A Novel Dual-Stage Evolutionary Algorithm for Finding Robust Solutions

TL;DR

This paper introduces DREA, a dual-stage evolutionary algorithm designed to efficiently find robust solutions in optimization problems by combining peak detection and robust solution search, outperforming existing methods.

Contribution

The paper presents a novel dual-stage approach that separates peak detection from robust solution search, improving efficiency and effectiveness in robust optimization.

Findings

DREA outperforms five state-of-the-art algorithms on 18 diverse test problems.

DREA demonstrates superior performance on high-dimensional problems (100-D and 200-D).

Experimental results confirm the effectiveness of the dual-stage approach.

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.