Covering Pareto sets by multilevel evolutionary subdivision techniques

Abstract

We present new hierarchical set oriented methods for the numerical solution of multi-objective optimization problems. These methods are based on a generation of collections of subdomains (boxes) in parameter space which cover the entire set of Pareto points. In the course of the subdivision procedure these coverings get tighter until a desired granularity of the covering is reached. For the evaluation of these boxes we make use of evolutionary algorithms. We propose two particular strategies and discuss combinations of those which lead to a better algorithmic performance. Finally we illustrate the efficiency of our methods by several examples. © Springer-Verlag Berlin Heidelberg 2003.