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<p>This study presents a transparent and reproducible framework for the fair comparison of metaheuristic algorithms in constrained engineering design optimization problems. Ten algorithms from various families were tested on 13 well-known benchmarks, with 30 independent runs and a fixed evaluation budget of 5000×D function evaluations. The performance of the algorithms was compared using eight complementary performance metrics, as well as a three-level success classification: Exact success with error &lt; 1%, Near success with error between 1% and 5%, and Fail with error &gt; 5%. The statistical validity of the comparison results was ensured using the Friedman test and Nemenyi post-hoc test with Bonferroni correction, and the robustness of the results was validated using threshold sensitivity, weight sensitivity, and correlation analyses. The best-performing algorithm, NSM-LSHADE-CnEpSin, achieved the highest weighted score of 3.48 with the highest Exact success rate of 91.79% and zero Near-success runs, confirming the exceptional reliability and precision of the algorithm. The second-best algorithm, the Polar Fox Algorithm, achieved the highest success rate of 92.05% with no constraint violations across all 13 test problems. The third-best algorithm, Starfish Optimization, achieved high Exact success rates of 83.08%. The weight sensitivity analysis confirmed that the top-ranked algorithm, NSM-LSHADE-CnEpSin, maintains the top rank across all weight scenarios in 98.5% of 1000 random perturbations, whereas the second-best algorithm, PFA, remains in the top three in 98.1% of these perturbations. The top-ranked algorithms are clustered very tightly, and the algorithm selection should be problem-oriented. The proposed framework provides a reproducible basis for fair algorithmic comparison and is publicly available at: <a href="https://zenodo.org/records/17943669">https://zenodo.org/records/17943669</a>.</p>

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Reproducible Multi-Metric Benchmarking Framework for Metaheuristic Algorithms in Constrained Engineering Optimization

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • Ahmad Ghiaskar,
  • Farid Taheri

摘要

This study presents a transparent and reproducible framework for the fair comparison of metaheuristic algorithms in constrained engineering design optimization problems. Ten algorithms from various families were tested on 13 well-known benchmarks, with 30 independent runs and a fixed evaluation budget of 5000×D function evaluations. The performance of the algorithms was compared using eight complementary performance metrics, as well as a three-level success classification: Exact success with error < 1%, Near success with error between 1% and 5%, and Fail with error > 5%. The statistical validity of the comparison results was ensured using the Friedman test and Nemenyi post-hoc test with Bonferroni correction, and the robustness of the results was validated using threshold sensitivity, weight sensitivity, and correlation analyses. The best-performing algorithm, NSM-LSHADE-CnEpSin, achieved the highest weighted score of 3.48 with the highest Exact success rate of 91.79% and zero Near-success runs, confirming the exceptional reliability and precision of the algorithm. The second-best algorithm, the Polar Fox Algorithm, achieved the highest success rate of 92.05% with no constraint violations across all 13 test problems. The third-best algorithm, Starfish Optimization, achieved high Exact success rates of 83.08%. The weight sensitivity analysis confirmed that the top-ranked algorithm, NSM-LSHADE-CnEpSin, maintains the top rank across all weight scenarios in 98.5% of 1000 random perturbations, whereas the second-best algorithm, PFA, remains in the top three in 98.1% of these perturbations. The top-ranked algorithms are clustered very tightly, and the algorithm selection should be problem-oriented. The proposed framework provides a reproducible basis for fair algorithmic comparison and is publicly available at: https://zenodo.org/records/17943669.