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In wireless environment, the increase in the number of users and the demand for a higher rate have triggered rapidly booming energy consumption at the base station. Therefore, energy efficient design in wireless networks has become essential. This paper studies the problem of energy efficient downlink resource allocation for multi-user OFDM system and proposes a scheme based on genetic simulated annealing algorithm. The proposed scheme can efficiently minimize total power consumption with constraints both on bit-error rate and transmission rate for users requiring different levels of services. The simulation results show that the scheme has fast convergence speed without performance degradation.