A-GWASF-GA: The New Version of GWASF-GA to Solve Many Objective Problems

Abstract

A new version of the evolutionary algorithm based on GWASF-GA [1] is proposed in this work. GWASF-GA is an aggregation-based algorithm which uses the Tchebychev metric plus an augmentation term as fitness function and two reference points (the utopian and nadir points) to classify the individuals according to a set of widely-distributed weight vectors. Although this algorithm obtains a good approximation of the Pareto front (PF) for multi-objective optimization problems, this may be more difficult to obtain for many-objective optimization problems due to the fact that the weight vectors used are never updated along the search process. For this reason, we propose a new version of the algorithm, called A-GWASF-GA, in which a dynamic adjustment of the weight vectors is carried out. The main idea is to re-calculate some weight vectors in order to obtain solutions in parts of the PF with a lack of solutions. Firstly, a percentage (p) of the total number of evaluations is performed with the original GWASF-GA [1]. Secondly, during the rest of evaluations (1-p), we re-calculate na times the projection directions determined by a subset of Na weight vectors. The re-calculation process is based on a scattering level, a measure based on the distance of each solution and the solutions around it. According to the scattering level of the generated solutions, we detect the Na weight vectors projecting toward overcrowded areas of the PF and we re-calculate them so that their new projection directions point towards areas of the PF which are not so well approximated. In order to show the effectiveness of A-GWASF-GA, we compare it with NSGA-III [2, 3], MOEA/D [4], MOEA/D-AWA [5] and the original GWASF-GA.To evaluate their performance, we use the IGD metric [6]. The results of the computational experiment demonstrate the good performance of A-GWASF-GA in the novel many-objective optimization benchmark problems considered.