A Lower Bound of the Choquet Integral Integrated Within Martins' Algorithm

Hugo Fouchal (1, 2) , Fabien Lehuédé (1) , Xavier Gandibleux (3)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 LINA - Laboratoire d'Informatique de Nantes Atlantique
3 OPTI

The problem investigated in this work concerns the integration of a decision-maker preference model within an exact algorithm in multiobjective combinatorial optimization. Rather than computing the complete set of efficient solutions and choosing a solution afterwards, our aim is to efficiently compute one solution satisfying the decision maker preferences elicited a priori. The preference model is based on the Choquet integral. The reference optimization problem is the multiobjective shortest path problem, where Martins' algorithm is used. A lower bound of the Choquet integral is proposed that aims to prune useless partial paths at the labeling stage of the algorithm. Various procedures exploiting the proposed bound are presented and evaluated on a collection of benchmarks. Numerical experiments show significant improvements compared to the exhaustive enumeration of solutions.

Mots clés: Choquet integral; Multiobjective optimization; Shortest paths

Domaines: Recherche opérationnelle [math.OC]

Hugo Fouchal, Fabien Lehuédé, Xavier Gandibleux. A Lower Bound of the Choquet Integral Integrated Within Martins' Algorithm. Shi, Yong and Wang, Shouyang and Kou, Gang and Wallenius, Jyrki. New State of MCDM in the 21st Century, Springer Berlin Heidelberg, pp.79-89, 2011, Lecture Notes in Economics and Mathematical Systems 648, ⟨10.1007/978-3-642-19695-9_7⟩. ⟨hal-00669556⟩