Column Generation for the Kidney Exchange Problem
Résumé
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.
Origine | Fichiers produits par l'(les) auteur(s) |
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