This paper examines a new model for hub location known as the hub location routing problem. The problem shares similarities with the well studied uncapacitated single allocation p-hub median problem except that the hubs are now connected to each other by a cyclical path (or tour) known as the global route, each cluster of non-hub nodes and assigned hub is also connected by a single tour known as a local route, and the length of the local routes is constrained to a maximum number of nodes. Thus, aside from the normal tasks of hub selection and allocation of non-hub nodes, up to p + 1 travelling salesman problems need to be solved. A heuristic based on the general variable neighborhood search framework is proposed here to solve this very complicated problem. The improvement phase of the algorithm uses a sequential variable neighborhood descent with multiple neighborhoods required to suit the complex nature of the problem. A best sequencing of the neighborhoods is established through empirical testing. The perturbation phase known as the shaking procedure also uses a well-structured selection of neighborhoods in order to effectively diversify the search to different regions of the solution space. Extensive computational testing shows that the new heuristic significantly outperforms the state-of-the-art. Out of 912 test instances from the literature, we are able to obtain 691 new best known solutions. Not only are the improvements in objective values quite impressive, but also these new solutions are obtained in a small fraction of the time required by the competing algorithms.

本文研究了一种新的集线器位置模型，称为集线器位置路由问题。该问题与经过充分研究的无能力的单分配p-hub中位数问题具有相似之处，不同之处在于，集线器现在通过称为全局路由的循环路径（或巡回路线）彼此连接，每个非集线器节点集群和指定的集线器相互连接也通过称为本地路由的单个巡回路线来连接，并且本地路由的长度限制为最大节点数。因此，除了集线器选择和非集线器节点分配的常规任务外，还需要解决多达p + 1个旅行推销员问题。本文提出了一种基于通用变量邻域搜索框架的启发式方法来解决这个非常复杂的问题。该算法的改进阶段使用具有多个邻域的顺序变量邻域下降，以适应问题的复杂性质。通过经验测试可以确定社区的最佳排序。被称为振荡过程的扰动阶段还使用结构良好的邻域选择，以有效地将搜索范围扩展到解空间的不同区域。大量的计算测试表明，新的启发式算法明显优于最新技术。从文献中的912个测试实例中，我们可以获得691个新的最著名的解决方案。不仅目标值的提高非常令人印象深刻，而且这些新的解决方案在竞争算法所需的一小部分时间内即可获得。