Hybrid Harmony Search Algorithm Integrating Differential Evolution and Lévy Flight for Engineering Optimization

Harmony search algorithm (HSA) is extensively utilized in engineering optimization. Nevertheless, it encounters problems of slow convergence and reduced accuracy, which hinder its capability to escape local optima. This paper proposes HSA-DELF, a novel hybrid algorithm that combines differential evolution (DE) and Lévy flight (LF) techniques to enhance the performance of HSA. HSA-DELF leverages multi-mutation strategies of DE and LF random walk combined with weighted individuals to improve exploration and exploitation based on population fitness standard deviation comparison, and adopts pairwise iterative updates of the population to achieve faster convergence and higher solution quality. Extensive experiments were conducted to validate performance on 23 classic benchmark functions and 12 CEC 2022 benchmark functions, followed by comprehensive testing on 7 engineering problems, demonstrating the superiority of HSA-DELF. Comparative analysis with 5 well-known algorithms (HSA, DE, CSA, GA, and PSO) and 4 HSA variants (IHS, MHSA, IHSDE, and IMGHSA) confirmed the robustness of HSA-DELF. Statistical results, including best, mean, standard deviation, and worst values, consistently highlight the superior performance of HSA-DELF in terms of convergence speed, solution quality, and robustness. The Wilcoxon signed-rank test further corroborated these significant advantages. HSA-DELF showed notable improvements in 6 out of 7 engineering problems, achieving an accuracy of 85.71%. This study establishes HSA-DELF as an effective and reliable method for solving complex engineering optimization problems.