The following optional group will configure the continuous variable Vanderbilt-Louie variant of the Simulated Annealing algorithm and will be processed if [ProgramType] is set to “VanderbiltSimulatedAnnealing”.

BeginSimulatedAlg
NumInitialTrials       [n_init]
TemperatureScaleFactor [tscale]
OuterIterations        [nouter]
InnerIterations        [ninner]
ConvergenceVal         [conval]
FinalTemperature       [tfinal]
TransitionMethod       [tmethd]
EndSimulatedAlg

BeginSimulatedAlg
NumInitialTrials       100
TemperatureScaleFactor 0.9
OuterIterations        20
InnerIterations        10
ConvergenceVal         1.00E-3
FinalTemperature       10.0
TransitionMethod       Gauss
EndSimulatedAlg

Figure 1: General Format (left) and Example (right) of the Vanderbilt-Louie Simulated Annealing Group

Where BeginSimulatedAlg and EndSimulatedAlg are parsing tags that wrap the following set of algorithm configuration variables:

• NumInitialTrials: This is the number of uphill moves that are attempted in the melting process. Larger values will result in more accurate estimates of the initial temperature, but at the expense of additional model runs. The default value is 100.
• TemperatureScaleFactor: After each (outer) iteration, the temperature is reduced by multiplying by this value. This value should be less than 1.00. The default value is 0.90.
• OuterIterations: This is the number of iterations in the overall algorithm, where one outer iteration corresponds to one temperature reduction. The default value is 20.
• InnerIterations: This is the number of iterations in each temperature equilibration, where one inner iteration corresponds to a single transitional move. The default value is 10.
• ConvergenceVal: This is the convergence value for the algorithm. If the relative difference between the current minimum and the median of the latest series of equilibration moves is less than or equal to this value, the algorithm will halt. The default value is 0.001.
• FinalTemperature: This variable can be used to set a specific value for the final temperature in the SA algorithm. The temperature scale factor will be adjusted to achieve the desired temperature. If a final temperature option or value is not specified, the final temperature will be determined from the initial melting phase using a procedure described by Vanderbilt and Louie (1984).
• TransitionMethod: This variable selects the method used to compute randomized parameter perturbations during the transition phase of the SA algorithm. Set this variable to “Vanderbilt” to sample according to the procedure outlined by Vanderbilt and Louie (1984). Use a value of “Gauss” to select a Gaussian (i.e. normal) distribution. The default value is “Gauss”.

References

Vanderbilt, D.,Louie, S. G. 1984. A Monte carlo simulated annealing approach to optimization over continuous variables. Journal of Computational Physics 56, 259-271.