On the convex piecewise linear unsplittable multicommodity flow problem

Bernard Fortz (1, 2) , Luis Gouveia (3) , Martim Joyce-Moniz (4)

1 INOCS - Integrated Optimization with Complex Structure
2 GOM - Graphes et Optimisation Mathématique [Bruxelles]
3 ULISBOA - Universidade de Lisboa = University of Lisbon
4 ULB - Université libre de Bruxelles

We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the associated polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.

Domaines: Recherche opérationnelle [math.OC]

Bernard Fortz, Luis Gouveia, Martim Joyce-Moniz. On the convex piecewise linear unsplittable multicommodity flow problem. 2016 12th International Conference on the Design of Reliable Communication Networks (DRCN), Mar 2016, Paris, France. pp.9--13, ⟨10.1109/DRCN.2016.7470829⟩. ⟨hal-01410555⟩