Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a meanfield approximation to the pure model proposed by Bouchaud and Mézard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP. PACS numbers: 75.10.Nr, 05.50.+q, 64.60.Cn § To whom correspondence should be addressed. Email: [email protected], Phone: **43 1 4277 52737, Fax: **43 1 4277 52793 The low autocorrelated binary string problem 2