In this paper, we investigate the extended cell assignment problem which optimally assigns new and split cells in PCS (Personal Communication Service) to switches in a wireless ATM network. Given cells and switches in an ATM network (whose locations are fixed and known), the problem is assigning cells to switches in an optimum manner. We would like to do the assignment in as attempt to minimize a cost criterion. The cost has two components: one is the cost of handoffs that involve two switches, and the other is the cost of cabling. This problem is modeled as a complex integer programming problem and finding an optimal solution to this problem is NP-complete. A stochastic search method, based on a genetic approach is proposed to solve this problem. Simulation results showtha t genetic algorithm is robust for this problem.