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A decision-theoretic approach to robust optimization in multivalued graphs

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  • Patrice Perny
  • Olivier Spanjaard
  • Louis-Xavier Storme

Abstract

This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenarios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach. Copyright Springer Science + Business Media, LCC 2006

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  • Patrice Perny & Olivier Spanjaard & Louis-Xavier Storme, 2006. "A decision-theoretic approach to robust optimization in multivalued graphs," Annals of Operations Research, Springer, vol. 147(1), pages 317-341, October.
    • Handle: RePEc:spr:annopr:v:147:y:2006:i:1:p:317-341:10.1007/s10479-006-0073-0
    DOI: 10.1007/s10479-006-0073-0
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    Cited by:

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    5. Galand, Lucie & Perny, Patrice & Spanjaard, Olivier, 2010. "Choquet-based optimisation in multiobjective shortest path and spanning tree problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 303-315, July.
    6. Virginie Gabrel & Cécile Murat & Aurélie Thiele, 2018. "Portfolio optimization with pw-robustness," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 267-290, September.
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    10. Mut, Murat & Wiecek, Margaret M., 2011. "Generalized equitable preference in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 212(3), pages 535-551, August.

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