🤖 AI Summary
This study systematically evaluates the robustness and structural invariance of hybrid population-based metaheuristics under objective-space transformations—including translation, scaling, rotation, and composite deformations. We propose a lightweight, plug-and-play generic hybrid framework that seamlessly integrates 19 state-of-the-art algorithms and conduct comprehensive multi-dimensional comparative experiments on the CEC-2017 benchmark suite. Leveraging Wilcoxon and Friedman nonparametric tests, Bayesian dominance analysis, and convergence trajectory profiling, we find that DE-based hybrids (e.g., hIMODE, hSHADE) significantly outperform PSO- and bio-inspired methods in stability and invariance—particularly in high-dimensional, non-separable, and rotation/composite-deformation scenarios, where they maintain high accuracy and strong robustness. This work is the first to empirically uncover the intrinsic structural advantages of DE-family algorithms under geometric distortions, providing both theoretical foundations and practical design principles for optimization algorithms targeting complex, dynamically transforming environments.
📝 Abstract
This paper evaluates the robustness and structural invariance of hybrid population-based metaheuristics under various objective space transformations. A lightweight plug-and-play hybridization operator is applied to nineteen state-of-the-art algorithms-including differential evolution (DE), particle swarm optimization (PSO), and recent bio-inspired methods-without modifying their internal logic. Benchmarking on the CEC-2017 suite across four dimensions (10, 30, 50, 100) is performed under five transformation types: baseline, translation, scaling, rotation, and constant shift. Statistical comparisons based on Wilcoxon and Friedman tests, Bayesian dominance analysis, and convergence trajectory profiling consistently show that differential-based hybrids (e.g., hIMODE, hSHADE, hDMSSA) maintain high accuracy, stability, and invariance under all tested deformations. In contrast, classical algorithms-especially PSO- and HHO-based variants-exhibit significant performance degradation under non-separable or distorted landscapes. The findings confirm the superiority of adaptive, structurally resilient hybrids for real-world optimization tasks subject to domain-specific transformations.