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Matrix-power energy-landscape transformation for finding NP-hard spin-glass ground states

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  • Markus Manssen
  • Alexander Hartmann

Abstract

A method for solving binary optimization problems was proposed by Karandashev and Kryzhanovsky that can be used for finding ground states of spin glass models. By taking a power of the bond matrix the energy landscape of the system is transformed in such a way, that the global minimum should become easier to find. In this paper we test the combination of the new approach with various algorithms, namely simple random search, a cluster algorithm by Houdayer and Martin, and the common approach of parallel tempering. We apply these approaches to find ground states of the three-dimensional Edwards–Anderson model, which is an NP-hard problem, hence computationally challenging. To investigate whether the power-matrix approach is useful for such hard problems, we use previously computed ground states of this model for systems of size $$10^3$$ 10 3 spins. In particular we try to estimate the difference in needed computation time compared to plain parallel tempering. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:183-192
    DOI: 10.1007/s10898-014-0153-7
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    References listed on IDEAS

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    1. Schneider, Johannes & Dankesreiter, Markus & Fettes, Werner & Morgenstern, Ingo & Schmid, Martin & Maria Singer, Johannes, 1997. "Search-space smoothing for combinatorial optimization problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 243(1), pages 77-112.
    2. 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.
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