The clustered vehicle-routing problem (CluVRP) is a variant of the classical capacitated vehicle-routing problem (CVRP) in which customers are partitioned into clusters, and it is assumed that each cluster must have been served completely before the next cluster is served. This decomposes the problem into three subproblems, i.e., the assignment of clusters to routes, the routing inside each cluster, and the sequencing of the clusters in the routes. The second task requires the solution of several Hamiltonian path problems, one for each possibility to route through the cluster. We pre-compute the Hamiltonian paths for every pair of customers of each cluster. We present a large multiple neighborhood search (LMNS) which makes use of multiple cluster destroy and repair operators and a variable-neighborhood descent (VND) for postoptimization. The VND is based on classical neighborhoods such as relocate, 2-opt, and swap all working on the cluster level and a generalization of the Balas-Simonetti neighborhood modifying simultaneously the intra-cluster routings and the sequence of clusters in a route. Computational results with our new approach compare favorably to existing approaches from the literature.

中文翻译：

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软聚类车辆路由问题的大型多邻域搜索

集群车辆路由问题 (CluVRP) 是经典的有能力车辆路由问题 (CVRP) 的变体，其中客户被划分为集群，并且假设在为下一个集群提供服务之前，每个集群必须已经完全得到服务。这将问题分解为三个子问题，即集群到路由的分配、每个集群内部的路由以及路由中集群的排序。第二个任务需要解决几个哈密顿路径问题，每个可能通过集群路由一个。我们为每个集群的每对客户预先计算哈密顿路径。我们提出了一个大型多邻域搜索 (LMNS)，它利用多个集群破坏和修复算子以及可变邻域下降 (VND) 进行后优化。VND 基于经典的邻域，例如重新定位、2-opt 和交换，所有工作都在集群级别上进行，并且对 Balas-Simonetti 邻域的泛化同时修改了集群内路由和路线中的集群序列。我们的新方法的计算结果优于文献中的现有方法。