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A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems

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Date
2010
Dewey
Recherche opérationnelle
Sujet
Branch and bound; Minimal spanning tree problem; Multicriteria combinatorial optimization; Choquet integral; Knapsack problem
Conference country
NEW ZEALAND
Book title
Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems Proceedings of the 19th International Conference on Multiple Criteria Decision Making, Auckland, New Zealand, 7th - 12th January 2008
Author
Wallenius, Jyrki
Publisher
Springer
Publisher city
Berlin Heidelberg
Year
2010
ISBN
978-3-642-04044-3
URI
https://basepub.dauphine.fr/handle/123456789/6082
Collections
  • LAMSADE : Publications
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Author
Galand, Lucie
Perny, Patrice
Spanjaard, Olivier
Type
Communication / Conférence
Item number of pages
389
Abstract (EN)
This paper is devoted to the search for Choquet-optimal solutions in multicriteria combinatorial optimization with application to spanning tree problems and knapsack problems. After recalling basic notions concerning the use of Choquet integrals for preference aggregation, we present a condition (named preference for interior points) that characterizes preferences favoring well-balanced solutions, a natural attitude in multicriteria optimization. When using a Choquet integral as preference model, this condition amounts to choosing a submodular (resp. supermodular) capacity when criteria have to be minimized (resp. maximized). Under this assumption, we investigate the determination of Choquet-optimal solutions in the multicriteria spanning tree problem and the multicriteria 0-1 knapsack problem. For both problems, we introduce a linear bound for the Choquet integral, computable in polynomial time, and propose a branch and bound procedure using this bound. We provide numerical experiments that show the actual efficiency of the algorithms on various instances of different sizes.

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