Robustness across heterogeneous optimization regimes remains a central challenge in bound-constrained continuous optimization. In practice, users often prefer optimizers that remain reliable across different dimensionalities, landscape structures, and evaluation budgets. Yet many Differential Evolution (DE) variants that perform strongly in one regime degrade substantially when transferred to others. To address this issue, we propose the Adaptive Restart--Refine Differential Evolution (ARRDE) algorithm, a DE variant designed explicitly for cross-regime robustness. ARRDE combines an adaptive restart--refine strategy, a nonlinear population-size reduction schedule that depends on problem dimensionality, and a budget-aware population-initialization rule for restricted-budget settings. Because robustness cannot be established credibly from a narrow experimental setting, we evaluate ARRDE on five benchmark suites: CEC2011, CEC2017, CEC2019, CEC2020, and CEC2022. These suites span markedly different dimensions, landscape characteristics, and evaluation budgets, making this, to the best of our knowledge, one of the most comprehensive robustness-oriented evaluations reported for a proposed DE variant in this context. Since their official performance metrics emphasize different aspects and are not directly comparable, 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 unified metric, ARRDE demonstrates consistently strong performance and one of the most stable aggregate profiles across the five suites. These results support ARRDE as a competitive DE variant for robust optimization across heterogeneous benchmark regimes.

翻译：跨异质优化场景的鲁棒性仍是带边界约束连续优化的核心挑战。实际应用中，用户往往偏好能在不同维度、地形结构和评估预算下保持可靠性的优化器。然而，许多差分进化变体虽在特定场景表现优异，但迁移至其他场景时性能显著退化。为解决此问题，本文提出自适应重启-精化差分进化算法——一种专为跨场景鲁棒性设计的差分进化变体。ARRDE融合了自适应重启-精化策略、依赖问题维度的非线性种群规模缩减调度，以及适用于受限预算场景的感知预算种群初始化规则。鉴于狭窄实验设置无法可靠验证鲁棒性，我们在CEC2011、CEC2017、CEC2019、CEC2020和CEC2022五个基准测试集上对ARRDE进行评测。这些测试集涵盖显著不同的维度、地形特征和评估预算，据我们所知，这使得本研究成为该领域针对差分进化变体最具综合性的鲁棒性评估之一。由于各测试集的官方性能指标侧重不同且不可直接比较，我们额外引入一种基于相对误差的有界精度评分指标以实现跨测试集鲁棒性评估。通过官方专用指标与所提统一指标的双重验证，ARRDE在五个测试集上展现出持续强劲的性能以及最稳定的聚合轮廓之一。这些结果支持ARRDE作为跨异质基准场景鲁棒优化的竞争力差分进化变体。