This paper addresses a variant of the many-to-many hub location-routing problem. Given an undirected edge-weighted complete graph \(G = (V, E)\), this problem consists in finding a subset of V designated as hub nodes, partitioning all the nodes of V into cycles such that each cycle has exactly one hub node, and determining a Hamiltonian cycle on the subgraph induced by hub nodes. The objective is to minimize the total cost resulting from all these cycles. This problem is referred to as Many-to-Many p-Location-Hamiltonian Cycle Problem (MMpLHP) in this paper. To solve this problem, one has to deal with aspects of subset selection, grouping, and permutation. The characteristics of MMpLHP change according to the values of its constituent parameters. Hence, this problem can be regarded as a general problem which encompasses a diverse set of problems originating from different combinations of values of its constituent parameters. Such a general problem can be tackled effectively by suitably selecting and combining several different heuristics each of which cater to a different characteristic of the problem. Keeping this in mind, we have developed a simple multi-start hyper-heuristic approach for MMpLHP. Further, we have investigated two different selection mechanisms within the proposed approach. Experimental results and their analysis clearly demonstrate the superiority of our approach over best approaches known so far for this problem.

本文解决了多对多集线器位置路由问题的一个变体。给定一个无向边加权完全图\(G = (V, E)\)，这个问题在于找到指定为中心节点的V的子集，划分V 的所有节点成循环，使得每个循环恰好有一个中心节点，并在由中心节点诱导的子图上确定一个哈密顿循环。目标是最小化所有这些循环产生的总成本。这个问题在本文中被称为多对多 p-位置-哈密尔顿循环问题 (MMpLHP)。为了解决这个问题，我们必须处理子集选择、分组和排列等方面的问题。MMpLHP 的特性根据其组成参数的值而变化。因此，这个问题可以被认为是一个普遍的问题，它包含了一系列不同的问题，这些问题源于其组成参数值的不同组合。可以通过适当地选择和组合几种不同的启发式方法来有效地解决这样的一般问题，每种启发式方法都迎合了问题的不同特征。牢记这一点，我们为 MMpLHP 开发了一种简单的多开始超启发式方法。此外，我们在所提出的方法中研究了两种不同的选择机制。实验结果及其分析清楚地证明了我们的方法优于迄今为止已知的解决此问题的最佳方法。