Local Model-Based Pareto Front Estimation for Multiobjective Optimization

Abstract

The Pareto front (PF) estimation has become an emerging strategy for solving multiobjective optimization problems in recent studies. By approximating the geometrical structure of the PF during the evolutionary procedure, some PF estimation approaches have been suggested and shown effectiveness in guiding the search direction of evolutionary algorithms. However, these approaches encounter difficulties in handling irregular PFs, whose geometrical structures are too complex to be properly approximated. To address this issue, this article proposes a novel PF estimation approach based on local models. In contrast to existing approaches estimating the PF via a reference point set or a single model, the proposed approach automatically divides the population into several groups and builds a local model for each group of solutions. In spite of the simplicity of each local model, the combination of all the local models can approximate the PFs with complex geometrical structures. An evolutionary algorithm is then developed based on the local model-based PF estimation approach and a novel fitness function and is compared with four evolutionary algorithms on 39 problems. Statistical results indicate that the proposed algorithm exhibits better performance than the compared algorithms, especially on problems with highly irregular PFs.