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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
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.
- 2.
- 3.
References
Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)
Bischl, B., Mersmann, O., Trautmann, H., Preuss, M.: Algorithm selection based on exploratory landscape analysis and cost-sensitive learning. In: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, GECCO 2012. ACM, New York (2012)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1–2), 43–62 (2001)
Helsgaun, K.: General k-opt submoves for the LinKernighan TSP heuristic. Math. Program. Comput. 1(2–3), 119–163 (2009)
Huberman, B.A., Lukose, R.M., Hogg, T.: An economics approach to hard computational problems. Science 275(5296), 51–54 (1997)
Hutter, F., Xu, L., Hoos, H.H., Leyton-Brown, K.: Algorithm runtime prediction: methods and evaluation. Artif. Intell. 206, 79–111 (2014)
Kotthoff, L.: LLAMA: leveraging learning to automatically manage algorithms. Technical report, June 2013. arXiv:1306.1031
Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. AI Mag. 35(3), 48–60 (2014)
Lacoste, J.D., Hoos, H.H., Stützle, T.: On the empirical time complexity of state-of-the-art inexact tsp solvers. (manuscript in preparation)
Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: IJCAI, August 2013
Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., Rudolph, G.: Exploratory landscape analysis. In: Proceedings of the 13th Annual Conference on Genetic and Vvolutionary Computation, GECCO 2011, pp. 829–836. ACM, New York (2011). http://doi.acm.org/10.1145/2001576.2001690
Mersmann, O., Bischl, B., Trautmann, H., Wagner, M., Bossek, J., Neumann, F.: A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem. Ann. Math. Artif. Intell. 69(2), 151–182 (2013)
Nagata, Y., Kobayashi, S.: A powerful genetic algorithm using edge assembly crossover for the traveling salesman problem. INFORMS J. Comput. 25(2), 346–363 (2013)
O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science, January 2008
Pihera, J., Musliu, N.: Application of machine learning to algorithm selection for TSP. In: Fogel, D., et al. (eds.) Proceedings of the IEEE 26th International Conference on Tools with Artificial Intelligence (ICTAI). IEEE press (2014)
Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)
Roussel, O.: Controlling a solver execution with the runsolver tool. JSAT 7(4), 139–144 (2011)
Seipp, J., Braun, M., Garimort, J., Helmert, M.: Learning portfolios of automatically tuned planners. In: ICAPS (2012)
Smith-Miles, K., van Hemert, J.: Discovering the suitability of optimisation algorithms by learning from evolved instances. Ann. Math. Artif. Intell. 61(2), 87–104 (2011)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. (JAIR) 32, 565–606 (2008)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: Hydra-MIP: automated algorithm configuration and selection for mixed integer programming. In: RCRA Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion at the International Joint Conference on Artificial Intelligence (IJCAI), pp. 16–30 (2011)
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-19084-6_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19083-9
Online ISBN: 978-3-319-19084-6
eBook Packages: Computer ScienceComputer Science (R0)