topic Re: Generate a dataset with optimized results for every parameters combination in Mathematical Optimization, Discrete-Event Simulation, and OR

Generate a dataset with optimized results for every parameters combination

Edoedoedo — Fri, 01 Mar 2019 15:44:30 GMT

Hi, I'm learning proc optmodel and I have a question. Suppose we have this problem:

proc fcmp outlib=work.funcs.f;
    function f1(Q, H);
        return (
            -21.570992+
            Q*1.972536+
            H*0.719408+
            Q**2*-0.03148+
            Q*H*-0.057026+
            H**2*-0.008104+
            Q**3*0.00117+
            Q**2*H*0.000098997+
            Q*H**2*0.000642+
            H**3*0.000030146+
            Q**4*-0.000015012+
            Q**3*H*-0.000001948+
            Q**2*H**2*-0.000000285+
            Q*H**3*-0.0000024+
            H**4*0
        );
    endsub;

    function f2(Q, H);
        return (
            -11.381931+
            Q*-0.176563+
            H*0.49236+
            Q**2*0.006618+
            Q*H*0.004691+
            H**2*-0.007303+
            Q**3*0.001559+
            Q**2*H*-0.001057+
            Q*H**2*0.00014+
            H**3*0.000035108+
            Q**4*-0.000015803+
            Q**3*H*-0.000005786+
            Q**2*H**2*0.000007708+
            Q*H**3*-0.000001467+
            H**4*0
        );
    endsub;
run;

options cmplib=work.funcs;

options nonotes;
proc optmodel;
    number P = 30.440000534;
    number H = 83.698883057;

    var Q1 >= 0;
    var Q2 >= 0;
    
    impvar P1 = Q1 * H * f1(Q1, H) * 9.81 / 1000;
    impvar P2 = Q2 * H * f2(Q2, H) * 9.81 / 1000;

    minimize Q = Q1 + Q2;

    constraint P = P1 + P2;

    solve with nlp / maxiter=10000000 nthreads=32;
    
    print Q Q1 Q2 (Q1/Q*100) (Q2/Q*100) P P1 P2 ;

run;

The input variables are P and H (given as constants in the example). The minimization objective function is Q.

If I run this code, I get (in the result window) the minimum Q for that specific values of P and H.

I would like to run the optimization for each P in range (0,50) by step 0.1 and for each H in range (50,100) by step 0.1 and output the results in one dataset like:

P | H | Q

0 50.0 <the optimal Q with these parameters>

0 50.1 <the optimal Q with these parameters>

...

0.1 50.0 <the optimal Q with these parameters>

0.1 50.1 <the optimal Q with these parameters>

...

How would I do that? Should I prepare a dataset with all the combinations of P and H, and then tell somehow to proc optmodel to use this dataset as input?

Thanks a lot

Regards

Re: Generate a dataset with optimized results for every parameters combination

RobPratt — Fri, 01 Mar 2019 18:05:27 GMT

Yes, an input data set with P and H values is one approach, as demonstrated in this SAS Usage Note. Alternatively, you can use nested DO loops over P and H as follows:

proc optmodel printlevel=0;
   number P;
   number H;

   var Q1 >= 0;
   var Q2 >= 0;

   impvar P1 = Q1 * H * f1(Q1, H) * 9.81 / 1000;
   impvar P2 = Q2 * H * f2(Q2, H) * 9.81 / 1000;

   minimize Q = Q1 + Q2;

   constraint P = P1 + P2;

   set PSET = 0..50 by 0.1;
   set HSET = 50..100 by 0.1;
   num Qopt {PSET, HSET};
   do P = PSET;
      do H = HSET;
         put P= H=;
         solve;
         Qopt[P,H] = Q.sol;
      end;
   end;
   create data Qdata from [P H] Q=Qopt;
quit;

Re: Generate a dataset with optimized results for every parameters combination

Edoedoedo — Mon, 04 Mar 2019 19:19:21 GMT

Thanks a lot!

One last question: how can I output in the dataset Qdata information about the solution, like the solution status, the optimality error etc, for each combination of (P,H)?

The solver is nlp, with maxiter=100; I need the status because for some (P,H) the solution can be found in a few iteration, but for other (P,H) the solution is unfeasable (so the Qsol is meaningless). Hence, in the final dataset Qdata I must know about how good is Qsol, to do other things for the values where the solution was unfeasable.

Thanks again

Regards

Re: Generate a dataset with optimized results for every parameters combination

RobPratt — Mon, 04 Mar 2019 19:34:19 GMT

Before the DO loops, declare new parameters:

   str solstatus {PSET, HSET};
   num opterror {PSET, HSET};

Inside the DO loops, populate these values:

         solstatus[P,H] = _solution_status_;
         opterror[P,H] = _OROPTMODEL_NUM_['OPTIMALITY_ERROR'];

After the DO loops, include the new parameters in the CREATE DATA statement:

   create data Qdata from [P H] Q=Qopt solstatus opterror;

Re: Generate a dataset with optimized results for every parameters combination

Edoedoedo — Mon, 04 Mar 2019 20:00:08 GMT

Great! Thank you a lot!!