Hierarchically controlled differential evolution algorithm

• We propose a hierarchical cooperative optimization strategy for scaling factor F and crossover probability CR, enabling real-time balance between global exploration and local exploitation through adaptive parameter control, thus overcoming the limitations of static parameter settings. • We develop a multilevel information archive that integrates historical potential solutions with the current population, enhancing the algorithm’s dynamic perception of complex objective landscapes via cross-level information fusion. • We introduce an improved entropy-based measurement strategy to quantitatively assess the distribution state of the population, allowing for precise identification and early warning of diversity degradation. • We present a cross-level coordinated scheme combining a restart mechanism with elite retention, which leverages diversity replenishment and high-quality individuals to suppress premature convergence. • Our proposed HCDE exhibits state-of-the-art performance, as demonstrated by its outstanding results on 10D, 30D, and 50D benchmark tests in IEEE CEC competitions. • We further demonstrate HCDE’s potential as an industrial optimization tool through its excellent performance on 57 real-world optimization problems in the CEC2020 competition, where it outperforms strategies focused solely on increasing or maintaining diversity for certain complex problems. 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.