A New Differential Evolution Algorithm for Minimax Optimization in Robust Design

Minimax optimization, which is actively involved in numerous robust design problems, aims at pursuing the solutions with best worst-case performances. Although considerable research has been devoted to the development of minimax optimization algorithms, there still exist several fundamental limitations for existing approaches, e.g., restriction on problem types, excessively high computational cost, and low optimization efficiency. To address these issues, a minimax differential evolution algorithm is proposed in this paper. First, a novel bottom-boosting scheme enables the algorithm to identify the promising solutions in a reliable yet efficient manner. After that, a partial-regeneration strategy together with a new mutation operator contribute to an in-depth exploration over solution space. Finally, a proper integration of these newly proposed mechanisms leads to an algorithmic structure that can appropriately handle various types of problems. Empirical comparison with seven famous methods demonstrates the statistical superiority of the proposed algorithm. Successful applications in two open problems of robust design further validate the effectiveness of the new approach.

I. Introduction

Minimax optimization problems, in which the solutions with best worst-case performances are preferred, can be utilized to model a wide variety of robust design tasks [1]–[8]. Unlike traditional optimization problems, two decision spaces are introduced simultaneously in minimax optimization, namely, solution space and scenario space . For each solution in , its fitness depends on the corresponding worst-case scenario in . Thus, solving a minimax optimization problem involves explorations and communications among two interrelated spaces. This makes minimax optimization problems inherently challenging and difficult to address [9].