This paper focuses on designing a diameter - constrained network where the maximum distance between any pair of nodes is bounded. The objective considered is to minimise a weighted sum of the total length of the links followed by the total length of the paths between the pairs of nodes. First, the problem is formulated in terms of Mixed Integer Linear Programming and Constraint Programming to provide two alternative exact approaches. Then, an adaptive large neighbourhood search (LNS) to overcome memory and runtime limitations of the exact methods in large size instances is proposed. Such approach is based on computing an initial solution and repeatedly improve it by solving relatively small subproblems. We investigate various alternatives for finding an initial solution and propose two different heuristics for selecting subproblems. We have introduced a tighter lower bound, which demonstrates the quality of the solution obtained by the proposed approach. The performance of the proposed approach is assessed using three real-world network topologies from Ireland, UK and Italy, which are taken from national telecommunication operators and are used to design a transparent optical core network. Our results demonstrate that the LNS approach is scalable to large networks and it can compute very high quality solutions that are close to being optimal.

本文重点设计一个直径受限的网络，其中任何一对节点之间的最大距离都是有界的。考虑的目标是最小化链路总长度和节点对之间路径总长度的加权和。首先，该问题根据混合整数线性规划和约束规划来表述，以提供两种替代的精确方法。然后，提出了一种自适应大邻域搜索（LNS）来克服大尺寸实例中精确方法的内存和运行时限制。这种方法基于计算初始解决方案，并通过解决相对较小的子问题来反复改进它。我们研究了寻找初始解决方案的各种替代方案，并提出了两种不同的启发式方法来选择子问题。我们引入了更严格的下界，这证明了所提出的方法获得的解决方案的质量。使用来自爱尔兰、英国和意大利的三种真实网络拓扑来评估所提出方法的性能，这些网络拓扑取自国家电信运营商，用于设计透明的光学核心网络。我们的结果表明，LNS 方法可扩展到大型网络，并且可以计算接近最优的高质量解决方案。