A Multi-point Interactive Method for Multi-objective Evolutionary Algorithms

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 this paper, we propose an interactive method allowing DM to specify a set of reference points. It used a generic algorithm framework of MOEA/D, a widely-used and decomposition-based MOEA for demonstration of concept. Basically MOEA/D decomposes a multi-objective optimization problem into a number of different single-objective optimization sub-problems and defines neighborhood relations among these sub-problems. Then a population-based method is used to optimize these sub-problems simultaneously. Each sub-problem is optimized by using information mainly from its neighboring sub-problems. In MOEA/D an ideal point is used to choose neighbored solutions for each run. Instead of using a single point, we introduce an alternative to the set of reference points. There are several way to take into account the information of the region specified by the set of reference points; here we used the mean of this set (or we call the combined point). The combined point which represents for the set of reference points from DM is used either to replace or adjust the current ideal point obtained by MOEA/D. We carried out a case study on several test problems and obtained quite good results.