Using generalized capacitated trees for designing the topology of local access networks

Abstract

The design of the topology of a local access network is a complex process which builds on many different combinatorial optimization problems such as the concentrator quantity problem, the concentrator location problem, the terminal clustering problem and the terminal layout problem. Usually, these four subproblems are solved separably and sequentially and the solution of one subproblem is used as data for the next subproblem. There are two main drawbacks associated to this four?phase approach: i) without knowing the optimal solution to the global problem it is difficult to set the parameters for some of the subproblems which appear in the earlier phases and ii) in many cases, wrong decisions taken at one of the earlier phases are "passed" to the subsequent phases. Our aim in this paper is to formulate the two last subproblems, clustering and layout, as one single generalized capacitated tree problem. We formulate the clustering/layout problem as a capacitated single?commodity network flow problem with adequate capacities on the arcs. We adapt a reformulation presented in (Gouveia, 1995) of a single?commodity flow model presented in (Gavish, 1983). We present several inequalities which can be used to tighten the LP relaxation of the original formulation. We present two heuristics for obtaining feasible solutions for the clustering/layout problem. Computational results taken from tests with 50, 100 and 200 nodes indicate that in most of the cases the best heuristic produces topologies with lower cost than the ones obtained by solving separately and sequentially the two individual subproblems.