  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.
