In this paper, we propose an approach to solve the power control issue in a Digital Cellular System(DS-CDMA) cellular system using Genetic Algorithms (GAs). The transmitter power control developed in this paper has been proven to be efficient to control co-channel interference, to increase bandwidth utilization and to balance the comprehensive services that are shared among all the mobiles with attaining a common Signal-to-Interference Ratio (SIR). In this paper, the optimal Centralized Power Control(CPC) vector is characterized and its optimal solution to CPC is presented using GAs, in which First In-First Out (FIFO) stacks and non-linear decreasing functions are derived in the investigation for enforceing the convergence rate. Emphasis is put on the balance of services and convergence rate by using GAs.