Rapid evolution in the field of communication networks requires high speed switching technologies. This involves a high degree of parallelism in switching control and routing performed at the hardware level. The multistage crossbar networks have always been attractive to switch designers. In this paper a neural network approach to controlling a three-stage Clos network in real time is proposed. This controller provides optimal routing of communication traffic requests on a call-by-call basis by rearranging existing connections, with a minimum length of rearrangement sequence so that a new blocked call request can be accommodated. The proposed neural network controller uses Paull's rearrangement algorithm, along with the special (least used) switch selection rule in order to minimize the length of rearrangement sequences. The functional behavior of our model is verified by simulations and it is shown that the convergence time required for finding an optimal solution is constant, regardless of the switching network size. The performance is evaluated for random traffic with various traffic loads. Simulation results show that applying the least used switch selection rule increases the efficiency in switch rearrangements, reducing the network convergence time. The implementation aspects are also discussed to show the feasibility of the proposed approach.