In this paper, we present a new technique for resource allocation in multi‐user orthogonal frequency division multiple access systems. The goal is to maximise the minimum data rate available to any user while minimising the total transmitted power. In order to achieve an optimal solution and capacity bounds, the subcarrier and power should be allocated simultaneously. Multi‐objective genetic algorithm can be used for joint allocation of subcarriers and power in such a case, and in this paper, it is achieved using non‐dominated sorting genetic algorithm‐II. The simulation results indicate that the proposed algorithm achieves high data rates as compared with previous algorithms. The algorithm allocates both subcarriers and bits jointly without being computationally expensive. The faster convergence of the algorithm to near optimal value, as compared with previous algorithms, is indicative of its less complexity. Copyright © 2013 John Wiley & Sons, Ltd.