How do I solve a series of different random problems with data drawn from the same distribution?

FAQs
1

Use AMPL’s reset data command to resample from all of the random-valued functions in the model. For example, in model steel4.mod from the AMPL book, suppose that parameter avail is changed so that its value is given by a random function:

param avail_mean {STAGE} >= 0; 
param avail_variance {STAGE} >= 0; 
param avail {s in STAGE} := 
   Normal (avail_mean[s], avail_variance[s]);

with corresponding data

param: avail_mean avail_variance := 
   reheat 35 5 
   roll 40 2 ;

Then AMPL will take new samples from the Normal distribution after each reset data :

ampl: model steel4.mod; 
ampl: data steel4.dat; 
ampl: solve; 
MINOS 5.4: optimal solution found. 
3 iterations, objective 187632.2489 
avail [*] := 
reheat 32.3504 
   roll 43.038 
; 
ampl: reset data avail; 
ampl: solve; 
MINOS 5.4: optimal solution found. 
4 iterations, objective 158882.901 
ampl: display avail; 
avail [*] := 
reheat 32.0306 
  roll 32.6855 
;

Using this feature together with one of AMPL’s looping commands, you can automatically solve a series of random realizations from the model, and summarize the results:

model steel4.mod; 
data steel4.dat; 
param nruns := 5; 
param optvalue {1..nruns}; 
for {k in 1..nruns} { 
   reset data avail; 
   solve; 
   let optvalue[k] := Total_Profit; 
} 
display (sum {k in 1..nruns} optvalue[k]) / nruns;

If you use reset rather than reset data , then AMPL’s random number generator is reset, and the values of avail repeat from the beginning. To get a different sequence of random numbers from the generator, you must change the random number seed; give the command option randseed n — where n is a positive integer — or option randseed 0 to have AMPL choose a seed based on the system clock.