Column Generation for the Kidney Exchange Problem

Lucie Pansart (1, 2) , Hadrien Cambazard (2) , Nicolas Catusse (2) , Gautier Stauffer (3)

1 G-SCOP_OC - Optimisation Combinatoire
2 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
3 Kedge Business School [Talence]

The Kidney Exchange Problem (KEP) aims at finding the best exchanges in a barter market where agents are patients with a willing but incompatible donor. (Abraham et al. 2007) introduced a natural (exponential) integer programming formulation called the cycle formulation that they could solve efficiently by a branch-and-price approach. Recently, several countries allowed for the participation of altruistic donors in the exchanges. The corresponding variant of KEP is harder to solve as the pricing problem becomes N P-complete. In this work, we study and experiment a column generation approach that takes into account altruistic donors. We use advanced techniques to circumvent the N P-hardness of the pricing problem and show that the corresponding method can provide excellent guaranteed feasible solutions in a small amount of time.

Mots clés: color coding; integer programming; Kidney exchange problem; column generation

Domaines: Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Lucie Pansart, Hadrien Cambazard, Nicolas Catusse, Gautier Stauffer. Column Generation for the Kidney Exchange Problem. 12 th International Conference on MOdeling, Optimization and SIMlation-MOSIM18, Jun 2018, Toulouse, France. ⟨hal-02010440⟩