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.

翻译：本研究源于有界约束问题数值优化中的一个鲁棒性问题：许多在特定基准测试集（如IEEE CEC2017问题集）上表现优异的算法，当应用于维度、景观复杂度或最大函数评估次数（$N_{\text{max}}$）不同的其他测试集时，往往难以保持同等性能水平。为解决此问题，我们提出自适应重启-精化差分进化（ARRDE）算法，这是差分进化（DE）的一种新变体。ARRDE以LSHADE算法为基础，融合了jSO的关键机制，并引入了非线性种群规模缩减策略与自适应重启-精化机制相结合的方法。我们在五个基准测试集（CEC2011、CEC2017、CEC2019、CEC2020和CEC2022）上评估ARRDE，据我们所知，这构成了算法比较领域迄今最广泛的实验研究，因为大多数先前工作仅考虑一至两个测试集。这种广泛评估能够对显著不同问题特征间的泛化能力进行严格评估。为进一步支持公平的跨测试集比较，我们还引入了一种基于相对误差推导的有界精度评分指标。通过使用基于排名和基于精度的指标，并与在CEC2017上表现强劲的算法（如jSO和LSHADE-cnEpSin）及在CEC2020上表现优异的算法（如j2020和NLSHADE-RSP）进行比较，ARRDE在所有考虑的基准测试集中均展现出顶级性能，排名首位。这些结果凸显了ARRDE的鲁棒性及其卓越的泛化能力。