A Framework to Handle Multi-modal Multi-objective Optimization in Decomposition-based Evolutionary Algorithms

TL;DR

This paper introduces a framework to enhance decomposition-based evolutionary algorithms for multi-modal multi-objective optimization by maintaining solution diversity through assignment, deletion, and addition operations, leading to improved performance.

Contribution

The proposed framework effectively handles multiple equivalent solutions in multi-modal multi-objective optimization, significantly improving existing algorithms' performance.

Findings

Improved algorithms outperform original versions on various test problems.

Framework maintains diversity by assigning multiple individuals to the same subproblem.

Enhanced algorithms show better convergence and solution diversity.

Abstract

Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multi-objective optimization, they are likely to perform poorly for multi-modal multi-objective optimization due to the lack of mechanisms to maintain the solution space diversity. To address this issue, this paper proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multi-modal multi-objective optimization. Our framework is based on three operations: assignment, deletion, and addition operations. One or more individuals can be assigned to the same subproblem to handle multiple equivalent solutions. In each iteration, a child is assigned to a subproblem based on its objective vector, i.e., its location in the objective space. The child is compared with its neighbors in the solution space assigned to the same subproblem. The performance of improved versions of six decomposition-based evolutionary algorithms by our framework is evaluated on various test problems regarding the number of objectives, decision variables, and equivalent Pareto optimal solution sets. Results show that the improved versions perform clearly better than their original algorithms.