Branch-price-and-cut is a leading methodology for solving various vehicle routing problems (VRPs). For many VRPs, the pricing subproblem of a branch-price-and-cut algorithm is highly time consuming, and to alleviate this difficulty, a relaxed pricing subproblem is used. In this paper, we introduce a new paradigm, called selective pricing, that can be applied in this context to reduce the time required for solving hard-to-solve VRPs by branch-price-and-cut. This paradigm requires the development of a labeling algorithm specific to the pricing subproblem. To illustrate selective pricing, we apply it to a branch-price-and-cut algorithm for the VRP with time windows, where the relaxed pricing subproblem is a shortest ng-path problem with resource constraints. We develop a labeling algorithm for this subproblem and show through computational experiments that it can yield significant time reductions (up to 32%) to reach a good lower bound on certain very-hard-to-solve VRPTW instances with 200 customers. We also introduce a new labeling heuristic which also leads to computational time reductions.

中文翻译：

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车辆路线选择中的分行减价算法中的选择性定价

降价支割是解决各种车辆路径问题（VRP）的领先方法。对于许多VRP，分支价格削减算法的定价子问题非常耗时，为了缓解这一困难，使用了一个宽松的定价子问题。在本文中，我们介绍了一种称为选择性定价的新范式，可以在这种情况下应用该范式，以减少通过分支降价来解决难以解决的VRP所需的时间。这种范例要求开发一种针对定价子问题的标记算法。为了说明选择性定价，我们将其应用于具有时间窗口的VRP的分支价格削减算法，其中宽松的定价子问题是具有资源约束的最短ng路径问题。我们针对此子问题开发了一种标记算法，并通过计算实验表明，它可以显着减少时间（最多减少32％），从而在具有200个客户的某些非常难解决的VRPTW实例上达到很好的下限。我们还介绍了一种新的标签启发式方法，该方法还可以减少计算时间。