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.
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Notes
- 1.
The terms “criterion” and “objective” are usual respectively in mcda and in mop. Even if they are not equivalent, they are considered as synonyms in this paper.
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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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Fouchal, H., Gandibleux, X., Lehuédé, F. (2011). A Lower Bound of the Choquet Integral Integrated Within Martins’ Algorithm. In: Shi, Y., Wang, S., Kou, G., Wallenius, J. (eds) New State of MCDM in the 21st Century. Lecture Notes in Economics and Mathematical Systems, vol 648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19695-9_7
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