A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization

Evolutionary algorithms have been very popular for solving multiobjective optimization problems, mainly because of their ease of use, and their wide applicability. However, multi-objective evolutionary algorithms (MOEAs) tend to consume an important number of objective function evaluations, in order to achieve a reasonably good approximation of the Pareto front. This is a major concern when attempting to use MOEAs for real-world applications, since we can normally afford only a fairly limited number of fitness function evaluations in such cases. Despite these concerns, relatively few efforts have been reported in the literature to reduce the computational cost of MOEAs. It has been until relatively recently, that researchers have developed techniques to achieve an effective reduction of fitness function evaluations by exploiting knowledge acquired during the search. In this chapter, we analyze different proposals currently available in the specialized literature to deal with expensive functions in evolutionary multi-objective optimization. Additionally, we review some real-world applications of these methods, which can be seen as case studies in which such techniques led to a substantial reduction in the computational cost of the MOEA adopted. Finally, we also indicate some of the potential paths for future research in this area.