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A competent permutation encoded genetic algorithm (GA) is proposed for solving the optimum time division multiple access (TDMA) broadcast scheduling problem in mobile ad hoc networks. The problem is widely known as non-deterministic polynomial (NP) complete and diverse heuristic algorithms were reported to solve this problem recently. In this study, the GA approach is developed to cooperate with a deterministic greedy-like algorithm to obtain the optimum schedules. The main feature of the proposed GA approach lies in employing a permutation encoding strategy and thus obviates the invalid solutions encountered by the conventional binary encoding scheme. Consequently, the problem search space is reduced to a great extent and the GA becomes more efficient in searching the optimum solutions. A variety of simulation scenarios were conducted to examine the evolutionary behaviour and the scheduling performance of the proposed GA approach. Simulation results suggest that the proposed GA approach exhibits superior search capability in obtaining lower frame length whilst maintaining higher slot utilisation compared with other recently proposed methods.