  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.
