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 \textit{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：在约束连续优化中，跨异构优化场景的鲁棒性仍是核心挑战。实际应用中，用户往往偏好能够在不同维度、不同景观结构及不同评估预算下保持稳定性的优化器。然而，许多在特定场景表现优异的差分进化(DE)变体在迁移至其他场景时性能显著下降。针对这一问题，我们提出自适应重启精炼差分进化(ARRDE)算法——一种专为跨场景鲁棒性设计的DE变体。ARRDE结合了自适应重启精炼策略、基于问题维度的非线性种群规模缩减调度机制，以及面向受限预算场景的预算感知种群初始化规则。由于鲁棒性无法通过狭窄的实验设置可信建立，我们在五个基准测试套件上评估了ARRDE：CEC2011、CEC2017、CEC2019、CEC2020和CEC2022。这些套件跨越显著不同的维度、景观特征和评估预算，据我们所知，这是本领域DE变体所报告的最全面的鲁棒性导向评估之一。鉴于各套件官方性能指标侧重点不同且不可直接比较，我们额外引入了一种基于相对误差的有界精确度评分指标，用于跨套件鲁棒性评估。通过使用官方套件特定指标和所提出的统一指标，ARRDE在五个套件上展现出持续强劲的性能和最稳定的聚合轮廓之一。这些结果支持ARRDE作为跨异构基准场景鲁棒优化的竞争性DE变体。