TY - JOUR

T1 - Convergence of simulated annealing using the generalized transition probability

AU - Nishimori, Hidetoshi

AU - Inoue, Jun Ichi

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 1998/7/3

Y1 - 1998/7/3

N2 - We prove the weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a reason to conjecture convergence of the simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analysed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.

AB - We prove the weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a reason to conjecture convergence of the simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analysed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.

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U2 - 10.1088/0305-4470/31/26/007

DO - 10.1088/0305-4470/31/26/007

M3 - Article

AN - SCOPUS:0032479095

VL - 31

SP - 5661

EP - 5672

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 26

ER -