Contribution à l'élicitation des paramètres en optimisation multicritère

Noureddine Aribi 1
1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe CEP
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : Many methods exist for solving multicriteria optimization problems, and it is not easy to choose the right method well adapted to a given multicriteria problem. Even after choosing a multicriteria method, various parameters (e.g. weight, utility functions, etc.) must be carefully determined either to find the optimal solution (best compromise) or to classify all feasible solutions (the set of alternatives). To overcome this potential difficulty, elicitation methods are used in order to help the decision maker to fix safely the parameters. Additionally, we assume that we have a set of feasible solutions, and we also make the assumption that we have prior information about the preferences of the decision maker, and we focus on how to use this information, rather than how to get them. In the first contribution of this work, we take advantage of a simple and quickly computable statistical measure, namely, the Spearman $rho$ correlation coefficient, to develop an gready approche, and two exact approaches based on constraint programming (CP) and linear integer programming (MIP). These methods are then used to automatically elicit the appropriate parameter of the lexicographic ordering method. We also propose some elicitation models for most commonly used multicriteria methods, such as MinLeximax method used to ensure fairness and efficiency requirements, the weighted sum method, and OWA operators. These elicitation models are based either on solving mixed integer linear programming, or constraints networks with an objective function.
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Noureddine Aribi. Contribution à l'élicitation des paramètres en optimisation multicritère. Autre [cs.OH]. Université Nice Sophia Antipolis, 2014. Français. ⟨NNT : 2014NICE4031⟩. ⟨tel-01065629⟩

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