Universally Hard Hamiltonian Cycle Problem Instances

Sleegers, Joeri; Thomson, Sarah L.; van den Berg, Daan

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 evolutionar-ily 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.

• Presentation Conference Type: Conference Paper (Published)
• Conference Name: ECTA 2022 : 14th International Conference on Evolutionary Computation Theory and Applications
• Start Date: Nov 24, 2022
• End Date: Nov 26, 2022
• Acceptance Date: Aug 24, 2022
• Online Publication Date: Nov 24, 2022
• Publication Date: 2022
• Deposit Date: Aug 16, 2023
• Publicly Available Date: Aug 17, 2023
• Volume: 1
• Pages: 105-111
• Book Title: Proceedings of the 14th International Joint Conference on Computational Intelligence
• ISBN: 9789897586118
• DOI: https://doi.org/10.5220/0011531900003332
• Related Public URLs: https://ijcci.scitevents.org