The Impact of Automated Algorithm Configuration on the Scaling Behaviour of State-of-the-Art Inexact TSP Solvers

Abstract

Automated algorithm configuration is a powerful and increasingly widely used approach for improving the performance of algorithms for computationally hard problems. In this work, we investigate the impact of automated algorithm configuration on the scaling of the performance of two prominent inexact solvers for the travelling salesman problem (TSP), EAX and LKH. Using a recent approach for analysing the empirical scaling of running time as a function of problem instance size, we demonstrate that automated configuration impacts significantly the scaling behaviour of EAX. Specifically, by automatically configuring the adaptation of a key parameter of EAX with instance size, we reduce the scaling of median running time from root-exponential (of the form \(a\cdot b^{\sqrt{n}}\)) to polynomial (of the form \(a\cdot n^{b}\)), and thus, achieve an improvement in the state of the art in inexact TSP solving. In our experiments with LKH, we noted overfitting on the sets of training instances used for configuration, which demonstrates the need for more sophisticated configuration protocols for scaling behaviour.