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

  • Hugo Fouchal
  • Xavier Gandibleux
  • Fabien Lehuédé
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 648)

Abstract

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.

Keywords

Choquet integral Multiobjective optimization Shortest paths 

Notes

Acknowledgements

The authors would like to thank the regional council of Pays de la Loire (France), MILES project, for their support of this research.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hugo Fouchal
    • 1
    • 2
  • Xavier Gandibleux
    • 1
  • Fabien Lehuédé
    • 2
  1. 1.LINAUniversité de NantesNantes Cedex-03France
  2. 2.IRCCyNÉcole des Mines de NantesNantesFrance

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