**Parent Command**`
>> OPTION
`

**Subcommand**`
>>>> ITERATION
>>>> LIST
>>>> SCHEDULE
>>>> STEP
>>>> TEMPERATURE
`

**Description**

This command invokes Simulated Annealing to minimize the objective function S.
The following steps are performed by iTOUGH2, controlled by a number of
fourth-level commands:

(1) Define the range of possible parameter values using command `>>>> RANGE``> PARAMETER.`

(2) Define an initial value of the control parameter tau using command
`>>>> TEMPERATURE.`

(3) iTOUGH2 generates random perturbations delta(**p**) of the parameter vector **p**.
The probability density function of the perturbation is either Gaussian
or uniform; the initial standard deviations of these distributions are
given by command `>>>> DEVIATION (p)`

(4) The objective function S(**p**_{k+1}) for the new parameter set
**p**_{k+1} = **p**_{k} + delta(**p**)

(5) If the objective function is decreased (i.e.,
**p**_{k+1}) - S(**p**_{k}) < 0)

(6) After a sufficient number of perturbations have been accepted
(see command `>>> STEP (a)``>>>> SCHEDULE).`

(7) Steps (3) through (6) are repeated until the maximum number of
temperature reductions (see command `>>>> ITERATION`

This scheme of always taking a downhill step and sometimes taking an uphill step with probability P depending on tau is known as the Metropolis algorithm. Simulated Annealing may be especially useful for the minimization of a discontinuous cost function in order to optimize operational parameters.

**Example**`
> PARAMETER
>> pumping RATE
>>> SINK: EXT_1
>>>> RANGE: -1E-1 -1E-4
>>>> LOGARITHM
<<<<
<<<
<<
> COMPUTATION
>> TIME: 1 [YEARS]
2.0
>> USER specified cost function: Extraction cost
>>> SINK: EXT_1
>>>> NO DATA
>>>> WEIGHT (=specific costs): 1.0
<<<<
<<<
<<
> COMPUTATION
>> OPTION
>>> a cost function is minimized using L1-ESTIMATOR
>>> perform minimization using Simulated ANNEALing
>>>> initial TEMPERATURE : -0.05 (=5 % of initial cost)
>>>> update after maximum : 100 STEPS
>>>> annealing SCHEDULE: 0.95
>>>> Simulated Annealing ITERATIONS: 50
<<<<
<<<
<<
`

**See Also**`
>>> GAUSS-NEWTON |
>>> GRID SEARCH |
>>> LEVENBERG-MARQUARDT |
>>>> ITERATION (a) |
>>>> SCHEDULE |
>>>> STEP (a) |
>>>> TEMPERATURE
`

Page updated: July 29, 1997