Solving Traveling Salesman Problem with Time Windows Using Hybrid Pointer Networks with Time Features

This paper introduces a time efficient deep learning-based solution to the traveling salesman problem with time window (TSPTW). Our goal is to reduce the total tour length traveled by -*the agent without violating any time limitations. This will aid in decreasing the time required to supply any type of service, as well as lowering the emissions produced by automobiles, allowing our planet to recover from air pollution emissions. The proposed model is a variation of the pointer networks that has a better ability to encode the TSPTW problems. The model proposed in this paper is inspired from our previous work that introduces a hybrid context encoder and a multi attention decoder. The hybrid encoder primarily comprises the transformer encoder and the graph encoder; these encoders encode the feature vector before passing it to the attention decoder layer. The decoder consists of transformer context and graph context as well. The output attentions from the two decoders are aggregated and used to select the following step in the trip. To the best of our knowledge, our network is the first neural model that will be able to solve medium-size TSPTW problems. Moreover, we conducted sensitivity analysis to explore how the model performance changes as the time window width in the training and testing data changes. The experimental work shows that our proposed model outperforms the state-of-the-art model for TSPTW of sizes 20, 50 and 100 nodes/cities. We expect that our model will become state-of-the-art methodology for solving the TSPTW problems.