Generating Small Instances with Interesting Features for the Traveling Salesperson Problem

Tianyu Liang, Zhize Wu, Matthias Thürer, Markus Wagner, Thomas Weise

2024

Abstract

The Traveling Salesperson Problem (TSP) is one of the most well-known NP-hard optimization tasks. A randomized local search (RLS) is not a good approach for solving TSPs, as it quickly gets stuck at local optima. FRLS, the same algorithm with Frequency Fitness Assignment plugged in, has been shown to be able to solve many more TSP instances to optimality. However, it was also assumed that its performance will decline if an instance has a large number M of different possible objective values. How can we explore these more or less obvious algorithm properties in a controlled fashion, if determining the number #L of local optima or the size BL of their joint basins of attraction as well as the feature M are NP-hard problems themselves? By creating TSP instances with a small number of cities for which we can actually know these features! We develop a deterministic construction method for creating TSP instances with rising numbers M and a sampling based approach for the other features. We determine all the instance features exactly and can clearly confirm the obvious (in the case of RLS) or previously suspected (in the case of FRLS) properties of the algorithms. Furthermore, we show that even with small-scale instances, we can make interesting new findings, such as that local optima seemingly have little impact on the performance of FRLS.

Paper Citation

in Harvard Style

Liang T., Wu Z., Thürer M., Wagner M. and Weise T. (2024). Generating Small Instances with Interesting Features for the Traveling Salesperson Problem. In Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA; ISBN 978-989-758-721-4, SciTePress, pages 173-180. DOI: 10.5220/0012888800003837

in Bibtex Style

@conference{ecta24,
author={Tianyu Liang and Zhize Wu and Matthias Thürer and Markus Wagner and Thomas Weise},
title={Generating Small Instances with Interesting Features for the Traveling Salesperson Problem},
booktitle={Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA},
year={2024},
pages={173-180},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012888800003837},
isbn={978-989-758-721-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA
TI - Generating Small Instances with Interesting Features for the Traveling Salesperson Problem
SN - 978-989-758-721-4
AU - Liang T.
AU - Wu Z.
AU - Thürer M.
AU - Wagner M.
AU - Weise T.
PY - 2024
SP - 173
EP - 180
DO - 10.5220/0012888800003837
PB - SciTePress