A combination of geometric buffer technique and ray based interactive methods for multi-objective evolutionary algorithms

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 of MOEAs, that is consideration of Decision Maker (DM) during the optimization process (interacting with DM) for checking, analyzing the results and giving the preference.In [2] and its next version in [9], a system of rays is used to maintain the diversity of the population during evolutionary process. The niching values are from the distance of solutions and rays are used to guide the evolutionary process ensures the balance between exploration and exploitation of the population. When DM interactive with the evolutionary process, a set of reference points are given as his/her expected area in objective space. Based on the concept of the system of rays, in [11], and its updated version in [12] the authors proposed a ray based interactive method with a set of reference points in different ways. In this paper, we indicated some issues on the method and we suggest to use a geometric buffer based technique to improve the method. We carried out a case study on several test problems and obtained quite good results.