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

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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 \(10^3\) spins. In particular we try to estimate the difference in needed computation time compared to plain parallel tempering.

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Acknowledgments

The simulations were performed at the C. v. O. Universität Oldenburg on the HERO cluster funded by the DFG (INST 184/108-1 FUGG) and the ministry of Science and Culture (MWK) of the Lower Saxony State. We would like to thank Simon Knowles for criticially reading the paper.

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  1. Institute of Physics, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Strasse 11, 26111 , Oldenburg, Germany

    Markus Manssen & Alexander K. Hartmann

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  1. Markus Manssen
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  2. Alexander K. Hartmann
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Correspondence to Markus Manssen.

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Manssen, M., Hartmann, A.K. Matrix-power energy-landscape transformation for finding NP-hard spin-glass ground states. J Glob Optim 61, 183–192 (2015). https://doi.org/10.1007/s10898-014-0153-7

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