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 issue, we propose the Adaptive Restart--Refine Differential Evolution (ARRDE) algorithm, a variant of Differential Evolution (DE) built on jSO. ARRDE is centered on two main design contributions: an adaptive restart--refine mechanism, which includes final-stage refinement and local exclusion during restart, and a nonlinear population-size reduction strategy whose shape depends on problem dimensionality. We evaluate ARRDE on five benchmark suites: CEC2011, CEC2017, CEC2019, CEC2020, and CEC2022. To the best of our knowledge, this is one of the most comprehensive experimental studies conducted in this context. Because the official metrics of these benchmark suites emphasize different performance aspects, we additionally introduce a bounded accuracy-based scoring metric derived from relative error for cross-suite robustness assessment. Using both the official suite-specific metrics and the proposed robustness-oriented metric, ARRDE consistently demonstrates top-tier performance and one of the most stable aggregate profiles across all benchmark suites. These results support ARRDE as a competitive and robust DE variant across heterogeneous benchmark regimes.

翻译：本文的研究动机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）上表现优秀的算法，在应用于维度、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，难以保持同等性能水平。针对这一问题，我们提出自适应重启-精炼差分进化（ARRDE）算法，这是一种基于jSO构建的差分进化（DE）变体。ARRDE的核心包含两项主要设计贡献：一种自适应重启-精炼机制（包含最终阶段的精炼和重启过程中的局部排除），以及一种形状取决于问题维度的非线性种群规模缩减策略。我们在五个基准测试集上对ARRDE进行评估：CEC2011、CEC2017、CEC2019、CEC2020和CEC2022。据我们所知，这是该领域内最全面的实验研究之一。由于这些基准测试集的官方指标侧重于不同的性能方面，我们还额外引入了一种基于相对误差的有界精度评分指标，用于跨测试集的鲁棒性评估。通过使用官方测试集特定指标和所提出的鲁棒性导向指标，ARRDE在所有基准测试集中始终展现出顶尖的性能和最稳定的综合表现。这些结果表明，ARRDE在异构基准测试环境下是一种具有竞争力和鲁棒性的DE变体。