On the Model–Building Issue of Multi–Objective Estimation of Distribution Algorithms Luis Mart´ ı, Jes´ us Garc´ ıa, Antonio Berlanga, and Jos´ e M. Molina GIAA, Dept. of Informatics, Universidad Carlos III de Madrid Av. Universidad Carlos III 22, Colmenarejo 28270 Madrid, Spain {lmarti,jgherrer}@inf.uc3m.es, {aberlan,molina}@ia.uc3m.es http://www.giaa.inf.uc3m.es/ Abstract. It has been claimed that perhaps a paradigm shift is necessary in order to be able to deal with this scalability issue of multi– objective optimization evolutionary algorithms. Estimation of distribu- tion algorithms are viable candidates for such task because of their adap- tation and learning abilities and simplified algorithmics. Nevertheless, the extension of EDAs to the multi–objective domain have not provided a significant improvement over MOEAs. In this paper we analyze the possible causes of this underachievement and propose a set of measures that should be taken in order to overcome the current situation. 1 Introduction Estimation of distribution algorithms (EDAs) [1] have been hailed as one of the cornerstones of modern evolutionary computation. Like most evolutionary algorithms [2], EDAs are population based optimization algorithms. However, in these algorithms, the step where the evolutionary operators are applied to the population, is substituted by construction of a statistical model of the most promising subset of the population. This model is then sampled to produce new individuals that are merged with the original population following a given substitution policy. On particular area where EDAs could yield important results is the one per- taining to multi–objective optimization problems (MOPs). In this class of prob- lems the optimizer must find one or more feasible solutions that correspond with the extreme values (either maximum or minimum) of two or more functions sub- ject to a set of constraint. Therefore, an optimizer’s solution is a set of equally good, trade–off solutions. The application of evolutionary computation to MOPs has prompted the cre- ation of what has been called multi–objective optimization evolutionary algo- rithms (MOEAs) [3]. However, those approaches tend to fail when faced with problems with a relatively large amount of objectives as they require an expo- nential increase of the resources made available to them (see [4,5] and [3] pp. 414–419]). E. Corchado et al. (Eds.): HAIS 2009, LNAI 5572, pp. 293–300, 2009. c  Springer-Verlag Berlin Heidelberg 2009