Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

中文翻译：

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用于车辆路线和相关问题的通用精确求解器

最近在车辆路径问题 (VRP) 的精确解决方案方面取得了重大进展。一些最经典的 VRP 变体的复杂分支削减和定价 (BCP) 算法现在可以解决多达数百个客户的许多实例。然而，为其他变体调整和重新实现那些成功的算法可能是一项非常艰巨的任务。这项工作为包含大量 VRP 的通用模型提出了 BCP 求解器。它结合了现有最佳 VRP 算法中的关键元素：ng-path 松弛、有限内存的 1 级切割、路径枚举和舍入容量切割；所有这些都通过“包装集”和“基本集”的新概念进行了概括。这些概念还用于根据累积的资源消耗导出分支规则并概括 Ryan 和 Foster 分支规则。对几个变体的大量实验表明，通用求解器具有出色的整体性能，在许多问题上都优于最佳的特定算法。甚至一些非 VRP，如 bin 打包、向量打包和广义分配，也可以建模并有效解决。