A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems
Galand, Lucie; Perny, Patrice; Spanjaard, Olivier (2010), A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems, in Wallenius, Jyrki, 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, Springer : Berlin Heidelberg, p. 389
TypeCommunication / Conférence
Conference countryNEW ZEALAND
Book titleMultiple 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
Book authorWallenius, Jyrki
MetadataShow full item record
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.
Subjects / KeywordsBranch and bound; Minimal spanning tree problem; Multicriteria combinatorial optimization; Choquet integral; Knapsack problem
Showing items related by title and author.
Bidirectional versus Unidirectional Heuristic Search for Multiojective Optimization in State Space Graphs Galand, Lucie; Ismaili, Anisse; Perny, Patrice; Spanjaard, Olivier (2013) Communication / Conférence