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Lexicographic Max-Ordering - A Solution Concept for Multicriteria Combinatorial Optimization

  • In this paper we will introduce the concept of lexicographic max-ordering solutions for multicriteria combinatorial optimization problems. Section 1 provides the basic notions of multicriteria combinatorial optimization and the definition of lexicographic max-ordering solutions. In Section 2 we will show that lexicographic max-ordering solutions are pareto optimal as well as max-ordering optimal solutions. Furthermore lexicographic max-ordering solutions can be used to characterize the set of pareto solutions. Further properties of lexicographic max-ordering solutions are given. Section 3 will be devoted to algorithms. We give a polynomial time algorithm for the two criteria case where one criterion is a sum and one is a bottleneck objective function, provided that the one criterion sum problem is solvable in polynomial time. For bottleneck functions an algorithm for the general case of Q criteria is presented.

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Author:Matthias Ehrgott
URN (permanent link):urn:nbn:de:hbz:386-kluedo-48498
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (268)
Document Type:Report
Language of publication:English
Publication Date:2017/10/16
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/16
Number of page:11
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)