my questions are :
1, How to calculate the ObjValue and Error in the tag of run in advanced experiments. is there any formula for reference?

2, In the tag of Variables, the variable criterion is used to indicate the difference between the variable's sub-critreia and the desired values, how to show the difference?
1) the ObjValue is computed as the weighted sum of the individual sub-objectives.
If you have 2 vars, 'v1' and 'v2', the obj for 'v1' is e.g. the mean of 'v1' multiplied by it own weight + the 95%-ile by its weight. Same for 'v2'.
The overall obj is the sum of the obj for 'v1' multiplied by the weight of 'v1' and the obj of 'v2' by the weight of 'v2'

The error is the difference of the obj to the reference, measured or imposed (e.g. zero)

2) not sure I understand this - can you elaborate?
For more information on the objective value computation process, you may also want to refer to pp. 104-110 of

[i]Filip Claeys. A Generic Framework for Modeling and Virtual Experimentation with Environmental Systems. PhD thesis. Ghent University,
Department of Applied Mathematics, Biometrics and Process Control (BIOMATH), Coupure Links 653, B-9000 Gent, Belgium, January 2008.[/i]

my second question regarding the difference is :

according to the specification in the latest user guide:

'[b]...Variable Criterion: Method that is to be used to compute the difference
between the variable's sub-criteria and their desired values.
The options are:
AbsSquared: Squared difference...[/b]'

How to show the difference? The desired values are the 'Desired value' of sub-tag in the tag of time series criteria?
The difference is computed internally and can currently not be visualized in the user interface. However, if it is felt that visualizing the difference would be generally helpful, we could implement it in a future version of the software.
Many thanks to Enrico and Filip.

I also referred to Filip's thesis.

I will be appreciated if you can educate me the specific meaning of
'...Maximum Number of Function Evaluations
Print Level
Maximum Number of Stops
Seed for Random Number Generator...' in the optimization method of Praxis

I tried to find the answer from the web, but do not really understand them.
Actually, in those advanced expriments, there are quite a lot proffessional math. terms. Is there any specific introduction or manual on these topic? For example, I got quite some knowledge on sensitivity analysis from Filip's thesis. thanks again.
Praxis is available through Netlib. The original reference is probably the following:

[i]Richard Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, 1972). (Reprinted by Dover, 2002.) [/i]

The meaning of the properties you mentioned is the following:

- Maximum Number of Function Evaluations: Maximum number of evaluations of the objective function. This is typically almost the same as the number of runs, although not entirely, as some objective function evaluation pre-runs may be done during initialization of the algorithm.
- Print Level: Determines the level of detail of the algorithm's log file (*.Optim.log.txt).
- Maximum Number of Stops: Determines the maximum number of times the stopping criterion is allowed to evaluate to true before the algorithm is actually terminated.
- Seed for Random Number Generator: Initial seed for the RNG used by the algorithm. This generator partly determines the next parameter vector that will be applied to the objective function. It is important to have a seed that is set non-automatically in order to be able to deterministically replay the algorithm.

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