We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of- the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance checks and the running time of the algorithm. We also show how the forward/backward route symmetry can be exploited and how to filter the bucket graph using reduced costs. The proposed algorithm can be especially beneficial for vehicle routing instances with large vehicle capacity and/or with time constraints. Computational experiments were performed on instances from the distance constrained vehicle routing problem, including multi-depot and site-depended variants, on the vehicle routing problem with time windows, and on the “nightmare” instances of the heterogeneous fleet vehicle routing problem. Very significant improvements over the best algorithms in the literature were achieved and many instances could be solved for the first time.

中文翻译：

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基于桶图的标注算法及其在车辆路径选择中的应用

我们认为资源约束最短路径问题是针对车辆路径选择问题的最新的“分支切割和价格”算法中的一个子问题。我们提出了一种双向标签校正算法的变体，其中标签根据所谓的存储桶图进行存储和扩展。标签的这种组织结构有助于显着减少优势检查的次数和算法的运行时间。我们还将展示如何利用前向/后向路线对称性以及如何使用降低的成本来过滤存储桶图。所提出的算法对于具有大的车辆容量和/或具有时间限制的车辆路线选择实例尤其有利。在距离受限的车辆路径问题上对实例进行了计算实验，包括多仓库和取决于站点的变体，带有时间窗的车辆路径问题以及异构车队车辆路径问题的“噩梦”实例。与文献中的最佳算法相比，实现了非常显着的改进，许多实例都可以首次得到解决。