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Increasing the attraction area of the global minimum in the binary optimization problem

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  • Iakov Karandashev
  • Boris Kryzhanovsky

Abstract

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10 3 in the case of the 10 × 10 Edwards–Anderson spin glass). Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Iakov Karandashev & Boris Kryzhanovsky, 2013. "Increasing the attraction area of the global minimum in the binary optimization problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1167-1185, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:1167-1185
    DOI: 10.1007/s10898-012-9947-7
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    References listed on IDEAS

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    1. Kate A. Smith, 1999. "Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 15-34, February.
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    Cited by:

    1. Markus Manssen & Alexander Hartmann, 2015. "Matrix-power energy-landscape transformation for finding NP-hard spin-glass ground states," Journal of Global Optimization, Springer, vol. 61(1), pages 183-192, January.
    2. Shen, Yao & Zhou, Chi-Chun & Chen, Yu-Zhu, 2022. "The elementary excitation of spin lattice models: The quasiparticles of Gentile statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).

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