Abstract
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.
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Notes
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A similar modification can in principle be applied to the current version 2.0.3 of LKH, but as we will see, the performance of version 1.3, for which the modification was made available to us, is sufficient to obtain better performance than EAX in many cases.
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Acknowledgements
We thank Thomas Stützle for letting us use the restart version of LKH 1.3 he implemented in the context of a different project and for helpful comments on earlier versions of this work. Holger Hoos acknowledges support from an NSERC Discovery Grant. Lars Kotthoff is supported by EU FP7 FET project 284715 (ICON) and an IRC “New Foundations” grant. Pascal Kerschke and Heike Trautmann acknowledge support from the European Center of Information Systems (ERCIS).
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Kotthoff, L., Kerschke, P., Hoos, H., Trautmann, H. (2015). Improving the State of the Art in Inexact TSP Solving Using Per-Instance Algorithm Selection. In: Dhaenens, C., Jourdan, L., Marmion, ME. (eds) Learning and Intelligent Optimization. LION 2015. Lecture Notes in Computer Science(), vol 8994. Springer, Cham. https://doi.org/10.1007/978-3-319-19084-6_18
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