A constrained shortest path is a minimum‐cost sequence of arcs on a directed network that satisfies knapsack‐type constraints on the resource consumption over the arcs. We propose an exact method based on a recursive depth‐first search procedure known as the pulse algorithm (PA). One of the key contributions of the proposal lies in a bidirectional search strategy leveraged on parallelism. In addition, we developed a pulse‐based heuristic that quickly finds near‐optimal solutions and shows great potential for column generation (CG) schemes. We present computational experiments over large real‐road networks with up to 6 million nodes and 15 million arcs. We illustrate the use of the bidirectional PA in a CG scheme to solve a multi‐activity shift scheduling problem, where the pricing problem is modeled as a constrained‐shortest path with multiple resource constraints.

中文翻译：

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约束最短路径的精确双向脉冲算法

受约束的最短路径是有向网络上满足弧形资源消耗的背包型约束的弧形的最小成本序列。我们提出一种基于递归深度优先搜索过程的精确方法，称为脉冲算法（PA）。该提案的主要贡献之一在于利用并行性的双向搜索策略。此外，我们开发了一种基于脉冲的启发式方法，可以快速找到接近最佳的解决方案，并在列生成（CG）方案中显示出巨大的潜力。我们提出了在多达600万个节点和1500万弧段的大型现实网络上的计算实验。我们说明了在CG方案中使用双向PA来解决多活动班次调度问题，