IGD+-EMOA: A multi-objective evolutionary algorithm based on IGD+

Abstract

In recent years, the design of selection mechanisms based on performance indicators has become a very popular trend in the development of new Multi-Objective Evolutionary Algorithms (MOEAs). The main motivation has been the well-known limitations of Pareto-based MOEAs when dealing with problems having four or more objectives (the so-called many-objective problems). The most commonly adopted indicator has been the hypervolume, mainly because of its nice mathematical properties (e.g., it is the only unary indicator which is known to be Pareto compliant). However, the hypervolume has a well-known disadvantage: its exact computation is very costly in high dimensionality, making it prohibitive for many-objective problems (this cost normally becomes unaffordable for problems with more than 5 objectives). Recently, a variation of the well-known inverse generational distance (IGD) was introduced. This indicator, which is called IGD+ was shown to be weakly Pareto compliant, and presents some evident advantages with respect to the original IGD. Here, we propose an indicator-based MOEA, which adopts IGD+. The proposed approach adopts a novel technique for building the reference set, which is used to assess the quality of the solutions obtained during the search. Our preliminary results indicate that our proposed approach is able to solve many-objective problems in an effective and efficient manner, being able to obtain solutions of a similar quality to those obtained by SMS-EMOA and MOEA/D, but at a much lower computational cost than required by the computation of exact hypervolume contributions (as adopted in SMS-EMOA).