Choquet-based optimisation in multiobjective shortest path and spanning tree problems
Galand, Lucie; Perny, Patrice; Spanjaard, Olivier (2010), Choquet-based optimisation in multiobjective shortest path and spanning tree problems, European Journal of Operational Research, 204, 2, p. 303-315. http://dx.doi.org/10.1016/j.ejor.2009.10.015
TypeArticle accepté pour publication ou publié
Journal nameEuropean Journal of Operational Research
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Abstract (EN)This paper is devoted to the search of Choquet-optimal solutions in finite graph problems with multiple objectives. The Choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives. We first present a condition on preferences (name hereafter preference for interior points) that characterizes preferences favouring compromise solutions, a natural attitude in various contexts such as multicriteria optimisation, robust optimisation and optimisation with multiple agents. Within Choquet expected utility theory, this condition amounts to using a submodular capacity and a convex utility function. Under these assumptions, we focus on the fast determination of Choquet-optimal paths and spanning trees. After investigating the complexity of these problems, we introduce a lower bound for the Choquet integral, computable in polynomial time. Then, we propose different algorithms using this bound, either based on a controlled enumeration of solutions (ranking approach) or an implicit enumeration scheme (branch and bound). Finally, we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes.
Subjects / KeywordsSubmodular capacity; Multiobjective discrete optimisation; Minimum spanning tree problem; Shortest path problem; Choquet integral
Showing items related by title and author.
Règles de dominance pour la recherche de solutions Choquet-optimales en optimisation combinatoire multi-objectifs Fouchal, Hugo; Galand, Lucie; Lesca, Julien; Perny, Patrice (2012) Communication / Conférence