A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem

Authors:
Francis Sourd;Olivier Spanjaard
Affiliations:
Laboratoire d'Informatique de Paris 6 (LIP6-UPMC), Université Pierre et Marie Curie, F-75252 Paris Cedex 05, France;Laboratoire d'Informatique de Paris 6 (LIP6-UPMC), Université Pierre et Marie Curie, F-75252 Paris Cedex 05, France
Venue:
INFORMS Journal on Computing
Year:
2008

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Abstract

This paper focuses on a multiobjective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto-optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded if one can define a separating hypersurface in the objective space between the set of feasible solutions in the subtree and the set of points corresponding to potential Pareto-optimal solutions. Numerical experiments on the biobjective spanning tree problem are provided that show the efficiency of the approach in a biobjective setting.