A ray based interactive method for direction based multi-objective evolutionary algorithm

Abstract

Many real-world optimization problems have more than one objective (and these objectives are often conflicting). In most cases, there is no single solution being optimized with regards to all objectives. Deal with such problems, Multi-Objective Evolutionary Algorithms (MOEAs) have shown a great potential. There has been a popular trend in getting suitable solutions and increasing the convergence ofMOEAs by considering by Decision Makers (DM) during the optimization process (interacting with DM) for checking, analyzing the results and giving the preference. In this paper, we propose an interactive method for DMEA, a direction-based MOEA for demonstration of concept. In DMEA, the authors used an explicit niching operator with a system of rays which divide the space evenly for the selection of non-dominated solutions to fill the archive and the next generation. We found that, by using the system of rays with a niching operator, solutions will be convergence to the Pareto Front via the corresponding to the distribution of rays in objective space. By this reason, we proposed an interactive method using set of rays which are generated from given reference points by DM. These rays replace current original rays in objective space. Based on the new distribution of rays, a niching is applied to control external population (the archive) and next generation for priority convergence to DM’s preferred region. We carried out a case study on several test problems and obtained quite good results.