In this paper, we investigate the optimal assignment problem, which assigns cells in Personal Communication Service to switches on Asynchronous Transfer Mode network in an optimum manner. 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 model as dual-homing cell assignment problem, which is a complex integer programming problem. Since finding an optimal solution of this problem is NP-hard, a stochastic search method, based on a genetic approach, is proposed to solve this problem. In this paper, domain-dependent heuristics are encoded into crossover operations, mutations of genetic algorithm (GA) to solve this problem. Simulation results show that GA is robust for this problem.