Differential evolution guided by approximated Pareto set for multiobjective optimization

Abstract

Differential evolution (DE), as an efficient evolutionary optimizer, has been widely applied to deal with multiobjective optimization problems. In DE generation operations, appropriate guiding solutions, the “best” solutions (denoted as xbest), will be in favor of the search for generating promising new trial solutions. However, it is still a challenge to define and select such xbest due to the Pareto property of multiobjective optimization. Facing this challenge, we propose a regularity model guided differential evolution (RMDE) for multiobjective optimization. Different from the existing studies that select xbest from non-dominated solutions or predefined preference solutions, the proposed RMDE aims to sample the guiding solutions from the regularity models that are built to approximate Pareto optimal set explicitly. In this way, four alternative RMDE mutation strategies with the sampled xbest are developed and investigated, including the search efficiency and parameter settings. Empirical studies are conducted to validate the performance of RMDE on 51 test instances. The experimental results demonstrate the advantages of the proposed method over seven other classical or newly developed algorithms from the literature.