Robust Differential Evolution via Nonlinear Population Size Reduction and Adaptive Restart: The ARRDE Algorithm

This study is motivated by a robustness issue in numerical optimization of bound-constrained problems: many algorithms that perform well on a particular benchmark suite, such as the IEEE CEC2017 problems, struggle to maintain the same level of performance when applied to other suites that differ in dimensionality, landscape complexity, or the maximum number of function evaluations ($N_{\text{max}}$). To address this, we propose the Adaptive Restart-Refine Differential Evolution (ARRDE) algorithm, a new variant of Differential Evolution (DE). ARRDE builds upon the LSHADE algorithm, incorporates key mechanisms from jSO, and introduces a nonlinear population-size reduction strategy combined with an adaptive restart-refine mechanism. We evaluate ARRDE on five benchmark suites (CEC2011, CEC2017, CEC2019, CEC2020, and CEC2022) which, to the best of our knowledge, constitutes the most extensive experimental study to date in the context of algorithmic comparison, as most prior works consider only one or two suites. This broad evaluation enables a rigorous assessment of generalization across markedly different problem characteristics. To further support fair cross-suite comparisons, we also introduce a bounded accuracy-based scoring metric derived from relative error. Using both rank-based and accuracy-based metrics, and comparing against algorithms that perform strongly on CEC2017 (e.g., jSO and LSHADE-cnEpSin) as well as those that excel on CEC2020 (e.g., j2020 and NLSHADE-RSP), ARRDE consistently demonstrates top-tier performance, ranking first across all benchmark suites considered. These results highlight ARRDE's robustness and its superior generalization capability.