2013 | OriginalPaper | Chapter
Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems
Authors : Oliver Schütze, Katrin Witting, Sina Ober-Blöbaum, Michael Dellnitz
Published in: EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation
Publisher: Springer Berlin Heidelberg
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In many applications, it is required to optimize several conflicting objectives 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 purpose of this chapter is to give an overview of recently developed set oriented techniques - subdivision and continuation methods - for the computation of Pareto sets
$\mathcal{P}$
of a givenMOP. All these methods have in common that they create sequences of box collections which aim for a tight covering of
$\mathcal{P}$
. 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-dimensionalMOPs. We illustrate all the methods on both academic and real world examples.