Hierarchically controlled differential evolution algorithm
Liangliang Sun, Zhenghao Song, Jing Liu, Haipeng Ji, Ge Guo, Natalja M. Matsveichuk, Yuri N. Sotskov
Abstract
Differential Evolution (DE), as a population-based metaheuristic global optimization technique, has demonstrated outstanding performance in solving continuous space optimization problems. However, when dealing with complex optimization tasks, DE still faces challenges such as susceptibility to local optima and slow convergence speed. To address these issues, this paper proposes a Hierarchically Controlled Differential Evolution (HCDE) algorithm. By employing a hierarchical control strategy, HCDE improves DE from three key aspects: parameter tuning, mutation strategy design, and population diversity maintenance. First, A dual-phase mechanism dynamically adjusts the scale factor F and crossover rate C R using logistic and Cauchy distributions, ensuring adaptive trade-offs between exploration and exploitation. Second, A multi-level archive framework synergizes historical elite solutions (preserved for global guidance) and promising non-elite candidates (retained for diversity maintenance) with the current population, enhancing landscape perception while avoiding redundant evaluations. Lastly, An entropy-based metric quantifies population diversity across dimensions, triggering hybrid perturbations (Gaussian-Cauchy) and restart strategies to escape local optima. To validate the performance of HCDE, comparative experiments were conducted on 88 benchmark functions from the CEC2014, CEC2017, and CEC2022 test suites. The HCDE algorithm was benchmarked against seven state-of-the-art DE variants. Experimental results demonstrate that HCDE exhibits significant advantages over traditional DE and its improved versions in terms of convergence accuracy, convergence speed, and robustness. Furthermore, HCDE was applied to a bridge structure optimization problem, further verifying its effectiveness in real-world engineering applications.