Non-orthogonal multiple access (NOMA) is one of the key technologies for 5G, where the system capacity can be increased by allowing simultaneous transmission of multiple users at the same radio resource. In this paper, we propose a genetic algorithm (GA) based multi-user radio resource allocation scheme for NOMA downlink systems. In our set-up, GA is used to determine the user groups to simultaneously transmit their signals at the same time and frequency resource while the optimal transmission power level is assigned to each user to maximize the geometric mean of user throughputs. The simulation results show that the GA based approach is a powerful heuristic to quickly converge to the target solution which balances the tradeoff between total system throughput and fairness among users.