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Quality-of-service (QoS) provisioning for a cognitive mesh network (CMN) with heterogeneous services has become a challenging area of research in recent days. Considering both real-time (RT) and non-real-time (NRT) traffic in a multihop CMN, [1] studied cross-layer resource management, including joint access control, route selection, and resource allocation. Due to the complexity of the formulated resource allocation problems, which are mixed-integer non-linear programming, a low-complexity yet efficient algorithm was proposed there to approximately solve the formulated optimization problems. In contrast, in this work, we present an application of genetic algorithm (GA) to re-address the hard resource allocation problems studied in [1]. Novel initialization, selection, crossover, and mutation operations are designed such that solutions with enough randomness can be generated and converge with as less number of attempts as possible, thus improving the efficiency of the algorithm effectively. Simulation results show the effectiveness of the newly proposed GA-based algorithm. Furthermore, by comparing the performance of the newly proposed algorithm with the one proposed in [1], more insights have been obtained in terms of the tradeoff among QoS provisioning for RT traffic, throughput maximization for NRT traffic, and time complexity of an algorithm for resource allocation in a multihop network such as CMN.