Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research has been introduced that fuses the strengths of machine learning and operational research algorithms. In particular, search perturbation operators have been used to improve the solution. Nevertheless, using the perturbation may not guarantee a quality solution. This paper presents "Learning to Guide Local Search" (L2GLS), a learning-based approach for routing problems that uses a penalty term and reinforcement learning to adaptively adjust search efforts. L2GLS combines local search (LS) operators' strengths with penalty terms to escape local optimals. Routing problems have many practical applications, often presetting larger instances that are still challenging for many existing algorithms introduced in the learning to optimise field. We show that L2GLS achieves the new state-of-the-art results on larger TSP and CVRP over other machine learning methods.

The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation instances. In recent years, learning to optimise approaches have shown success in solving TSP problems. However, they focus on one type of TSP problem, namely ones where the points are uniformly distributed in Euclidean spaces and have issues in generalising to other embedding spaces, e.g., spherical distance spaces, and to TSP instances where the points are distributed in a non-uniform manner. An aim of learning to optimise is to train once and solve across a broad spectrum of (TSP) problems. Although supervised learning approaches have shown to achieve more optimal solutions than unsupervised approaches, they do require the generation of training data and running a solver to obtain solutions to learn from, which can be time-consuming and difficult to find reasonable solutions for harder TSP instances. Hence this paper introduces a new learning-based approach to solve a variety of different and common TSP problems that are trained on easier instances which are faster to train and are easier to obtain better solutions. We name this approach the non-Euclidean TSP network (NETSP-Net). The approach is evaluated on various TSP instances using the benchmark TSPLIB dataset and popular instance generator used in the literature. We performed extensive experiments that indicate our approach generalises across many types of instances and scales to instances that are larger than what was used during training.