In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.

翻译：在鲁棒优化问题中，扰动的幅度相对较小。因此，当引入扰动时，某些区域内的解更不可能代表鲁棒最优解。因此，更高效的搜索过程应得益于增加探索全局最优解或良好局部最优解所在的有前途区域的机会。本文提出了一种名为双阶段鲁棒进化算法（DREA）的新型鲁棒进化算法，旨在发现鲁棒解。DREA 分两个阶段运行：峰值检测阶段和鲁棒解搜索阶段。峰值检测阶段的主要目标是识别原始优化问题的适应度景观中的峰值。相反，鲁棒解搜索阶段则侧重于利用初始阶段发现的峰值信息快速识别鲁棒最优解。这两个阶段共同使所提出的 DREA 能够高效获得优化问题的鲁棒最优解。该方法通过将最优解和鲁棒最优解的搜索过程分离，实现了解的最优性与鲁棒性之间的平衡。实验结果表明，在18个具有不同复杂性的测试问题上，DREA 显著优于五种最先进的算法。此外，在更高维度的鲁棒优化问题（100维和200维）上评估时，DREA 也表现出优于所有五种对比算法的性能。