Learning to optimise general TSP instances

The Travelling Salesman Problem is a classical combinatorial optimisation problem (COP). In recent years, learning to optimise approaches have shown success in solving TSP problems. However, they focus on one type of TSP instance, where the points are uniformly distributed in Euclidean spaces (easy instances). Such approaches cannot generalise to other embedding spaces that represent various levels of difficult instances, e.g., TSP instances where the points are distributed in a non-uniform manner and spherical spaces. Obtain optimal solutions for easy instances is achievable and can be used as training data to solve various TSP instances. However, acquire optimal solutions for complex TSP instances is difficult and time-consuming. Hence, this paper introduces a new learning-based approach based on a convolutional neural network combined with a Long Short-Term Memory, referred to as the non-Euclidean TSP network (NETSP), that utilises randomly generated instances (easy instances) to solve various common TSP instances (complex TSP instances). We have demonstrated its superiority over state-of-the-art methods for various TSP instances. We performed extensive experiments that indicate our approach generalises across many instances and scales to larger instances.