In the future asynchronous transfer mode （ATM） networks

an efficient virtual path（VP） control strategy should be developed to improve the utilization of network resources.Many advantages can be taken using the multistage VP control method which is designed to execute the adjustment of VPs in three stages with specific tasks for each stage.The VP topology optimization （VPTO） problem in this method is of great importance since it is a critical issue in both the first and third stages.In this paper

we first present the mathematical formulation of this problem with a liner objective fuction in which the tradeoff between the network throughput and processing costs is considered

and then propose a neural network（NN） approach to solve it.The numerical results demonstrate our algorithm can yield optimal or near optimal solutions with high stability and validity.