The problem of assigning customers to satellite channels is a difficult combinatorial optimization problem and is NP-complete. For this combinatorial optimization problem, standard optimization methods take a large computation time and so genetic algorithms (GA) and ant colony optimization (ACO) can be used to obtain the best and/or optimal assignment of customers to satellite channels. In this paper, we present a comparative study of GA and ACO to this problem. Various issues related to genetic algorithms approach to this problem, such as solution representation, selection methods, genetic operators and repair of invalid solutions are presented. We also discuss an ACO for this problem. In ACO methodology, three strategies, ACO with only ranking, ACO with only max-min ant system (MMAS), and ACO with both ranking and MMAS, are considered. A comparison of these two approaches (i,e., GA and ACO) with the standard optimization method is presented to show the advantages of these approaches in terms of computation time.