Abstract. 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.

In this paper, we present a Multi-objective Particle Swarm Optimizer (MOPSO) based on a decomposition approach, which is proposed to solve Constrained Multi-Objective Aerodynamic Shape Optimization Problems (CMO-ASOPs). The constraint-handling technique adopted in this approach is based on the well-known ε-constraint method. Since the ε-constraint method was initially proposed to deal with constrained single-objective optimization problems, we adapted it so that it could be incorporated into a MOPSO. Our main focus is to solve CMO-ASOPs in an efficient and effective manner. The proposed constrained MOPSO guides the search by updating the position of each particle using a set of solutions considered as the global best according to both the decomposition approach and the ε-constraint method. Our preliminary results indicate that our proposed approach is able to outperform a state-of-the-art MOEA in several CMO-ASOPs.

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In this paper, we present a novel Multi-Objective Evolutionary Algorithm (MOEA) called MODE-LD+SS, which combines Differential Evolution with local dominance and a scalar selection mechanism for improving both its convergence rate and its distribution of solutions along the Pareto front. In order to assess the performance of the proposed approach, we use a set of standard test functions and performance measures taken from the specialized literature. Results are compared with respect to three MOEAs representative of the state-of-the-art in the area: NSGA-II, SPEA2, and MOEA/D.978-1-4244-8126-2/10/$26.00 ©2010 IEEE