book chapter
On the Potential of Normalized TSP Features for Automated Algorithm Selection
Jonathan
Heins
author
Jakob
Bossek
author 1029790000-0002-4121-4668
Janina
Pohl
author
Moritz
Seiler
author
Heike
Trautmann
author
Pascal
Kerschke
author
819
department
Classic automated algorithm selection (AS) for (combinatorial) optimization problems heavily relies on so-called instance features, i.e., numerical characteristics of the problem at hand ideally extracted with computationally low-demanding routines. For the traveling salesperson problem (TSP) a plethora of features have been suggested. Most of these features are, if at all, only normalized imprecisely raising the issue of feature values being strongly affected by the instance size. Such artifacts may have detrimental effects on algorithm selection models. We propose a normalization for two feature groups which stood out in multiple AS studies on the TSP: (a) features based on a minimum spanning tree (MST) and (b) a k-nearest neighbor graph (NNG) transformation of the input instance. To this end we theoretically derive minimum and maximum values for properties of MSTs and k-NNGs of Euclidean graphs. We analyze the differences in feature space between normalized versions of these features and their unnormalized counterparts. Our empirical investigations on various TSP benchmark sets point out that the feature scaling succeeds in eliminating the effect of the instance size. Eventually, a proof-of-concept AS-study shows promising results: models trained with normalized features tend to outperform those trained with the respective vanilla features.
Association for Computing Machinery2021
eng
automated algorithm selectiongraph theoryinstance featuresnormalizationtraveling salesperson problem (TSP)
Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms
978-1-4503-8352-3
1–15
yes
Heins, Jonathan, et al. “On the Potential of Normalized TSP Features for Automated Algorithm Selection.” <i>Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, Association for Computing Machinery, 2021, pp. 1–15.
@inbook{Heins_Bossek_Pohl_Seiler_Trautmann_Kerschke_2021, place={New York, NY, USA}, title={On the Potential of Normalized TSP Features for Automated Algorithm Selection}, booktitle={Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms}, publisher={Association for Computing Machinery}, author={Heins, Jonathan and Bossek, Jakob and Pohl, Janina and Seiler, Moritz and Trautmann, Heike and Kerschke, Pascal}, year={2021}, pages={1–15} }
Heins, J., Bossek, J., Pohl, J., Seiler, M., Trautmann, H., & Kerschke, P. (2021). On the Potential of Normalized TSP Features for Automated Algorithm Selection. In <i>Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i> (pp. 1–15). Association for Computing Machinery.
J. Heins, J. Bossek, J. Pohl, M. Seiler, H. Trautmann, and P. Kerschke, “On the Potential of Normalized TSP Features for Automated Algorithm Selection,” in <i>Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, New York, NY, USA: Association for Computing Machinery, 2021, pp. 1–15.
Heins, Jonathan, Jakob Bossek, Janina Pohl, Moritz Seiler, Heike Trautmann, and Pascal Kerschke. “On the Potential of Normalized TSP Features for Automated Algorithm Selection.” In <i>Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, 1–15. New York, NY, USA: Association for Computing Machinery, 2021.
J. Heins, J. Bossek, J. Pohl, M. Seiler, H. Trautmann, P. Kerschke, in: Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, Association for Computing Machinery, New York, NY, USA, 2021, pp. 1–15.
Heins J, Bossek J, Pohl J, Seiler M, Trautmann H, Kerschke P. On the Potential of Normalized TSP Features for Automated Algorithm Selection. In: <i>Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>. Association for Computing Machinery; 2021:1–15.
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