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

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 plet...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science Vol. 940; pp. 123 - 145
Main Authors: Heins, Jonathan, Bossek, Jakob, Pohl, Janina, Seiler, Moritz, Trautmann, Heike, Kerschke, Pascal
Format: Journal Article
Language:English
Published: Elsevier B.V 09.01.2023
Subjects:
Algorithm selection
Feature normalization
Traveling salesperson problem
Algorithm selection
Feature normalization
Traveling salesperson problem
ISSN:0304-3975, 1879-2294
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. •Study on the effects of feature normalization in algorithm selection for the TSP.•Normalization into [0,1] of features from important TSP feature groups.•Derivation of lower and upper bounds for feature values on Euclidean TSP instances.•Normalization reduced correlations between features, which benefits ML studies.•Algorithm selection models trained using the normalized features are preferable.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.10.019