Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2007-10-10
J. Stat. Mech. (2008) P01003
Physics
Condensed Matter
Soft Condensed Matter
6 pages, 9 figures. To appear in JSTAT. Author website: http://www.bgoncalves.com
Scientific paper
10.1088/1742-5468/2008/01/P01003
The recently proposed Hysteretic Optimization (HO) procedure is applied to the 1D Ising spin chain with long range interactions. To study its effectiveness, the quality of ground state energies found as a function of the distance dependence exponent, $\sigma$, is assessed. It is found that the transition from an infinite-range to a long-range interaction at $\sigma=0.5$ is accompanied by a sharp decrease in the performance . The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite-range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way auto-correlations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.
Boettcher Stefan
Goncalves Bruno
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