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

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.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Interactive Decomposition Multi-Objective Optimization via Progressively Learned Value Functions

Decomposition has become an increasingly popular technique for evolutionary multi-objective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, the decision maker (DM) might only be interested in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee to find the preferred solutions when tackling many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation and optimization. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behavior. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward to the ROI. The optimization module, which can be any decomposition-based EMO algorithm in principle, utilizes the biased reference points to direct its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions.Comment: 25 pages, 18 figures, 3 table