Convergence of the generalized simulated annealing method with independent parameters for the acceptance probability, visitation distribution, and temperature functions

In their original form, the Generalized Simulated Annealing (GSA), proposed by Tsallis and Stariolo, was defined with two independent parameters, q a and q v , used in the definition of the acceptance probability, visitation distribution, and temperature functions. In the posterior applications of this algorithm, however, another independent parameter has been introduced, replacing q v in the definition of the temperature function, becoming more efficient and allowing a convergence with a small number of cycles. Nevertheless, there is no convergence proof of the GSA algorithm to the absolute minimum in this case. In this work it is presented a convergence proof of the GSA method to the absolute minimum, with three independent parameters, q a , q v , and q T , to define the acceptance probability, visitation distribution, and temperature functions, using a modified form of the distribution function, ′ g   q   v ,q   T, in the formulation of the algorithm. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008