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Journal of Global Optimization

, Volume 61, Issue 1, pp 183–192 | Cite as

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

  • Markus Manssen
  • Alexander K. Hartmann
Article

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.

Keywords

Spin glass model Binary minimization Energy landscape transformation Monte Carlo method NP-hardness 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of PhysicsCarl von Ossietzky University of OldenburgOldenburgGermany

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