带容量获利旅行商问题的一种开放、可重现的分支定界法：组件研究
An open, reproducible branch-and-cut for the capacitated profitable tour problem: a component study
AI总结：
针对带容量获利旅行商问题及其变体提出开放可重现的分支定界算法，在开放混合整数规划栈上重新实现相关公式和割集族，并进行组件研究，明确各组件贡献及运行时间去向。
摘要：
我们提出了一种针对带容量获利旅行商问题（CPTP）及其开放的s-t路径变体——容量受限基本最短路径问题的开放、可重现的分支定界（B&C）算法。该求解器在完全开放的混合整数规划栈（HiGHS；Huangfu和Hall，2018）上重新实现了Jepsen等人（2014）的公式和割集族，并添加了基于边界的预处理、域传播和降低成本的变量固定。我们没有声称有新方法；贡献有两方面。首先，一个开放、可重现的工件：据我们所知，这是在完全开放的栈上针对此类问题的第一个分支定界法，其公式、每个分离器和所有基准脚本都已发布，因此下面的结果可以重新运行，并且求解器可以作为基线被重用和扩展。其次，对这个常见的现代栈进行了组件研究，与动态规划/标记参考进行了基准测试，该研究分解了哪些组件有成效以及运行时间花在哪里。我们发现容量类割集基本上带来了全部好处（将它们添加到仅连通性的基线中，从76个实例中解决的实例数量从52个增加到64个，并且搜索树缩小了十多倍），而梳状和舍入广义大星割集、降低成本的固定和基于边界的传播没有带来可测量的收益。我们还报告了一个负面结果：最短路径不兼容（SPI）割集，即García（2009）节点优先级不等式的一个变体，在任何实例上都没有发现违反的不等式。求解器和所有实验都作为开放、可重现的软件发布（Spoorendonk，2026）。
英文摘要：
We present an open, reproducible branch-and-cut (B&C) algorithm for the capacitated profitable tour problem (CPTP) and its open s-t path variant, the capacity-constrained elementary shortest-path problem. The solver re-implements the formulation and cut families of Jepsen et al. (2014) on a fully open mixed-integer programming stack (HiGHS; Huangfu and Hall, 2018), and adds bound-based preprocessing, domain propagation, and reduced-cost variable fixing. We claim no new method; the contribution is twofold. First, an open, reproducible artifact: to our knowledge the first branch-and-cut for this problem class on a fully open stack, with the formulation, every separator, and all benchmark scripts released, so the results below can be rerun and the solver reused and extended as a baseline. Second, a component study on this common modern stack, benchmarked against a dynamic-programming/labelling reference, that decomposes which components pay off and where the running time goes. We find that the capacity-class cuts account for essentially the entire benefit (adding them to a connectivity-only baseline lifts the number of instances solved from 52 to 64 of 76 and shrinks the search tree more than tenfold), while comb and rounded generalized-large-multistar cuts, reduced-cost fixing, and bound-based propagation add nothing measurable. We also report a negative result: the shortest-path-incompatibility (SPI) cut, a variant of the node-precedence inequalities of García (2009), finds no violated inequality on any instance. The solver and all experiments are released as open, reproducible software (Spoorendonk, 2026).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
