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Méthodes exactes pour les problèmes combinatoires bi-objectif : Application sur les problèmes de tournées de véhicules

Estele Glize 1
1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Real-world problems involve several different criteria to take into account. For instance, a route may be associated with multiple features such as its cost, its ecological footprint, its duration, or its length. Resulting mathematical problems are addressed by multi-objective optimization. In general, there is no feasible solution able to maximize or minimize all objectives. Thus, decision makers want to examine the trade-off between the objectives in order to select the most suitable solution for them. Solving a multi-objective optimization problem consists of finding a set of points in the objective space, called non dominated points. No point in the objective space is better than a point of this set for all objectives. Few exact methods exist in literature to solve NP-hard multi- objective combinatorial problems, especially those with a NP-hard mono-objective variant. This thesis works on exact methods for such multi-objective problems, and the class of bi-objective vehicle routing problems is used as reference. The manuscript presents a column generation based-approach which aims to efficiently enumerate the set of non dominated points of the problems. We seek the best way to explore the objective space, and we propose different acceleration techniques based on structural properties. To show its generic aspect, the approach is applied to several bi-objective variants of the vehicle routing problem : the vehicle routing problem with time windows, the covering tour problem and the team-orienteering problem with time windows. Extensive computational experiments highlight the efficiency of the proposed method.
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Estele Glize. Méthodes exactes pour les problèmes combinatoires bi-objectif : Application sur les problèmes de tournées de véhicules. Automatique / Robotique. INSA de Toulouse, 2019. Français. ⟨NNT : 2019ISAT0023⟩. ⟨tel-02404217v2⟩

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