In the future asynchronous transfer mode (ATM) networks, an efficient virtual path (VP) control strategy must be applied to guarantee the network has high throughput with tolerable node processing load. The multistage VP control may be the best candidate since the tasks in this method are shared by the central node and local nodes, and it allows us to track the traffic changes while maintain a good state of the VP topology by reconfiguring it at regular or need based intervals. In this paper, we focus on the VP topology optimization problem in the multistage VP control. We first present the problem formulation in which the tradeoff between the network throughput and processing costs is considered, and then employ an algorithm based on a route-neuron Hopfield neural network (HNN) model to solve this problem. The numerical results demonstrate the HNN can converge to optimal solutions with high probability and stability while in other cases to near optimal solutions if the values of the system parameters in the route-neuron model are chosen according to some empirical formulas provided in this paper.