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

Francis Sourd 1 Olivier Spanjaard 2
1 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
2 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
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.
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Francis Sourd, Olivier Spanjaard. A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem. INFORMS Journal on Computing, Institute for Operations Research and the Management Sciences (INFORMS), 2008, 20 (3), pp.472-484. ⟨10.1287/ijoc.1070.0260⟩. ⟨hal-01170228⟩

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