A study on the effects of normalized TSP features for automated algorithm selection

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

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)

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) nearest neighbor relationships of the input instance. To this end we theoretically derive minimum and maximum values for properties of MSTs and k-nearest neighbor graphs (NNG) 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. A proof-of-concept AS-study shows promising results: models trained with normalized features tend to outperform those trained with the respective vanilla features.

Original languageEnglish
Pages (from-to)123-145
Number of pages23
JournalTheoretical computer science
Volume940
DOIs
Publication statusPublished - 9 Jan 2023
Externally publishedYes

Keywords

  • Algorithm selection
  • Feature normalization
  • Traveling salesperson problem
  • n/a OA procedure

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