Simulated annealing, Boltzmann statistics and threshold acceptance

Simulated annealing, Boltzmann statistics and threshold acceptance 

To elude this problem, generalized simulated annealing (GSA) was introduced [7]. Instead of calculating the acceptance probability of a detrimental configuration p(Xj g ) based on an external absolute temperature, GSA uses the optimization progress towards the expected extreme function value 4 (Xgj  

Viewing the SA algorithm in terms of Markov chains, Greene and Supowit [8] pointed out that any type of function may be used for the decision making process about acceptance of new configurations, provided the detailed balance equation for the Markov process is satisfied. 

A rigorous generalization of the acceptance criterion was introduced by Dueck and Scheuer [9] with the so called threshold acceptance algorithm (TA). The relatively computationally expensive Boltzmann statistic is substituted by the rule (for minimization) accept all improving and detrimental configurations with a response value equal to or less than + t, with threshold t 0. Explicitly, 

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