Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems

摘要

In many applications, it is required to optimize several conflicting ob jectives concurrently leading to a multobjective optimization problem (MOP). The solution set of a MOP, the Pareto set, typically forms a (k - 1 )-dimensional object, where k is the number of objectives involved in the optimization problem. The pur pose of this chapter is to give an overview of recently developed set oriented tech niques - subdivision and continuation methods - for the computation of Pareto sets Φ of a given MOP. All these methods have in common that they create sequences of box collections which aim for a tight covering of Φ. Further, we present a class of multiobjective optimal control problems which can be efficiently handled by the set oriented continuation methods using a transformation into high-dimensional MOPs. We illustrate all the methods on both academic and real world examples.