Improving the State of the Art in Inexact TSP Solving Using Per-Instance Algorithm Selection

We investigate per-instance algorithm selection techniques for solving the Travelling Salesman Problem (TSP), based on the two state-of-the-art inexact TSP solvers, LKH and EAX. Our comprehensive experiments demonstrate that the solvers exhibit complementary performance across a diverse set of instances, and the potential for improving the state of the art by selecting between them is significant. Using TSP features from the literature as well as a set of novel features, we show that we can capitalise on this potential by building an efficient selector that achieves significant performance improvements in practice. Our selectors represent a significant improvement in the state-of-the-art in inexact TSP solving, and hence in the ability to find optimal solutions (without proof of optimality) for challenging TSP instances in practice.