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Recherche de flots stables dans des réseaux de transport multi-agents

Nadia Chaabane 1
1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : In this work, multi-agent network flow problems are addressed. Three types of agentsare considered, namely the producer, transportation and customer agents and various network topologies are tackled. Every transportation agent controls the capacities of a set of elementary routes (arcs), each one having a capacity that can be increased up to a certain point at a given cost. The other agents (i.e., customers/producers) are interesting in maximizing their flow of products. For that aim, we assume that they offer to the transportation agents a reward that is proportional to the realized flow value. This particular multi-agent framework is referred to as a multi-agent network expansion game. The transportation agent’s strategy consists in deciding upon the capacity of its arcs, an extra-cost being incurred for any capacity expansion. It receives in return a part of the total reward. It is interested in the maximization of its profit and behaves accordingly. Beside that, the producers/customers’ strategies consist in deciding the sharing policy for their reward for maximizing their own flow of products. The total network flow value eventually depends on all agents’ strategies. We take interest in characterizing and finding particular stable strategies (i.e., Nash Equilibria) that are of interest for this game under various assumptions. Based on this characterization, several cases are defined and studied. The analysis of the complexity of some decision problems is made. We particularly focus on the problem of finding a Nash Equilibrium that maximizes the value of the total flow. We prove that this problem is NP-hard in the strong sense and show how such a strategy can be characterized considering paths in specific reduced agent-networks. We also provide a mixed integer linear programming (MILP) formulation that solves the problem in the case of a single producer/customer agent and a set of transportation agents. Computational experiments are provided to prove the effectiveness of our approach
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Nadia Chaabane. Recherche de flots stables dans des réseaux de transport multi-agents. Automatique. INSA de Toulouse, 2016. Français. ⟨NNT : 2016ISAT0028⟩. ⟨tel-01291878v2⟩

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