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Parameter Tuning Patterns for Random Graph Coloring with Quantum Annealing

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  • Olawale Titiloye
  • Alan Crispin

Abstract

Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and/or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades.

Suggested Citation

  • Olawale Titiloye & Alan Crispin, 2012. "Parameter Tuning Patterns for Random Graph Coloring with Quantum Annealing," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-9, November.
    • Handle: RePEc:plo:pone00:0050060
    DOI: 10.1371/journal.pone.0050060
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. Lü, Zhipeng & Hao, Jin-Kao, 2010. "A memetic algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 203(1), pages 241-250, May.
    3. Dimitris Achlioptas & Assaf Naor & Yuval Peres, 2005. "Rigorous location of phase transitions in hard optimization problems," Nature, Nature, vol. 435(7043), pages 759-764, June.
    4. Enrico Malaguti & Michele Monaci & Paolo Toth, 2008. "A Metaheuristic Approach for the Vertex Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 302-316, May.
    5. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
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    Cited by:

    1. Alex Gliesch & Marcus Ritt, 2022. "A new heuristic for finding verifiable k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 28(1), pages 61-91, February.
    2. Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.

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