We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique “virtual” path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn associated a “physical” path in the lower layer. This particular hierarchical and unsplittable requirement for routing arises in the design of optical networks, including optical OFDM based networks. In this paper, we give an ILP formulation to the CMLND-U problem and we take advantage of its sub-problems to provide a partial characterization of the CMLND-U polytope including several families of facets. Based on this polyhedral study, we develop a Branch-and-Cut algorithm for the problem and show its effectiveness though a set of experiments, conducted on SNDlib-derived instances and also on real instances.

我们考虑具有不可拆分需求的容量多层网络设计（CMLND-U）问题。给定一个两层网络和一组交通需求，这个问题是由上层，使每个需求沿着独特的“虚拟”路径路由上安装成本最小容量（偶用的是独特的层中的每个链路），每个已安装的容量又与较低层中的“物理”路径相关联。路由的这种特定的层次性和不可拆分的需求出现在光网络的设计中，包括基于OFDM的光网络。在本文中，我们为CMLND-U问题提供了ILP公式，并利用它的子问题提供了CMLND-U多表位的部分特征，包括多个小平面家族。基于此多面体研究，我们开发了针对该问题的分支剪切算法，并通过在SNDlib派生实例和真实实例上进行的一组实验来证明其有效性。