topic PROC GA under non-linear constraint in Mathematical Optimization, Discrete-Event Simulation, and OR

PROC GA under non-linear constraint

KarolinaA — Mon, 10 Apr 2017 13:47:10 GMT

Hello,

I have a function I neet to optimize using PROC GA and it is simple -- 0.1*x*y. But then I have constraint which is not that simple x**2 + y**2 <= (5+2.2*cos(10*atan(x/y)))**2. How can I solve this in SAS? Sorry, I am very new with SAS. My code so far looks like:

proc ga seed = 12 maxiter = 30; 
 
function funkc(selected[*]); 
array x[2] /nosym; 
call ReadMember(selected,1,x); 
x1 = x[1]; 
x2 = x[2]; 
F= 0.1*x1*x2; 
return(F);
endsub; 
 
call SetEncoding('R2'); 
array LowerBound[2] /nosym (-10 -6); 
array UpperBound[2] /nosym (10 6); 
call SetBounds(LowerBound, UpperBound);  
call SetObjFunc('funkc',0); 
call SetCrossProb(0.65); 
call SetCross('Heuristic'); 
call SetMutProb(0.15); 
array del[2] /nosym (0.2 0.2); 
call SetMut('Delta','nchange', 1, 'delta',del); 
call SetSel('tournament','size', 2); 
call SetElite(2); 
call Initialize('DEFAULT',150); 
run; 
quit;

Re: PROC GA under non-linear constraint

Ksharp — Tue, 11 Apr 2017 12:36:34 GMT

Some thought.

function funkc(selected[*]); 
 
call ReadMember(selected,1,x); 
F= 0.1*x[1]*x[2]; 

 if (5+2.2*cos(10*atan(x[1]/x[2])))**2 - x[1]**2 - x[2]**2 < 0 then F=9999999;

return(F);
endsub;

and make population size bigger.

call Initialize('DEFAULT',15000);

Re: PROC GA under non-linear constraint

KarolinaA — Mon, 10 Apr 2017 14:38:16 GMT

Nice idea. Got an error: ERROR: The array 'x' cannot be an argument of the '**' operation.

Re: PROC GA under non-linear constraint

KarolinaA — Mon, 10 Apr 2017 14:43:54 GMT

Okay. It was very simple. Could you please edit your post and change x to x[1] and y to x[2] and then it would be a solution 🙂

Re: PROC GA under non-linear constraint

RobPratt — Mon, 10 Apr 2017 15:23:56 GMT

Here's how you can solve it with the NLP solver in PROC OPTMODEL:

proc optmodel;
   var x >= -10 <= 10 init 1;
   var y >= -6  <= 6  init 1;
   min F = 0.1*x*y;
   con Mycon:
      x**2 + y**2 <= (5+2.2*cos(10*atan(x/y)))**2;
   solve with nlp / ms;
   print x y;
quit;