Distance Transformation for Network Design Problems

Ali Ridha Mahjoub (1) , Michael Poss (2) , Luidi Simonetti (3) , Eduardo Uchoa (4)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 MAORE - Methods, Algorithms for Operations REsearch
3 IC-UFF - Instituto de Computação [Niteroi-Rio de Janeiro]
4 UFF - Universidade Federal Fluminense [Rio de Janeiro]

We propose a new generic way to construct extended formulations for a large class of network design problems with given connectivity requirements. The approach is based on a graph transformation that maps any graph into a layered graph according to a given distance function. The original connectivity requirements are in turn transformed into equivalent connectivity requirements in the layered graph. The mapping is extended to the graphs induced by fractional vectors through an extended linear integer programming formulation. While graphs induced by binary vectors are mapped to isomorphic layered graphs, those induced by fractional vectors are mapped to a set of graphs having worse connectivity properties. Hence, the connectivity requirements in the layered graph may cut off fractional vectors that were feasible for the problem formulated in the original graph. Experiments over instances of the Steiner Forest and Hop-constrained Survivable Network Design problems show that significant gap reductions over the state-of-the art formulations can be obtained.

Mots clés: Extended Formulations; Network Design; Benders decomposition; Benders decomposition AMS subject classifications

Domaines: Recherche opérationnelle [math.OC]

Ali Ridha Mahjoub, Michael Poss, Luidi Simonetti, Eduardo Uchoa. Distance Transformation for Network Design Problems. SIAM Journal on Optimization, 2019, 29 (2), pp.1687-1713. ⟨10.1137/16M1108261⟩. ⟨hal-01632972v3⟩