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<p>Optimization is crucial for solving complex problems across diverse domains; however, selecting the most suitable algorithm, given practical requirements and real-world constraints, remains a major challenge. The primary aim of this study is to conduct a comprehensive comparison of optimization algorithms and to develop a more accurate and reliable evaluation framework. The first innovation of this research is the introduction of a new method called Statistical Ranking of Algorithms (SRA), designed to overcome the limitations of existing ranking and comparison techniques, such as the Friedman test, which may overlook subtle differences among algorithms. The proposed SRA approach is not only innovative in comparing optimizer performance but also provides a comprehensive and general framework for both individual and group comparisons across different domains, provided that algorithm performance is measured using the same quantitative or ordinal criteria. Moreover, it supports multi-criteria weighted evaluation, allowing the influence of each criterion on the overall ranking to be adjusted according to its importance. The second innovation of this study is the implementation of a comprehensive comparative analysis of 58 optimization algorithms, encompassing Evolutionary Algorithms (EA), Swarm Intelligence (SI), and Physics/Mathematics-Based (PMB) methods, covering both established and recently developed approaches. The main contribution of this part lies in the development of a unified and comprehensive framework that integrates a wide range of optimization algorithms, diverse evaluation criteria, and both intra- and inter-category comparisons. This framework provides a holistic understanding of individual and group-level algorithm performance through an interpretable ranking system ranging from “very high” to “very low.” It identifies the strengths and weaknesses of each algorithm and offers practical guidance for selecting the most appropriate optimizer based on specific problem objectives. The evaluation criteria include exploration, exploitation, exploration–exploitation balance, convergence, execution time, scalability, stability, and real-world applicability. Evaluations were performed using standard benchmark functions and the CEC2017, CEC2019, CEC2020, and CEC2022 test suites. Among the 58 evaluated algorithms, the Chaotic Evolution Optimization (CEO) algorithm demonstrated overall dominance across most criteria, while the Mantis Search Algorithm (MSA), Nutcracker Optimization Algorithm (NOA), Spider Wasp Optimizer (SWO), and Light Spectrum Optimizer (LSO) also showed consistently strong and reliable performance. When comparing the three categories, EA excelled in statistical performance and convergence but sacrificed execution speed; SI offered high execution speed but compromised stability and convergence; and PMB provided balanced performance across all criteria. The source code of the proposed SRA method, along with the evaluation results for all algorithms in a MATLAB.mat file, is available at: <a href="https://github.com/MSNFV/SRA-Statistical-Ranking-of-Algorithms">https://github.com/MSNFV/SRA-Statistical-Ranking-of-Algorithms</a>.</p>

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A Comprehensive Comparative Study of Evolutionary, Swarm Intelligence, and Physics/Mathematics-Based Optimization Algorithms by the Novel SRA Algorithm

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Najibeh Farzi-Veijouyeh,
  • Mohammad-Reza Feizi-Derakhshi

摘要

Optimization is crucial for solving complex problems across diverse domains; however, selecting the most suitable algorithm, given practical requirements and real-world constraints, remains a major challenge. The primary aim of this study is to conduct a comprehensive comparison of optimization algorithms and to develop a more accurate and reliable evaluation framework. The first innovation of this research is the introduction of a new method called Statistical Ranking of Algorithms (SRA), designed to overcome the limitations of existing ranking and comparison techniques, such as the Friedman test, which may overlook subtle differences among algorithms. The proposed SRA approach is not only innovative in comparing optimizer performance but also provides a comprehensive and general framework for both individual and group comparisons across different domains, provided that algorithm performance is measured using the same quantitative or ordinal criteria. Moreover, it supports multi-criteria weighted evaluation, allowing the influence of each criterion on the overall ranking to be adjusted according to its importance. The second innovation of this study is the implementation of a comprehensive comparative analysis of 58 optimization algorithms, encompassing Evolutionary Algorithms (EA), Swarm Intelligence (SI), and Physics/Mathematics-Based (PMB) methods, covering both established and recently developed approaches. The main contribution of this part lies in the development of a unified and comprehensive framework that integrates a wide range of optimization algorithms, diverse evaluation criteria, and both intra- and inter-category comparisons. This framework provides a holistic understanding of individual and group-level algorithm performance through an interpretable ranking system ranging from “very high” to “very low.” It identifies the strengths and weaknesses of each algorithm and offers practical guidance for selecting the most appropriate optimizer based on specific problem objectives. The evaluation criteria include exploration, exploitation, exploration–exploitation balance, convergence, execution time, scalability, stability, and real-world applicability. Evaluations were performed using standard benchmark functions and the CEC2017, CEC2019, CEC2020, and CEC2022 test suites. Among the 58 evaluated algorithms, the Chaotic Evolution Optimization (CEO) algorithm demonstrated overall dominance across most criteria, while the Mantis Search Algorithm (MSA), Nutcracker Optimization Algorithm (NOA), Spider Wasp Optimizer (SWO), and Light Spectrum Optimizer (LSO) also showed consistently strong and reliable performance. When comparing the three categories, EA excelled in statistical performance and convergence but sacrificed execution speed; SI offered high execution speed but compromised stability and convergence; and PMB provided balanced performance across all criteria. The source code of the proposed SRA method, along with the evaluation results for all algorithms in a MATLAB.mat file, is available at: https://github.com/MSNFV/SRA-Statistical-Ranking-of-Algorithms.