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Authors: Joeri Sleegers 1 ; Sarah Thomson 2 and Daan van Den Berg 3

Affiliations: 1 Mice & Man Software and A.I. Development, Amsterdam, The Netherlands ; 2 Department of Computing Science & Mathematics, University of Stirling, U.K. ; 3 Department of Computer Science, Vrije Universiteit Amsterdam, The Netherlands

Keyword(s): Exact Algorithms, Instance Hardness, Evolutionary Algorithms, Phase Transition.

Abstract: In 2021, evolutionary algorithms found the hardest-known yes and no instances for the Hamiltonian cycle problem. These instances, which show regularity patterns, require a very high number of recursions for the best exact backtracking algorithm (Vandegriend-Culberson), but don’t show up in large randomized instance ensembles. In this paper, we will demonstrate that these evolutionarily found instances of the Hamiltonian cycle problem are hard for all major backtracking algorithms, not just the Vandegriend-Culberson. We compare performance of these six algorithms on an ensemble of 91,000 randomized instances plus the evolutionarily found instances. These results present a first glance at universal hardness for this NP-complete problem. Algorithms, source code, and input data are all publicly supplied to the community.

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Paper citation in several formats:
Sleegers, J.; Thomson, S. and van Den Berg, D. (2022). Universally Hard Hamiltonian Cycle Problem Instances. In Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - ECTA; ISBN 978-989-758-611-8; ISSN 2184-3236, SciTePress, pages 105-111. DOI: 10.5220/0011531900003332

@conference{ecta22,
author={Joeri Sleegers. and Sarah Thomson. and Daan {van Den Berg}.},
title={Universally Hard Hamiltonian Cycle Problem Instances},
booktitle={Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - ECTA},
year={2022},
pages={105-111},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011531900003332},
isbn={978-989-758-611-8},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - ECTA
TI - Universally Hard Hamiltonian Cycle Problem Instances
SN - 978-989-758-611-8
IS - 2184-3236
AU - Sleegers, J.
AU - Thomson, S.
AU - van Den Berg, D.
PY - 2022
SP - 105
EP - 111
DO - 10.5220/0011531900003332
PB - SciTePress

- Science and Technology Publications, Lda.
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