The concept of virtual paths has become the key technology in ATM networks. A control scheme based on genetic algorithms and neural networks is proposed and applied to the bandwidth allocation of virtual paths in ATM networks. The proposed control scheme is capable of selecting adaptively optimal step sizes of virtual paths according to the traffic characteristics and network environment. As the optimisation problem is constrained, traditional genetic algorithms are no longer applicable to this problem. The authors propose the masked genetic algorithms with seeds (MGAS) to solve the optimisation problem. Simulation results demonstrate the superiority of the MGAS algorithm. To achieve better performance, the relationships among the QOS measures, the evaluation of seed scores, and the selection of relearning data records are discussed. Finally, a simplified control scheme is proposed to reduce not only the complexity of the neural networks but also the processing time.