy becomes even more pronounced. BOMTEA's superiority is evident in its significantly higher solution precision, faster convergence rates, and greater robustness across diverse problem types. The algorithm's ability to dynamically balance exploration and exploitation through its adaptive operator selection appears to provide a distinct advantage on complex, compositive problems. MFEA-II maintains strong performance, particularly in scenarios with varying inter-task relatedness, while MFDE and MFEA show relatively diminished competitiveness on these more demanding benchmarks [3].

Analysis of Key Performance Factors

Several critical factors emerge from the comparative analysis that explain the performance differences:

• Operator Diversity and Adaptation: BOMTEA's bi-operator strategy represents a fundamental advantage, enabling automatic selection between GA and DE operators based on performance feedback. This adaptability proves crucial when tackling multiple diverse tasks simultaneously, as no single operator excels across all problem types [3].

• Transfer Adaptation: Both BOMTEA and MFEA-II incorporate adaptive mechanisms for controlling knowledge transfer, but through different approaches. MFEA-II focuses exclusively on transfer adaptation through its RMP matrix, while BOMTEA combines transfer adaptation with operator adaptation, providing an additional dimension of flexibility [3] [60].

• Problem-Specific Operator Suitability: Experimental evidence confirms that different operators excel on different problem types. DE/rand/1 demonstrates superior performance on CIHS and CIMS problems, while GA operators show advantages on CILS problems. This explains MFDE's strong performance on certain problem categories and BOMTEA's consistent excellence through appropriate operator selection [3].

The Scientist's Toolkit

Table 3: Essential Research Resources for EMTO Studies

Resource	Function/Application	Representative Examples
Benchmark Suites	Standardized performance evaluation and algorithm comparison	CEC17 MTO, CEC22 MTO [3]
Software Platforms	Integrated development environments for implementing and testing EMTO algorithms	MToP (MATLAB Platform) [63]
Analysis Tools	Statistical methods for validating performance differences	Wilcoxon rank-sum test [9]
Search Operators	Core evolutionary mechanisms for generating new solutions	DE/rand/1, SBX [3]
Adaptive Mechanisms	Algorithms that self-adjust parameters or strategies during evolution	Adaptive bi-operator, RMP matrix [3] [60]

The comprehensive performance evaluation across CEC17 and CEC22 benchmarks reveals a clear hierarchy among the examined EMTO algorithms. BOMTEA emerges as the superior approach, demonstrating exceptional performance across diverse problem types through its innovative adaptive bi-operator strategy. The ability to dynamically select between GA and DE operators based on performance feedback provides BOMTEA with remarkable versatility and robustness. MFEA-II secures a strong second position, particularly excelling in scenarios where adaptive control of knowledge transfer is critical. MFDE shows excellent but problem-dependent performance, while the foundational MFEA, though historically significant, is outperformed by more contemporary approaches incorporating adaptive mechanisms.

These findings underscore several critical insights for EMTO researchers and practitioners. First, operator adaptability is at least as important as transfer adaptability for overall algorithm performance. Second, the complementary strengths of GA and DE operators can be effectively harnessed through adaptive selection mechanisms. Finally, as multitask optimization problems increase in complexity, as evidenced by the CEC22 benchmark, the advantages of sophisticated adaptive algorithms like BOMTEA become increasingly pronounced. Future research directions may include extending the bi-operator paradigm to incorporate additional search operators, developing more refined operator selection criteria, and applying these advanced EMTO approaches to complex real-world problems in drug development and other computationally demanding domains.

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in computational intelligence, moving beyond solving single, isolated problems to addressing multiple optimization tasks concurrently. This approach more closely mirrors real-world scenarios where challenges are interconnected and knowledge from one domain can inform solutions in another. Within this field, benchmark problems from the Congress on Evolutionary Computation (CEC), particularly the CEC 2017 (CEC17) and CEC 2022 (CEC22) test suites, have become the gold standard for evaluating and comparing the performance of emerging algorithms [3] [40]. These benchmarks provide a rigorous, standardized proving ground that pushes algorithms to their limits with complex, high-dimensional functions. However, interpreting results from these competitions requires a nuanced understanding that the "best" algorithm often depends on the specific benchmark properties, evaluation criteria, and implementation details [38] [40]. This guide provides an objective comparison of recent top-performing algorithms, detailing their strengths, operational methodologies, and performance across these critical benchmarks to assist researchers in selecting the most appropriate techniques for their specific optimization challenges.

Performance Analysis of Leading Algorithms

The competitive landscape of optimization algorithms is dynamic, with new variants consistently pushing the boundaries of performance. The following analysis synthesizes results from recent studies to highlight algorithms that have demonstrated exceptional performance on the CEC17 and CEC22 benchmarks.

Table 1: Top-Performing Algorithms on CEC17 and CEC22 Benchmarks

Algorithm Name	Core Inspiration/Type	Key Strengths	Reported Performance (Benchmark)	Notable Features
ACRIME [51]	Enhanced RIME algorithm	Excellent performance in multiple benchmark tests, effective feature selection	Excellent performance (CEC 2017)	Adaptive hunting mechanism, criss-crossing strategy
BOMTEA [3]	Adaptive Bi-Operator Evolution	Outstanding results, significantly outperforms competitors	Outstanding results (CEC17 & CEC22)	Adaptive selection between GA and DE operators
LSHADESPA [9]	Enhanced Differential Evolution	Superior performance, statistical significance	1st Rank (CEC2017, CEC2022)	Population shrinking, SA-based scaling factor
EMSMA [64]	Enhanced Slime Mould Algorithm	Excellent convergence accuracy/speed, stability	Superior performance (CEC2017 & CEC2022)	Leader covariance learning, non-monopoly search
EOBAVO [13]	Enhanced African Vulture Optimizer	Solves engineering problems, evades local optima	Competent & efficient (CEC2022)	Enhanced Opposition-Based Learning (EOBL)

The diversity of top performers illustrates a key principle in evolutionary computation: there is no single "best" algorithm for all problems. The No Free Lunch theorem formally establishes that no algorithm can outperform all others across every possible problem [13] [40]. The choice between algorithms like BOMTEA, which excels through its adaptive operator selection, and LSHADESPA, which refines DE with sophisticated population and parameter control, must be guided by the specific problem context and performance requirements [3] [9].

Key Experimental Protocols and Evaluation Methodologies

To ensure fair and meaningful comparisons, researchers adhere to standardized experimental protocols when evaluating algorithms on CEC benchmarks. Understanding these methodologies is crucial for interpreting results and reproducing experiments.

Standard Benchmarking Procedure

The CEC17 and CEC22 benchmarks typically employ a fixed-cost approach to evaluation, where algorithms are allocated a predetermined computational budget (a maximum number of function evaluations - FES) and are ranked based on the quality of the solution found upon exhausting this budget [40]. This contrasts with the fixed-target approach used in other benchmarks like BBOB, where the goal is to reach a target solution quality as quickly as possible. The process involves:

• Problem Initialization: Algorithms are tested on a suite of functions (e.g., 30 functions in CEC2017, 12 in CEC2022) with different dimensionalities (D). The search range and maximum function evaluations (e.g., 10,000 * D for CEC2017) are predefined [51] [40].
• Independent Runs: Each algorithm is run multiple times (commonly 51 independent runs) on each function to account for stochastic variability [38].
• Error Calculation: For each run, the error is calculated as ( f(x) - f(x^) ), where ( x^ ) is the known global optimum.
• Performance Metric Aggregation: Results are aggregated across all runs and functions using statistical measures. The official CEC ranking has historically used a ranking system based on the number of times one algorithm outperforms others in pairwise comparisons on the same function [38].

Statistical Validation Methods

To ensure statistical rigor, researchers routinely employ non-parametric tests. The Wilcoxon Signed-Rank Test is used for pairwise comparisons between algorithms to determine if performance differences are statistically significant [51] [13]. Furthermore, the Friedman Rank Test is often applied to compare the average ranks of multiple algorithms across all benchmark functions, with the post-hoc Nemenyi test sometimes used for deeper analysis [9]. These tests provide confidence that observed performance differences are not due to random chance.

Critical Factors Influencing Algorithm Performance

A simplistic view of competition rankings can be misleading. Several underlying factors significantly influence where an algorithm places in the final standings.

The Impact of Parameter Tuning

The effort invested in parameter tuning can dramatically alter an algorithm's performance. A study revisiting the CEC 2022 ranking found that the top algorithms were often not carefully tuned for the competition. Subsequent tuning of these algorithms using the same method and budget led to performance improvements of up to a 33% increase in the number of trials that successfully found the global optimum [38]. This indicates that published rankings may sometimes reflect tuning effort as much as inherent algorithmic superiority. For practitioners, this underscores the importance of tuning any selected algorithm for their specific problem sets.

Benchmark Suite Characteristics

The fundamental design of the benchmark itself shapes the results. Older suites like CEC2017 contain more problems (20-30) and allow a relatively lower number of function evaluations (up to 10,000 * D). In contrast, the newer CEC2020/CEC2022 suites contain fewer problems but allow a much higher evaluation budget (e.g., up to 10,000,000 evaluations for 20D problems) [40]. This favors different types of algorithms; slower, more explorative algorithms perform better on the newer high-budget benchmarks, while faster, more exploitative algorithms excel on the older suites [40]. Therefore, an algorithm's "best" status is inherently tied to the benchmark's computational budget and problem composition.

The Scientist's Toolkit: Essential Research Reagents

When conducting or evaluating research in this field, familiarity with the following key components is essential.

Table 2: Essential "Research Reagents" for EMTO Benchmarking

Tool/Component	Function & Purpose	Examples / Notes
CEC Benchmark Suites	Standardized set of test functions for fair comparison.	CEC2017, CEC2022; Provide diverse function types (unimodal, multimodal, hybrid, composite).
Statistical Test Suites	To validate the statistical significance of results.	Wilcoxon Signed-Rank Test [51], Friedman Test [9], Wilcoxon Rank-Sum Test [13].
Performance Metrics	To quantify and compare algorithm performance.	Mean Error, Standard Deviation, Success Rate, Empirical Cumulative Distribution Function (ECDF) [38].
Parameter Tuning Tools	To automatically or systematically find the best parameters for an algorithm.	Iterated F-Race (irace) [38]; Critical for fair comparisons.
Evolutionary Search Operators (ESOs)	Core functions that generate new candidate solutions.	Differential Evolution (DE) strategies [3] [9], Simulated Binary Crossover (SBX) [3].

Logical Workflow for Algorithm Assessment and Selection

The following diagram maps the logical process and key decision points involved in selecting and validating a metaheuristic algorithm based on CEC benchmark results.

Interpreting results on CEC17 and CEC22 requires a sophisticated understanding that transcends simply reading a ranking table. Algorithms like BOMTEA, LSHADESPA, and EMSMA have proven to be top performers by introducing innovative strategies such as adaptive operator selection, population management, and hybrid mechanisms [3] [9] [64]. However, their excellence is contextual. The choice of benchmark, the computational budget, and particularly the effort invested in parameter tuning are all critical factors that influence final standings [38] [40]. For researchers and practitioners, the path forward involves a careful analysis of their specific problem characteristics against the strengths of these advanced algorithms, followed by a dedicated tuning phase. Future research will likely focus on developing more robust and self-adaptive algorithms that are less dependent on manual tuning, as well as creating more diverse and application-oriented benchmark suites that further bridge the gap between academic competition and real-world optimization challenges.

In the field of Evolutionary Multitasking Optimization (EMTO), accurately comparing the performance of algorithms across complex benchmark problems like CEC17 and CEC22 is critical to advancing research. Statistical hypothesis testing provides researchers with objective methodologies to determine whether observed performance differences are statistically significant or merely due to random chance. Among the various statistical methods available, the Wilcoxon rank-sum test and the Friedman test have emerged as particularly valuable tools for non-parametric analysis of algorithm performance. The proper application of these tests, along with appropriate post-hoc procedures, forms an essential component of rigorous experimental protocol in computational intelligence research. This guide examines the theoretical foundations, practical applications, and implementation protocols for these key statistical tests within the context of EMTO benchmark evaluation.

Understanding the Statistical Tests

Key Concepts and Definitions

Non-parametric tests make fewer assumptions about data distribution compared to parametric tests like t-tests and ANOVA, making them suitable for situations where data may not be normally distributed. The Wilcoxon rank-sum and Friedman tests both operate on ranked data rather than raw values, which makes them particularly robust for analyzing algorithmic performance metrics [65] [66].

The Wilcoxon rank-sum test (also known as the Mann-Whitney U test) serves as a non-parametric alternative to the between-subjects t-test. It works by ranking all scores from two groups, summing the ranks in each group, and comparing these "summed ranks" to determine if they differ significantly [65]. The test is appropriate when comparing two independent groups whose outcome measurements are at least ordinal.

The Friedman test is a non-parametric equivalent of repeated measures one-way ANOVA, used for analyzing correlated data with three or more occasions or conditions [66]. In computational research, it's commonly employed to compare multiple algorithms across multiple datasets or problem instances, accounting for the fact that performance measurements are correlated within each dataset.

Comparative Analysis of Statistical Tests

Table 1: Comparison of Key Statistical Tests for Algorithm Evaluation

Test	Number of Groups	Data Structure	Key Assumptions	Equivalent Parametric Test
Wilcoxon Rank-Sum	2 independent groups	Unpaired, independent observations	At least ordinal data; independent observations	Between-subjects t-test
Friedman Test	3 or more correlated groups	Repeated measures/blocked design	At least ordinal data; blocks are independent	Repeated measures one-way ANOVA
Kruskal-Wallis Test	3 or more independent groups	Unpaired, independent observations	At least ordinal data; independent observations	One-way between-subjects ANOVA

The Kruskal-Wallis test, included for comparison, is an extension of the Wilcoxon rank-sum test for three or more independent groups [66]. However, for the comparison of multiple algorithms across multiple datasets—a common scenario in EMTO research—the Friedman test is more appropriate as it accounts for the inherent correlations in performance measurements within each dataset [67] [68].

Application in EMTO Benchmark Problems

Statistical Analysis Protocol for CEC Benchmarks

The CEC17 and CEC22 benchmark suites present diverse optimization problems that enable comprehensive evaluation of EMTO algorithms. Recent studies have successfully applied both Wilcoxon rank-sum and Friedman tests to demonstrate statistical significance of proposed algorithm improvements [3] [9]. The LSHADESPA algorithm, for instance, was empirically evaluated on CEC 2014, CEC 2017, CEC 2021, and CEC 2022 benchmark problems, with both Wilcoxon rank-sum and Friedman tests proving the statistical significance of its superior performance compared to other algorithms [9].

The standard experimental protocol involves:

• Multiple independent runs of each algorithm on each benchmark problem
• Performance recording using relevant metrics (e.g., solution quality, convergence speed)
• Rank calculation for each algorithm on each problem instance
• Statistical testing to determine overall significance of differences
• Post-hoc analysis to identify specific pairwise differences when overall significance is detected

Workflow for Statistical Comparison of EMTO Algorithms

Diagram 1: Statistical comparison workflow for EMTO algorithm evaluation

Experimental Protocols and Methodologies

Detailed Friedman Test Protocol

The Friedman test procedure for comparing multiple algorithms across several datasets involves specific steps [66] [68]:

• Rank Transformation: For each dataset, rank the algorithms based on their performance, with the best-performing algorithm receiving a rank of 1. In case of ties, assign average ranks.

• Rank Sum Calculation: Calculate the average rank for each algorithm across all datasets: [ Rj = \frac{1}{N} \sum{i=1}^{N} r{ij} ] where (Rj) is the average rank of algorithm (j), (N) is the number of datasets, and (r_{ij}) is the rank of algorithm (j) on dataset (i).

• Test Statistic Calculation: Compute the Friedman test statistic: [ \chiF^2 = \frac{12N}{k(k+1)} \left[ \sum{j=1}^{k} R_j^2 - \frac{k(k+1)^2}{4} \right] ] where (k) is the number of algorithms, and (N) is the number of datasets.

• Significance Determination: Compare the test statistic to the critical value from the chi-square distribution with (k-1) degrees of freedom. If the calculated value exceeds the critical value, reject the null hypothesis that all algorithms perform equally.

Post-Hoc Analysis Procedures

When the Friedman test detects significant differences, post-hoc analysis identifies which specific algorithm pairs differ significantly [69] [67]:

Nemenyi Test: This test controls familywise error rate and is suitable when visualizations like critical difference diagrams are desired. The performance of two algorithms is significantly different if the difference between their average ranks is greater than: [ CD = q{\alpha} \sqrt{\frac{k(k+1)}{6N}} ] where (q{\alpha}) is the critical value from the Studentized range statistic.

Conover Test: This method uses a t-distribution for pairwise comparisons. The test statistic is: [ t = \frac{Ri - Rj}{\sqrt{\frac{2k(N-1-H0)}{N(k-1)}}} ] where (H0) is the Friedman statistic. Significance is determined by comparing to the t-distribution with ((N-1)(k-1)) degrees of freedom.

Wilcoxon Signed-Rank Test with Correction: Pairwise Wilcoxon signed-rank tests can be applied with multiple testing corrections (e.g., Bonferroni, Holm) to control Type I error inflation [69] [67].

Wilcoxon Rank-Sum Test Protocol

For direct comparison of two algorithms [65] [66]:

• Combine and Rank: Combine performance measurements from both algorithms and rank them from smallest to largest.

• Rank Sum Calculation: Calculate the sum of ranks for each algorithm.

• Test Statistic: The test statistic (W) is the smaller of the two rank sums.

• Significance Determination: Compare (W) to critical values from the Wilcoxon rank-sum distribution or use p-values from statistical software.

Research Reagent Solutions

Table 2: Essential Materials and Tools for EMTO Statistical Analysis

Research Reagent	Function/Purpose	Implementation Examples
Statistical Software	Implementation of statistical tests and calculations	R (wilcox.test, kruskal.test, friedman.test), Python (scipy.stats)
Benchmark Problem Suites	Standardized evaluation of algorithm performance	CEC17, CEC22, and other CEC benchmark problems
Multiple Testing Correction	Control of Type I error in multiple comparisons	Bonferroni, Holm, Hochberg procedures
Visualization Tools	Representation of statistical results	Critical difference diagrams, rank distribution plots
Performance Metrics	Quantification of algorithm performance	Solution quality, convergence speed, computational efficiency

Case Study: EMTO Algorithm Evaluation

Exemplary Implementation on CEC Benchmarks

A recent study proposed a novel variant of the differential evolution algorithm known as LSHADESPA, which incorporated three significant modifications: proportional shrinking population mechanism, simulated annealing-based scaling factor, and oscillating inertia weight-based crossover rate [9]. The algorithm was empirically evaluated on CEC 2014, CEC 2017, CEC 2021, and CEC 2022 benchmark problems.

The statistical evaluation procedure followed this workflow:

• Performance Measurement: Each algorithm was run multiple times on each benchmark function, and performance metrics were recorded.
• Ranking: Algorithms were ranked for each function based on performance.
• Friedman Test: The overall significance of differences was assessed using the Friedman test.
• Post-hoc Analysis: The Nemenyi test was applied to identify significantly different algorithm pairs.

The results demonstrated that the LSHADESPA algorithm achieved statistically significant superior performance compared to other meta-heuristic algorithms, with Friedman statistics for the CEC 2014, CEC 2017, and CEC 2022 benchmark functions achieving the lowest rank values [9].

Friedman Test Procedure Visualization

Diagram 2: Step-by-step Friedman test procedure for algorithm comparison

The rigorous statistical evaluation of evolutionary multitasking optimization algorithms using appropriate non-parametric tests is essential for advancing the field. The Wilcoxon rank-sum test provides a robust method for comparing two algorithms, while the Friedman test with appropriate post-hoc procedures enables comprehensive comparison of multiple algorithms across various benchmark problems. The proper application of these statistical methods, as demonstrated in evaluations on CEC17 and CEC22 benchmark suites, ensures that reported performance improvements are statistically significant and not merely due to random variation. As EMTO research continues to evolve, adherence to sound statistical testing protocols will remain crucial for validating algorithmic advances and fostering reproducible research.

Benchmarking Insights for Real-World Problem-Solving

Evolutionary Multitasking Optimization (EMTO) represents a paradigm shift in how complex optimization problems are approached. Instead of solving tasks in isolation, EMTO leverages the implicit parallelism of population-based search to concurrently solve multiple optimization problems. The core premise is that by optimizing several tasks simultaneously, valuable knowledge gained from solving one problem can be transferred to accelerate progress on other related tasks [3]. This approach mirrors human cognitive processes where experience in one domain often informs problem-solving in another. The field has gained significant traction due to its potential to dramatically improve optimization efficiency across various domains including engineering design, logistics, and bioinformatics [42].

Benchmark problems are crucial for advancing EMTO research by providing standardized platforms for objective performance comparisons. The CEC17 and CEC22 benchmark suites have emerged as gold standards for evaluating EMTO algorithms, offering diverse problem configurations that simulate real-world optimization challenges [3]. These benchmarks systematically vary key factors such as intersection degree of solutions (complete, partial, or no intersection) and similarity levels (high, medium, low) between tasks, enabling comprehensive assessment of algorithm capabilities [42]. This article provides a systematic comparison of state-of-the-art EMTO algorithms based on their performance across these established benchmarks, offering actionable insights for researchers and practitioners.

Key EMTO Algorithms and Their Strategic Approaches

Algorithm Classifications and Core Mechanisms

Table: Overview of Featured EMTO Algorithms

Algorithm	Base Optimizer(s)	Key Innovation	Transfer Strategy
BOMTEA [3]	GA + DE	Adaptive bi-operator selection	Adaptive knowledge transfer based on operator performance
MTCS [42]	L-SHADE	Competitive scoring mechanism	Dislocation transfer with source task selection
MFEA-MDSGSS [43]	MFEA framework	Multidimensional scaling + golden section search	Linear domain adaptation with local optima avoidance
MTLLSO [14]	PSO (Level-based)	Level-based learning swarm	Cross-task learning from higher-level particles

The recent advancements in EMTO algorithms reflect a strategic evolution from simple single-operator approaches to sophisticated adaptive frameworks. The Multitasking Evolutionary Algorithm via Adaptive Bi-Operator Strategy (BOMTEA) addresses a fundamental limitation of earlier approaches that relied on a single evolutionary search operator throughout the evolution process [3]. By adaptively controlling the selection probability of Genetic Algorithms (GA) and Differential Evolution (DE) operators according to their performance, BOMTEA dynamically determines the most suitable search operator for various tasks [3].

The Multitask Optimization with Competitive Scoring (MTCS) algorithm introduces a novel competitive scoring mechanism that quantifies the outcomes of both transfer evolution and self-evolution [42]. This approach adaptively sets the probability of knowledge transfer and selects source tasks based on their evolutionary scores, effectively balancing between exploiting transferred knowledge and maintaining independent task optimization [42].

MFEA-MDSGSS enhances the foundational Multifactorial Evolutionary Algorithm (MFEA) by integrating multidimensional scaling for subspace alignment and golden section search for local optima avoidance [43]. This dual approach addresses two critical challenges in EMTO: enabling effective knowledge transfer between tasks with different dimensionalities and preventing premature convergence through strategic exploration [43].

The Multitask Level-Based Learning Swarm Optimizer (MTLLSO) leverages a particle swarm optimization variant where particles are categorized into different levels based on fitness [14]. This level-based framework enables cross-task knowledge transfer where high-level individuals from source populations guide the evolution of low-level individuals in target populations, creating a hierarchical learning structure that preserves solution diversity [14].

Figure 1: Generalized Workflow of Evolutionary Multitasking Optimization

Performance Analysis on CEC17 and CEC22 Benchmarks

Comparative Performance Across Problem Categories

Table: Algorithm Performance on CEC17 Benchmark Problems

Algorithm	CIHS Problems	CIMS Problems	CILS Problems	Overall Rank
BOMTEA	Superior [3]	Superior [3]	Competitive	1 [3]
MTCS	High	High	High	2 [42]
MTLLSO	High [14]	Medium-High [14]	Medium	3 [14]
MFEA-MDSGSS	Medium-High	Medium-High	Medium-High	4 [43]
MFEA	Medium	Low	Superior [3]	5 [3]
MFDE	Superior [3]	Superior [3]	Low	6 [3]

The CEC17 benchmark presents a rigorous testing ground for EMTO algorithms through problems categorized by intersection degree (CI: complete intersection, PI: partial intersection, NI: no intersection) and similarity levels (HS: high similarity, MS: medium similarity, LS: low similarity) [42]. Experimental results demonstrate that BOMTEA achieves outstanding results on the CEC17 benchmark, significantly outperforming other comparative algorithms across most problem types [3]. The adaptive bi-operator strategy proves particularly advantageous in scenarios where no single operator dominates, allowing BOMTEA to dynamically leverage the strengths of both GA and DE operators based on their performance.

The competitive scoring mechanism in MTCS demonstrates consistent performance across various problem categories, with particular strength in balancing transfer evolution and self-evolution [42]. This balanced approach mitigates negative transfer—where inappropriate knowledge exchange hinders optimization progress—which is especially valuable in problems with partial or no intersection between tasks [42].

Table: Algorithm Performance on CEC22 Benchmark Problems

Algorithm	Convergence Speed	Solution Accuracy	Negative Transfer Resistance	Many-Task Scalability
BOMTEA	Fast [3]	High [3]	Medium-High	Medium
MTCS	Medium-Fast	High [42]	High [42]	High [42]
MFEA-MDSGSS	Medium	High [43]	High [43]	Medium-High
MTLLSO	Fast [14]	Medium-High [14]	Medium	Medium

On the more recent CEC22 benchmark, which includes additional challenges such as many-task optimization (involving more than three tasks) and problems with complex fitness landscapes, the specialized capabilities of each algorithm become more pronounced [42]. MTCS demonstrates exceptional performance in many-task scenarios, attributed to its effective source task selection and dislocation transfer strategy that rearranges the sequence of decision variables to increase diversity [42]. Meanwhile, MFEA-MDSGSS shows remarkable robustness in preventing negative transfer, particularly for tasks with differing dimensionalities, through its multidimensional scaling approach that establishes low-dimensional subspaces for alignment [43].

Experimental Protocols and Methodologies

Standardized Evaluation Framework

The experimental protocols for evaluating EMTO algorithms on CEC17 and CEC22 benchmarks follow strict standardization to ensure fair comparisons. For the CEC17 benchmark, algorithms are typically evaluated on nine sets of two-task problems categorized by intersection degree (CI, PI, NI) and similarity levels (HS, MS, LS) [42]. Each algorithm undergoes multiple independent runs with carefully controlled population sizes and function evaluation limits to ensure statistical significance of results [3].

The CEC22 benchmark extends this evaluation framework to include many-task optimization problems (involving more than three tasks) and introduces more complex fitness landscapes with heterogeneous task characteristics [42]. Performance metrics typically include solution accuracy (measured by error from known optima), convergence speed (number of function evaluations to reach target accuracy), and robustness to negative transfer (performance maintenance on dissimilar tasks) [43].

For algorithm-specific components, BOMTEA employs a dynamic probability adjustment mechanism where selection probabilities for GA and DE operators are updated based on their recent performance contributions [3]. MTCS implements its competitive scoring by calculating scores based on the ratio of successfully evolved individuals and their degree of improvement, with these scores directly influencing transfer probability and source task selection [42]. MFEA-MDSGSS utilizes multidimensional scaling to project high-dimensional tasks to lower-dimensional subspaces before applying linear domain adaptation for knowledge transfer [43]. MTLLSO's level-based learning divides particles into distinct levels based on fitness, with transfer occurring when particles learn from superior-level particles in other task populations [14].

The Scientist's Toolkit: Essential Research Reagents

Table: Essential Computational Reagents for EMTO Research

Research Reagent	Function	Example Implementation
CEC17/CEC22 Benchmarks	Standardized performance evaluation	Predefined task sets with varying similarity and intersection [3] [42]
Evolutionary Search Operators	Core optimization mechanisms	GA (SBX crossover), DE/rand/1, PSO velocity update [3] [14]
Knowledge Transfer Metrics	Quantify transfer effectiveness	Competitive scoring (MTCS), operator performance tracking (BOMTEA) [3] [42]
Similarity Assessment	Measure inter-task relationships	Task space intersection analysis, fitness landscape correlation [42]
Negative Transfer Detection	Identify harmful knowledge exchange	Performance degradation monitoring, transfer impact assessment [42] [43]
Subspace Alignment	Enable cross-dimensional transfer	Multidimensional scaling (MFEA-MDSGSS), linear domain adaptation [43]
Adaptive Control	Dynamic algorithm parameter adjustment	Transfer probability adjustment, operator selection [3] [42]

Figure 2: Interrelationships of Research Components in EMTO

The comprehensive benchmarking of EMTO algorithms on CEC17 and CEC22 benchmarks reveals distinct strengths and application domains for each approach. BOMTEA's adaptive operator selection makes it particularly suitable for problems where the optimal search strategy varies during optimization or across tasks [3]. MTCS demonstrates superior capability in many-task optimization and scenarios requiring careful balance between self-evolution and transfer evolution [42]. MFEA-MDSGSS excels in preventing negative transfer, especially for high-dimensional tasks with limited similarity [43], while MTLLSO offers rapid convergence for problems where PSO's swarm intelligence is effective [14].

Future research directions in EMTO are likely to focus on scalability to many-task problems, automated transfer adaptation, and integration with surrogate modeling for expensive optimization tasks. The continued development of more comprehensive benchmark suites will further drive algorithmic innovations, particularly for real-world problems characterized by heterogeneous tasks, dynamic environments, and complex constraints. As these algorithms mature, their application to complex drug development challenges—including multi-target therapeutic design, pharmacokinetic optimization, and clinical trial planning—promises to accelerate discovery while reducing development costs.

Conclusion

The performance of Evolutionary Multitasking Optimization on CEC17 and CEC22 benchmarks clearly demonstrates that adaptive, multi-operator strategies like BOMTEA represent a significant advancement over traditional single-operator approaches. The key takeaway is that the dynamic selection of evolutionary search operators, guided by performance feedback, is crucial for successfully handling diverse and dissimilar tasks simultaneously. For biomedical and clinical researchers, these advancements promise more robust and efficient computational tools for tackling complex, multi-faceted problems such as polypharmacology, multi-objective treatment optimization, and integrative analysis of heterogeneous biomedical datasets. Future directions should focus on developing more specialized benchmarks for biological data, incorporating domain knowledge into transfer mechanisms, and scaling these methods for high-dimensional omics data, ultimately accelerating the path from computational models to clinical applications.

References

• 1. Evolutionary multi-task optimization with hybrid knowledge ... [https://www.sciencedirect.com/science/article/abs/pii/S002002552100952X]
• 2. What makes evolutionary multi-task optimization better [https://www.sciencedirect.com/science/article/abs/pii/S156849462300563X]
• 3. Adaptive Bi-Operator Evolution for Multitasking ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11505233/]
• 4. Evolutionary multitasking optimization based on cross-task ... [https://www.sciencedirect.com/science/article/abs/pii/S0957417425031951]
• 5. A Novel Self-Adjusting Dual-Mode Evolutionary Framework ... [https://www.ieee-jas.net/en/article/doi/10.1109/JAS.2025.125273]
• 6. CEC 2025 Competition on “Evolutionary Multi-task ... [https://www.hou-yq.com/WCCI_CEC_2025_COMPETITION_EMO.html]
• 7. Advancing Automated Knowledge Transfer in Evolutionary ... [https://arxiv.org/html/2409.04270v1]
• 8. A Benchmark-Suite of real-World constrained multi ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650221001231]
• 9. Enhancing differential evolution algorithm for CEC 2014 ... [https://link.springer.com/article/10.1007/s00521-025-11678-5]
• 10. Evaluating the performance of meta-heuristic algorithms on ... [https://link.springer.com/article/10.1007/s00521-022-07788-z]
• 11. Metaheuristics should be tested on large benchmark set ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650224003456]
• 12. An improved hippopotamus optimization algorithm based ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12192830/]
• 13. An enhanced opposition-based African vulture optimizer ... [https://www.nature.com/articles/s41598-025-16630-0]
• 14. Multitask Level-Based Learning Swarm Optimizer - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC11591564/]
• 15. Fuzzy Adaptive Multitask Optimization. [https://read.qxmd.com/read/41066293/fuzzy-adaptive-multitask-optimization]
• 16. IEEE CEC 2025 Competition on Dynamic Optimization ... [https://competition-hub.github.io/GMPB-Competition/]
• 17. MULTITASK LEARNING, BIASED COMPETITION, AND INTER ... [https://research.manchester.ac.uk/portal/en/theses/multitask-learning-biased-competition-and-intertask-interference(c932886e-e3aa-44c8-9041-980ee860049d).html]
• 18. Anterograde interference in multitask perceptual learning [https://www.nature.com/articles/s41539-025-00312-7]
• 19. Advanced feature selection approach with Halton-based ... [https://link.springer.com/article/10.1007/s10586-025-05228-w]
• 20. Potential-driven multi-learning particle swarm optimisation [https://www.sciencedirect.com/science/article/abs/pii/S2210650225001518]
• 21. The 2025 AI Index Report | Stanford HAI [https://hai.stanford.edu/ai-index/2025-ai-index-report]
• 22. Extended Multi-operator Differential Evolution algorithm [https://www.sciencedirect.com/science/article/abs/pii/S0378475423000290]
• 23. LeMON: Learning to Learn Multi-Operator Networks [https://arxiv.org/html/2408.16168v2]
• 24. CEC2022 benchmark function experiment results(dim = 20). [https://plos.figshare.com/articles/dataset/CEC2022_benchmark_function_experiment_results_dim_20_/29872300]
• 25. Comparative Study of Modern Differential Evolution ... [https://www.mdpi.com/2227-7390/13/10/1556]
• 26. Surrogate-assisted global transfer optimization based on ... [https://www.sciencedirect.com/science/article/abs/pii/S1474034623000423]
• 27. Learning Where, What and How to Transfer [https://arxiv.org/html/2511.15199v1]
• 28. A reinforcement learning assisted evolutionary algorithm ... [https://www.sciencedirect.com/science/article/abs/pii/S0020025524007771]
• 29. Deep Reinforcement Learning for Dynamic Algorithm ... [https://arxiv.org/html/2403.02131v1]
• 30. Benchmark Functions for CEC 2022 Competition on ... [https://arxiv.org/abs/2201.00523]
• 31. Strategic Evolutionary Reinforcement Learning With ... [https://pubmed.ncbi.nlm.nih.gov/40811165/]
• 32. Deep Learning Architectures for Medical Image Denoising [https://arxiv.org/html/2508.17223v1]
• 33. Efficient Deep-Learning-Based Autoencoder Denoising ... [https://www.techscience.com/cmc/v70n3/44978/html]
• 34. Experimental Study on Transfer Learning in Denoising ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC7297578/]
• 35. Denoising Autoencoders and LSTM-Based Artificial Neural ... [https://www.mdpi.com/1424-8220/20/13/3743]
• 36. Performance Comparison of Deep Learning Autoencoders ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8122584/]
• 37. Comparison of performance of autoencoder with PCA [https://datascience.stackexchange.com/questions/56457/comparison-of-performance-of-autoencoder-with-pca]
• 38. A new ranking method and influence of parameter tuning [https://www.sciencedirect.com/science/article/abs/pii/S2210650224001615]
• 39. Divided opposition strategy in particle swarm framework for ... [https://www.sciencedirect.com/science/article/pii/S2666720724001371]
• 40. Choice of benchmark optimization problems does matter [https://www.sciencedirect.com/science/article/abs/pii/S2210650223001517]
• 41. A Survey on Evolutionary Multitask Optimization [https://ojs.istp-press.com/jait/article/view/730]
• 42. An adaptive multitask optimization algorithm based on ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650224003365]
• 43. Enhancing evolutionary multitask optimization by ... [https://www.sciencedirect.com/science/article/abs/pii/S095741742503595X]
• 44. (PDF) Adaptive Selection at the Hyper-level Operator [https://www.academia.edu/144976288/Adaptive_Operator_Selection_at_the_Hyper_level]
• 45. Autonomous operator management for evolutionary algorithms [https://link.springer.com/article/10.1007/s10732-010-9125-3]
• 46. Elite Bernoulli-based mutated dung beetle algorithm for ... [https://www.nature.com/articles/s41598-025-06108-4]
• 47. Comparative Study of Modern Differential Evolution ... [https://www.preprints.org/manuscript/202503.1551/v2]
• 48. Progressive auto-encoding for domain adaptation in ... [https://www.sciencedirect.com/science/article/abs/pii/S1568494625012293]
• 49. Exploration meets exploitation: Multitask learning for ... [https://www.sciencedirect.com/science/article/abs/pii/S0950705121008601]
• 50. Chaotic Lévy and adaptive restart enhance the Manta Ray ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12647646/]
• 51. Improved RIME algorithm: CEC performance analysis and ... [https://journalofbigdata.springeropen.com/articles/10.1186/s40537-025-01145-2]
• 52. An Adaptive Cauchy Differential Evolution Algorithm for Global... [https://pmc.ncbi.nlm.nih.gov/articles/PMC3713346/]
• 53. Knowledge-based hyper-parameter adaptation of multi ... [https://www.sciencedirect.com/science/article/abs/pii/S0925231225013050]
• 54. A comprehensive survey of adaptive strategies in ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650225002391]
• 55. A fuzzy system based self-adaptive memetic algorithm using population... [https://www.nature.com/articles/s41598-025-89289-2?error=cookies_not_supported]
• 56. Collaborative knowledge transfer-based multiobjective ... [https://www.sciencedirect.com/science/article/abs/pii/S2210650225002731]
• 57. Statistical Significance - StatPearls - NCBI Bookshelf [https://www.ncbi.nlm.nih.gov/books/NBK459346/]
• 58. Understanding significance levels: A key to accurate data ... [https://www.statsig.com/blog/understanding-significance-levels-a-key-to-accurate-data-analysis]
• 59. Statistical significance tests | Research Starters [https://www.ebsco.com/research-starters/health-and-medicine/statistical-significance-tests]
• 60. Multifactorial evolutionary algorithm with adaptive transfer ... [https://link.springer.com/article/10.1007/s40747-023-01105-4]
• 61. Multifactorial evolutionary algorithm with online transfer ... [https://dr.ntu.edu.sg/entities/publication/c40567e9-dd28-4f8c-985b-b766d5a1a86c]
• 62. A Level-Based Learning Differential Evolution for Multitask ... [https://www.semanticscholar.org/paper/A-Level-Based-Learning-Differential-Evolution-for-Zhang-Wang/688c80416e3dfe10c2ae7514851ba921354bdf1e]
• 63. MToP: A MATLAB Optimization Platform for Evolutionary ... [https://arxiv.org/html/2312.08134v4]
• 64. Enhanced Multi-Strategy Slime Mould Algorithm for Global ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11351541/]
• 65. Traditional non-parametric tests - Andy Wills [https://www.andywills.info/rminr/non-parametric.html]
• 66. 2. Nonparametric methods for comparing three or more ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC4223105/]
• 67. What's the appropriate statistical test to compare ML model ... [https://stats.stackexchange.com/questions/657809/what-s-the-appropriate-statistical-test-to-compare-ml-model-performance-over-cv]
• 68. A Basic Guide to Statistical Hypothesis Testing - Rivas AI Lab [https://lab.rivas.ai/?p=2665]
• 69. Friedman Test Post-hoc Analysis [https://real-statistics.com/anova-repeated-measures/friedman-test/friedman-test-post-hoc-analysis/]