A Tabu Search approach to solve a network design problem with user-optimal flows

Antonio Mauttone (1) , Martine Labbé (2) , Rosa Figueiredo (3)

1 UDELAR - Universidad de la República [Montevideo]
2 ULB - Département d'Informatique [Bruxelles]
3 CIDMA - Center for Research & Development in Mathematics and Applications [Aveiro]

In this work, we formulate a network design problem with user-optimal flows as a mixed discrete bilevel linear programming problem. The upper level objective function minimizes the sum of fixed and variable costs associated with edges. The lower level problem defines a set of independent shortest path problems on the network resulting from the decisions taken in the upper level. Using the Bellman optimality conditions for the shortest path problems in the lower level, we obtain a one-level integer formulation for the network design problem. We implemented a tabu search metaheuristic based in a framework proposed in the literature to solve discrete bilevel problems. We propose a hybrid strategy that uses information coming from the linear relaxation of the one level formulation to select the initial solutions in the tabu search. Preliminary computational results are discussed as well as some directions to continue this research.

Mots clés: Network design; shortest path routing; discrete bilevel programming; tabu search

Domaines: Recherche opérationnelle [math.OC]

Antonio Mauttone, Martine Labbé, Rosa Figueiredo. A Tabu Search approach to solve a network design problem with user-optimal flows. ALIO/EURO Workshop on Applied Combinatorial Optimization, 2008, Buenos Aires, Argentina. ⟨hal-01882382⟩