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.
Author: | Matthias Ehrgott |
---|---|
URN: | urn:nbn:de:hbz:386-kluedo-48498 |
Series (Serial Number): | Preprints (rote Reihe) des Fachbereich Mathematik (268) |
Document Type: | Report |
Language of publication: | English |
Date of Publication (online): | 2017/10/16 |
Year of first Publication: | 1995 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2017/10/16 |
Page Number: | 11 |
Faculties / Organisational entities: | Kaiserslautern - 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) |