NeuralGLS: learning to guide local search with graph convolutional network for the traveling salesman problem

The traveling salesman problem (TSP) aims to find the shortest tour that visits each node of a given graph exactly once. TSPs have significant importance as numerous practical problems can be naturally formulated as TSPs. Various algorithms have been developed for solving TSPs, including combinatorial optimization algorithms and deep learning-based approaches. However, these algorithms often face a trade-off between providing exact solutions with long running times and delivering fast but approximate solutions. Therefore, achieving both efficiency and solution quality simultaneously remains a major challenge. In this study, we propose a data-driven algorithm called NeuralGLS to address this challenge. NeuralGLS is a hybrid algorithm that combines deep learning techniques with guided local search (GLS). It incorporates a self-adaptive graph convolutional network (GCN) that takes into account neighborhoods of varying sizes, accommodating TSP instances with different graph sizes. This GCN calculates a regret value for each edge in a given TSP instance. Subsequently, the algorithm utilizes a mixed strategy to construct an initial tour and then employs a GLS module to iteratively improve the tour guided by the acquired regret values until a high-quality tour is obtained. Experimental results on diverse benchmark datasets and real-world TSP instances demonstrate the effectiveness of NeuralGLS in generating high-quality solutions within reasonable computation time. Furthermore, when compared to several state-of-the-art algorithms, our NeuralGLS algorithm exhibits superior generalization performance on both real-world and larger-scale TSP instances. Notably, NeuralGLS also outperforms another hybrid algorithm that also incorporates GLS by reducing the mean optimality gap for real-world TSP instances from 1.318% to 0.958%, with both methods achieving results within the same computation time. This remarkable improvement in solution quality amounts to an impressive relative enhancement of 27.31%.