Solving the Traveling Salesman Problem via Semantic Segmentation with Convolutional Neural Networks

Abstract

The Traveling Salesman Problem (TSP) is a problem that has been formally studied since the 1930s and attracts great theoretical and practical interest. The theoretical aspects are particularly interesting as the TSP is an NP-hard problem and exact solutions for large TSPs are difficult to obtain. On the practical side, the growth of e-Commerce has resulted in more deliveries and it is increasingly important to obtain higher quality routes to increase efficiency. To that end, we introduce a Human Inspired Heuristic (HIH) that converts a road network semantic map into a truncated distance matrix that can be passed to a traditional TSP solution algorithm. The HIH can be further augmented in the image domain with our proposed novel Convolutional Neural Network (CNN). Our proposed CNN takes as input this original road network semantic map and outputs a reduced road network of plausible paths that are learned from near-optimal route instances. Through extensive numerical experiments, we find that additional pre-processing done by the CNN does not improve the performance of the HIH. In the context of real-world applications, a HIH designed based on physical constraints already works well. While the CNN in its current form in general fails to outperform a HIH, we did find one instance where it outperformed. This suggests that there is potential for CNNs to outperform and a promising research direction is to predict semantic maps in an autoregressive manner and reduce the reliance or remove entirely, the HIH.