Clustering and routing models and algorithms for the design of telecommunication networks

Abstract

We consider several clustering and routing problems for the design of capacitated telecommunication networks. We present integer programming formulations of the problems and algorithms for them. First, we consider the switching node location problem for the design of ATM (Asynchronous Transfer Mode) networks. In this problem, there are two kinds of facilities, called hub facilities and remote facilities, with different capacities and installation costs. We are given a set of customers with demand requirements, a set of candidate sites for facility installation, and connection costs between facilities. We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub via installed remote facilities. The objective is to minimize the total cost while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this study, we present a preprocessing procedure to tighten the formulation and develop a branch-and-price algorithm. In the algorithm, we consider the integer knapsack problem to solve the column generation problem. Computational experiments show that the algorithm gives optimal solutions in a reasonable time. Second, we consider the clustering problem for the design of ATM VP (Virtual Path)-based leased line networks. In this problem, we are given a network, which is composed of a set of access nodes with demand requirements and conduits connecting the access nodes, a set of candidate edge nodes chosen from the access nodes, and a set of facilities with different capacities and installation costs. We need to determine a partitioning of the whole network into clusters, and the facility types to be installed at the edge nodes to accommodate the demand requirements of the access nodes with minimum cost. Each cluster contains one edge node and a subset of access nodes, an...