Comparing extremal and thermal explorations of energy landscapes

S. Boettcher () and P. Sibani

The European Physical Journal B: Condensed Matter and Complex Systems, 2005, vol. 44, issue 3, 317-326

Abstract: Using a non-thermal local search, called Extremal Optimization (EO), in conjunction with a recently developed scheme for classifying the valley structure of complex systems, we analyze a short-range spin glass. In comparison with earlier studies using a thermal algorithm with detailed balance, we determine which features of the landscape are algorithm dependent and which are inherently geometrical. Apparently a characteristic for any local search in complex energy landscapes, the time series of successive energy records found by EO is also characterized approximately by a Poisson statistic with logarithmic time arguments. Differences in the results provide additional insights into the performance of EO. In contrast with a thermal search, the extremal search visits dramatically higher energies while returning to more widely separated low-energy configurations. Two important properties of the energy landscape are independent of either algorithm: first, to find lower energy records, progressively higher energy barriers need to be overcome. Second, the Hamming distance between two consecutive low-energy records is linearly related to the height of the intervening barrier. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Date: 2005
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DOI: 10.1140/epjb/e2005-00131-6

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