On spanning tree problems with multiple objectives

  • We investigate two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights. First, we want to minimize the maximum of Q linear objective functions taken over the set of all spanning trees (max linear spanning tree problem ML-ST). Secondly, we look for efficient spanning trees (multi criteria spanning tree problem MC-ST). Problem ML-ST is shown to be NP-complete. An exact algorithm which is based on ranking is presented. The procedure can also be used as an approximation scheme. For solving the bicriterion MC-ST, which in the worst case may have an exponential number of efficient trees, a two-phase procedure is presented. Based on the computation of extremal efficient spanning trees we use neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.

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Author:Horst W. Hamacher, Günther Ruhe
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (239)
Document Type:Report
Language of publication:English
Date of Publication (online):2017/10/16
Year of first Publication:1993
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/16
Page Number:28
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)