New Algorithms for Hierarchical Optimization in Kidney Exchange Programs

Abstract

New Exact Approaches Tailored for Kidney Exchange Programs with Hierarchical Objectives Kidney exchange programs increase the rate of living donor kidney transplantation. Whereas effective integer programming models aimed at maximizing the total number of transplants have been proposed in the literature, these cannot always be extended to handle a hierarchy of objectives, which is often a requirement in practice. In “New Algorithms for Hierarchical Optimization in Kidney Exchange Programs,” Delorme, García, Gondzio, Kalcsics, Manlove, and Pettersson introduce a new integer programming framework to solve large-size instances of kidney exchange programs. The authors use an ad hoc preprocessing and a reduced-cost variable fixing algorithm to dramatically decrease the size of the models, and they devise a diving algorithm that exploits the hierarchical structure of the problem to significantly reduce the number of integer programs that need to be solved. They also show that it is possible to transition between models as different layers are traversed in the hierarchy, allowing each layer to be solved with the most effective model. Experiments on three different European kidney exchange programs show that running times can be reduced by up to three orders of magnitude.

Half-cycle: A new formulation for modelling kidney exchange problems

“…Considering that the bound obtained by the LP-relaxation of HCF is as tight as the bound obtained by the cycle formulation, we can follow the path of Delorme et al [11] and apply the concept of a destructive bound together with a reduced-cost variable fixing strategy to reduce the number of variables that needs to be considered in the model. To do so, we start by solving the LPrelaxation of model ( 4)- (8), save the objective value ẑ, and use it to derive a valid upper bound U = ẑ on the maximum number of transplants.…”

“…In category (ii), as far as improving the algorithmic performance of existing models is concerned, we mention the work of Lam and Mak-Hau [19] who solved the cycle formulation with a branch-and-price framework, and the work of Delorme et al [11] who used reduced-cost variable fixing together with preprocessing techniques and a diving algorithm to enhance the performance of the cycle formulation for KEPs with hierarchical optimisation. Finally, for category (iii), the literature aiming at adapting existing approaches to real-world applications is very large.…”

“…Finally, for category (iii), the literature aiming at adapting existing approaches to real-world applications is very large. We only mention a few main areas such as realistic instance generators [12,29], stochastic optimisation [2,22], and hierarchical optimisation [7,11].…”

“…The model is inspired by the cycle formulation and represents a cycle by two compatible halves. We detail some algorithmic enhancements for HCF; these include the use of a reduced-cost variable fixing framework [11] that could also be applied to PIEF. We show that HCF together with these algorithmic enhancements obtains better empirical performance when solved with a commercial IP solver than other mathematical models when the cycle size limit is set to 4, 5, or 6, depending on the density of the compatibility graph.…”

Computing Balanced Solutions for Large International Kidney Exchange Schemes

“…This is an updated version of[47], a data generator which is commonly used in experimental studies (see e.g [21,25,35,38]…”