Efficient solution of the 3G network planning problem

Abstract

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time (St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method (St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.