Differential Evolution with Perturbation Estimation Strategy for Multiobjective Optimization

In recent years, multiobjective differential evolution (DE) algorithms have gained significant attention due to their effective search capabilities for multiobjective optimization problems (MOPs). The differential mutations of DE operators distinguish them from other generators. However, the efficiency of DE operators heavily relies on the selection of parents used to generate differential perturbation vectors. To address this challenge, this work proposes a novel algorithm, called perturbation estimation strategy based DE algorithm (PESDE), for multiobjective optimization. In PESDE, at each iteration, it utilizes a clustering approach to partition the population, and then constructs a probability model to estimate the distributions of differential perturbation vectors of the solutions within a cluster. Specifically, the differential perturbation vectors of solutions are regarded as trial points in building a probability model in the proposed approach. In this way, perturbation vectors are sampled from the built probability model, and then embedded in the solutions to generate new trial solutions. Empirical experimental studies are conducted to investigate the performance of PESDE by comparing it with five representative multiobjective evolutionary algorithms on several test instances with complicated Pareto set and front shapes. The results have demonstrated the advantages of the proposed algorithm over other approaches.