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This paper has proposed a distributed power control algorithm that uses a stochastic search technique in order to solve linear systems of equations for power update in CDMA cellular radio systems. The proposed algorithm is developed by applying Bremermann's evolutionary computation algorithm to the CDMA power control problem. The major gain from the applied evolutionary computation algorithm is more rapid optimization on linear systems of equations compared with the simple genetic algorithm (SGA). Employing the distributed constrained power control (DCPC) as a reference algorithm, we have designed and implemented computational experiments on the DS-CDMA system. The results indicate that the proposed algorithm significantly enhances the optimization speed of power control. The proposed algorithm is also compared with the bang-bang type algorithm used in the IS-95 and the W-CDMA systems. The results show that our proposed algorithm also has a high potential advantage for increasing the CDMA cellular radio network capacity and decreasing the mobile terminal power consumption.