## A Level Set Method for Multiobjective Combinatorial Optimization: Application to the Quadratic Assignment Problem

• Multiobjective combinatorial optimization problems have received increasing attention in recent years. Nevertheless, many algorithms are still restricted to the bicriteria case. In this paper we propose a new algorithm for computing all Pareto optimal solutions. Our algorithm is based on the notion of level sets and level curves and contains as a subproblem the determination of K best solutions for a single objective combinatorial optimization problem. We apply the method to the Multiobjective Quadratic Assignment Problem (MOQAP). We present two algorithms for ranking QAP solutions and nally give computational results comparing the methods.

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Author: Matthias Ehrgott, Thomas Stephan, Dagmar Tenfelde-Podehl urn:nbn:de:hbz:386-kluedo-12366 Report in Wirtschaftsmathematik (WIMA Report) (84) Preprint English 2002 2002 Technische Universität Kaiserslautern Combinatorial optimization ; K-best solution; Level sets ; Multiobjective programming Fachbereich Mathematik 510 Mathematik 90C27 Combinatorial optimization 90C29 Multi-objective and goal programming

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