Abstract:The main goal of routing solutions is to satisfy the requirements of the Quality of Service (QoS) for every admitted connection as well as to achieve a global efficiency in resource utilization. In this paper proposes a solution based on Hopfield neural network (HNN) to deal with one of representative routing problems in uni-cast routing, i. e. the multi-constrained (MC) routing problem. Computer simulation shows that we can obtain the optimal path very rapidly with our new Lyapunov energy functions. This work is supported by National Natural Science Foundation of China (No. 60277022), Outstanding Youth Foundation of Henan Province, Natural Science Foundation of Tianjin (No. 023800811), the Research Fund for the Doctoral Program of Higher education (No.20030055022). The Project-sponsored by SRF for ROCS, SEM.