An efficient branch and cut algorithm for minimization of number of base stations in mobile radio networks

The paper is concerned with the analysis, mathematical modeling and solution of an important mobil e radio network design problem. The problem involves finding the minimum number of base stations needed for a cellular system whilst minimizing the network installation costs, maintaining an acceptable grade of service, tackling non-homogenous traffic distributions, guaranteeing minimum acceptable radio signal strength availability at the cell boundaries and satisfying other system performance requirements. The problem is modeled by discretizing the network design area into a grid and developing various constraints in terms of linear (in)equalities. The resulting model is a discrete optimization problem. An efficient branch and cut (B&C) algorithm is then used to solve it. Special techniques are put forward for generating stronger valid inequalities for the knapsack constraint. A novel approach using the concept of maximum independent sets is presented for developing the contiguity and topological constraints. These constraints act like cliques and facilitate the faster convergence of the B&C algorithm to optimality. In addition, special heuristics are developed for reducing the dimensionality of the problem before invoking the B&C algorithm. The practicability and computational performance of the technique is evaluated by considering several benchmark problems. The techniques are general and can interact with various radio propagation prediction models and can be used with GSM or CDMA systems.