处理肾脏交换问题中的基本路径
Dealing with elementary paths in the Kidney Exchange Problem
摘要：
研究了求解肾交换问题的列生成方案定价步骤中的基本路径问题。后者的目的是在肾移植的病人和捐赠者中寻找捐赠的交换。非正式地，问题是确定一组有限长度的循环和链，最大化有向图中的医疗效益。循环公式，一个大规模模型的问题限制到捐赠周期，有效地解决了通过分支和价格。然而，当包含捐赠链时，定价子问题就变成了NP难问题。本文提出了一个新的完整的列生成计划，考虑到这些链发起的利他捐助者。定价问题的非精确动态方法的发展，NG-路线放松和颜色编码启发式，导致一个有效的列生成过程。
英文摘要：
We study an elementary path problem which appears in the pricing step of a column generation scheme solving the kidney exchange problem. The latter aims at finding exchanges of donations in a pool of patients and donors of kidney transplantations. Informally, the problem is to determine a set of cycles and chains of limited length maximizing a medical benefit in a directed graph. The cycle formulation, a large-scale model of the problem restricted to cycles of donation, is efficiently solved via branch-and-price. When including chains of donation however, the pricing subproblem becomes NP-hard. This article proposes a new complete column generation scheme that takes into account these chains initiated by altruistic donors. The development of non-exact dynamic approaches for the pricing problem, the NG-route relaxation and the color coding heuristic, leads to an efficient column generation process.
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