Universally Hard Hamiltonian Cycle Problem Instances

Citation

Sleegers J, Thomson SL & Van Den Berg D (2022) Universally Hard Hamiltonian Cycle Problem Instances. In: Bäck T, van Stein B, Wagner C, Garibaldi J, Lam H, Cottrell M, Doctor F, Filipe J, Warwick K & Kacprzyk J (eds.) Proceedings of the 14th International Joint Conference on Computational Intelligence - ECTA. ECTA 2022 : 14th International Conference on Evolutionary Computation Theory and Applications, Valletta, Malta, 24.10.2022-26.11.2022. SCITEPRESS – Science and Technology Publications, pp. 105-111. https://doi.org/10.5220/0011531900003332

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.

Keywords
Exact Algorithms; Instance Hardness; Evolutionary Algorithms; Phase Transition