In this thesis, we investigate the use of neural networks for solving the Traveling Salesman Problem (TSP). First, we review the main elements of the theory of NP-completeness. Then, we explain what makes some problems computationally intractable. We review some heuristic approaches used to provide near-optimal solutions to NP-complete problems. Then, we introduce the topic of neural networks and describe some of the most popular neural network models. We pay a special attention to a recent model, named the Hybrid Neural Network model (HNN), used for solving optimization problems and the Hybrid ...