Abstract-This paper deals with the problem of resources allocation in the downlink of the radio mobile systems. The allocation of resources is established in the context of multi-path effect and Doppler effect. These phenomena cause randomly variations of the channel and make difficult the allocation of the resources. Therefore, the problem of resources allocation is a high non linear optimization problem. Thus, we propose an implementation of genetic algorithms approach to increase the total throughput of users while minimizing the consumption of the total power of the base station. Like the evolutionary algorithms approach, this method is characterized by its robustness, permitting to efficiently solve a non linear optimization problem.