A Novel Dual-Stage Evolutionary Algorithm for Finding Robust Solutions
Wei Du, Wenxuan Fang, Chen Liang, Yang Tang, Yaochu Jin
TL;DR
This work introduces DREA, a dual-stage evolutionary framework for robust optimization that first identifies a fixed number of peaks in the original fitness landscape using an external Archive, and then rapidly locates robust optima by guiding a differential evolution search with information from those peaks. The peak-detection stage isolates promising regions without considering perturbations, while the robust solution-searching stage uses a DE variant to optimize the mean effective objective $f^{\text{eff}}$, estimated via neighbourhood sampling around the peaks. Experimental results on 18 robust-optimization test cases and higher-dimensional problems (100D and 200D) show that DREA consistently outperforms five state-of-the-art approaches in both solution quality and convergence speed, albeit with higher compute time due to the peak-detection overhead. The paper also analyzes the sensitivity to the number of detected peaks and demonstrates the method's scalability, highlighting its potential for real-world robust and high-dimensional optimization tasks. Overall, DREA provides a novel and effective integration of optimality and robustness by leveraging peaks from the original problem to guide robust search regions.
Abstract
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.