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

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 ow problems are addressed. Three types of agents are 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 ow of products. For that aim, we assume that they o er to the transportation agents a reward that is proportional to the realized ow 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 ow of products. The total network ow 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 de ned 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 ow. 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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Cited literature [101 references]

https://tel.archives-ouvertes.fr/tel-01291878
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Submitted on : Tuesday, March 22, 2016 - 11:35:08 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:26 AM
Long-term archiving on: : Sunday, November 13, 2016 - 10:31:09 PM

### Identifiers

• HAL Id : tel-01291878, version 1

### Citation

Nadia Chaabane. Recherche de flots stables dans des réseaux de transport multi-agents. Automatique. INSA Toulouse, 2016. Français. ⟨tel-01291878v1⟩

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