Generalizing Graph Network Models for the Traveling Salesman Problem with Lin-Kernighan-Helsgaun Heuristics

Existing graph convolutional network (GCN) models for the traveling salesman problem (TSP) cannot generalize well to TSP instances with larger number of cities than training samples, and the NP-Hard nature of the TSP renders it impractical to use large-scale instances for training. This paper proposes a novel approach that generalizes well a pre-trained GCN model for a fixed small TSP size to large scale instances with the help of Lin-Kernighan-Helsgaun (LKH) heuristics. This is realized by first devising a Sierpinski partition scheme to partition a large TSP into sub-problems that can be efficiently solved by the pre-trained GCN, and then developing an attention-based merging mechanism to integrate the sub-solutions as a whole solution to the original TSP instance. Specifically, we train a GCN model by supervised learning to produce edge prediction heat maps of small-scale TSP instances, then apply it to the sub-problems of a large TSP instance generated by partition strategies. Controlled by an attention mechanism, all the heat maps of the sub-problems are merged into a complete one to construct the edge candidate set for LKH. Experiments show that this new approach significantly enhances the generalization ability of the pretrained GCN model without using labeled large-scale TSP instances in the training process and also outperforms LKH in the same time limit.