On Two New Formulations for the Fixed Charge Network Design Problem with Shortest Path Constraints

Ikram Bouras (1) , Rosa Figueiredo (2) , Michael Poss (3) , Fen Zhou (2)

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 LIA - Laboratoire Informatique d'Avignon
3 MAORE - Methods, Algorithms for Operations REsearch

We study the fixed charge network design problem with shortest path constraints which is modeled as a bi-level program. We first review three one-level formulations obtained by applying the complementarity slackness theorem, Bellman's optimality conditions and cycle elimination constraints. We propose two new binary integer programming (BILP) formulations inspired by path and cycle inequalities. The two formulations have exponential numbers of constraints. We incorporate the path and the cycle based formulations in a branch-and-cut algorithm and in another cutting-plane based method. Numerical experiments are performed on real instances, and random data sets generated with different criteria to examine the difficulty of the instances. The results show that the proposed cutting plane algorithms can solve up to 19% more instances than the classic branch-and-bound algorithms.

Mots clés: Cutting plane; Bi-level programming; Network design; Branch-and-cut

Domaines: Optimisation et contrôle [math.OC]; Combinatoire [math.CO]; Réseaux sociaux et d'information [cs.SI]; Recherche opérationnelle [math.OC]; Réseaux et télécommunications [cs.NI]; Mathématique discrète [cs.DM]

Ikram Bouras, Rosa Figueiredo, Michael Poss, Fen Zhou. On Two New Formulations for the Fixed Charge Network Design Problem with Shortest Path Constraints. Computers and Operations Research, 2019, 108, pp.226-237. ⟨10.1016/j.cor.2019.04.007⟩. ⟨hal-02013557v2⟩