On the Potential of Normalized TSP Features for Automated Algorithm Selection

Heins Jonathan, Bossek Jakob, Pohl Janina, Seiler Moritz, Trautmann Heike, Kerschke Pascal


Abstract

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.

Keywords
Mathematics of computing; Grah Theory; Supervised Learning; Computing methodologie



Publication type
Forschungsartikel in Sammelband (Konferenz)

Peer reviewed
Yes

Publication status
Published

Year
2021

Conference
16th ACM/SIGEVO Workshop on Foundations of Genetic Algorithms (FOGA XVI)

Venue
Dornbirn, Austria

Book title
Proceedings of the 16th ACM/SIGEVO Conference on Foundations of genetic Algorithms (FOGA XVI)

Editor
Association for Computing Machinery

Start page
1

End page
15

Publisher
Association for Computing Machinery

Place
Dornbirn, Austria

Language
English

DOI

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