Separating the Yes- from the No-Instances in the Number Partitioning Problem

Ruben Horn, Reitze Jansen, Okke van Eck, Daan van den Berg, Daan van den Berg

2024

Abstract

The (two-way) number partitioning problem (NPP) is a well known NP-complete decision problem in which a set of (positive) integers must be split in such a way that the sum of both resulting subsets is equal. However, its optimization problem variant is even harder, since the verification of partitions is only possible in polynomial time for instances which have a perfect partition. We investigate the distribution of instances that have and that do not have a perfect partition, and find that they are not randomly distributed in the instance space. Thus, the hardness of any given instance might be predictable to some extent. We demonstrate that it is possible to separate these two instance types visually using a linear time embedding into R2 for instances of the same template. Furthermore, we compare three greedy heuristic algorithms (greedy captains, greedy coach, and greedy tyrant) and their difference to the solution from an exact branch-and-bound (BB) algorithm.

Paper Citation

in Harvard Style

Horn R., Jansen R., van Eck O. and van den Berg D. (2024). Separating the Yes- from the No-Instances in the Number Partitioning Problem. In Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA; ISBN 978-989-758-721-4, SciTePress, pages 181-188. DOI: 10.5220/0012907000003837

in Bibtex Style

@conference{ecta24,
author={Ruben Horn and Reitze Jansen and Okke van Eck and Daan van den Berg},
title={Separating the Yes- from the No-Instances in the Number Partitioning Problem},
booktitle={Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA},
year={2024},
pages={181-188},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012907000003837},
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 - Separating the Yes- from the No-Instances in the Number Partitioning Problem
SN - 978-989-758-721-4
AU - Horn R.
AU - Jansen R.
AU - van Eck O.
AU - van den Berg D.
PY - 2024
SP - 181
EP - 188
DO - 10.5220/0012907000003837
PB - SciTePress