Projection Recurrent Neural Network Model: A New Strategy to Solve Maximum Flow Problem

We study the maximum flow problem (MFP) employing the concepts of Recurrent Neural Networks (RNN)s. The aim of the present attempt is to find a solution for MFP utilizing projection RNN models based on mixed linear complementarity problem (MLCP). The Karush-Kuhn-Tucker (KKT) optimality conditions of the original problem are applied to develop the projection RNN model based on MLCP. Besides, the Lyapunov stability and the global convergence of the projection RNN model are proved. Finally, several illustrative examples are given to demonstrate the performance of this approach. The obtained results are compared with previous approaches to solving MFP.