A Framework to Handle Multimodal Multiobjective Optimization in Decomposition-Based Evolutionary Algorithms

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.

A Multipopulation Evolutionary Algorithm for Solving Large-Scale Multimodal Multiobjective Optimization Problems

“…In [29], a framework for enhancing the performance of decomposition based MOEAs on MMOPs was proposed. Specifically, each offspring solution is first assigned to a subproblem via an assignment operation, and the offspring solution is compared to the others assigned to the same subproblem and close to it in the decision space, where the better ones are kept and the worse ones are ignored.…”

A soft computing based multi-objective optimization approach for automatic prediction of software cost models

“…Plenty of approaches have been proposed to resolve the diversity issue in MODE Algorithm [4][5][6][7][8][9][10][11][12]. In [4],…”

“…However, the diversity problem was still not resolved as observed in experimental analysis when tested benchmark functions. In [7], the authors proposed a Handle multi-modalbased multi-objective optimization is proposed. They tried to capture the search space issue, i.e., exploration and exploitation strategy.…”

“…The list of advantages over the existing approaches are shown as follows [4][5][6][7][8][25][26][27][28]:…”

A Multi-Modal Multi-Objective Differential Algorithm Based on Hybrid Strategy

“…In order to improve the diversity of the population, a new distance mechanism based elite selection was introduced. Tanabe [5] proposed a decomposition based evolutionary algorithm framework.The decomposition strategy is beneficial for reducing the difficulty of multi-modal multi-objective problems. Although Liu [6] et al found more Pareto optimal solutions, the diversity and convergence of the objective space deteriorated.…”