Our aim is investigating the Shortest Path Problem (SPP) by employing the Recurrent Neural Networks (RNNs). The Karush–Kuhn–Tucker (KKT) optimality conditions play an essential role to present the RNN model. In fact, the KKT conditions are reformulated as a Nonlinear Complementarity Problem (NCP). Indeed, the stability theorem of the RNN is provided. By testing some examples, we show the performance of the model. Also, we apply the approach to solve a real-world problem as a case study.

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