## Generalized Multiple Objective Bottleneck Problems

• We consider multiple objective combinatiorial optimization problems in which the first objective is of arbitrary type and the remaining objectives are either bottleneck or k-max objective functions. While the objective value of a bottleneck objective is determined by the largest cost value of any element in a feasible solution, the kth-largest element defines the objective value of the k-max objective. An efficient solution approach for the generation of the complete nondominated set is developed which is independent of the specific combinatiorial problem at hand. This implies a polynomial time algorithm for several important problem classes like shortest paths, spanning tree, and assignment problems with bottleneck objectives which are known to be NP-hard in the general multiple objective case.

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Author: Jochen Gorski, Kathrin Klamroth, Stefan Ruzika urn:nbn:de:hbz:386-kluedo-16686 Report in Wirtschaftsmathematik (WIMA Report) (131) Preprint English 2010 2010 Technische Universität Kaiserslautern bottleneck ; combinatorial optimization ; k-max; multiple objective Fachbereich Mathematik 510 Mathematik

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