A widely studied non-deterministic polynomial time (NP) hard problem lies in finding a route between the two nodes of a graph. Often meta-heuristics algorithms such as $A^{*}$ are employed on graphs with a large number of nodes. Here, we propose a deep recurrent neural network architecture based on the Sequence-2-Sequence (Seq2Seq) model, widely used, for instance in text translation. Particularly, we illustrate that utilising a context vector that has been learned from two different recurrent networks enables increased accuracies in learning the shortest route of a graph. Additionally, we show that one can boost the performance of the Seq2Seq network by smoothing the loss function using a homotopy continuation of the decoder's loss function.