A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme

Authors:
Anthony Przybylski;Xavier Gandibleux;Matthias Ehrgott
Affiliations:
LINA (Laboratoire d'Informatique de Nantes Atlantique), Unité Mixte de Recherche Centre National de la Recherche Scientifique 6241, Université de Nantes, 44322 Nantes, France;LINA (Laboratoire d'Informatique de Nantes Atlantique), Unité Mixte de Recherche Centre National de la Recherche Scientifique 6241, Université de Nantes, 44322 Nantes, France;Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
Venue:
INFORMS Journal on Computing
Year:
2010

Citing 4
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Abstract

In this paper, we present two versions of an algorithm for the computation of all nondominated extreme points in the outcome set of a multiobjective integer programme. We define adjacency of these points based on weight space decomposition. Thus, our algorithms generalise the well-known dichotomic scheme to compute the set of nondominated extreme points in the outcome set of a biobjective programme. Both algorithms are illustrated with and numerically tested on instances of the assignment and knapsack problems with three objectives.