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

Markus Manssen () and Alexander Hartmann

Journal of Global Optimization, 2015, vol. 61, issue 1, 183-192

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

Keywords: Spin glass model; Binary minimization; Energy landscape transformation; Monte Carlo method; NP-hardness (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-014-0153-7

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