Gams-Global Optimization Example

Given the bilinear NLP below:

min f = x1 - x2 - y1 -x1y1 + x1y2 + x2y1 -x2y2

st. x1 + 4x2 ≤ 8

4x1 + x2 ≤ 12

3x1 + 4x2 ≤ 12

2y1 + y2 ≤ 8

y1 + 2y2 ≤ 8

y1 + y2 ≤ 5

0 ≤ x1, x2, y1, y2 ≤ 10

 ¿¿¿¿¿¿Question??????? 

Solve the problem with a random strategy in which we start a local optimizer from several randomly generated initial guesses and keep finally the solution with better objective function value.  


Gams Programi ile cozum kodlari asagidadir.
Ve programi indirme linki de --  https://hotfile.com/dl/189462700/7fa60ac/a)bilinearnlp.rar.html


sets
i iterations/1*10/ ;

variables
x1,x2,y1,y2,func;

parameters
objfun(i)
x1par
x2par
y1par
y2par;
equations
eq,q1,q2,q3,q4,q5,q6;


eq.. func=e=x1-x2-y1-x1*y1+x1*y2+x2*y1-x2*y2;
q1.. x1+4*x2=l=8;
q2.. 4*x1+x2=l=12;
q3.. 3*x1+4*x2=l=12;
q4.. 2*y1+y2=l=8;
q5.. y1+2*y2=l=8;
q6.. y1+y2=l=5;

x1.lo=0;
x2.lo=0;
y1.lo=0;
y2.lo=0;
y2.up=10;
y1.up=10;
x2.up=10;
x1.up=10;


*starting point
*x1.l=0;
*x2.l=0;
*y1.l=0;
*y2.l=0;

*model Exercise /all/;
model bilinear/all/;

loop (i,
x1.l=uniform(0,10);
x1par(i)=x1.l;
x2.l=uniform(0,10);
x2par(i)=x2.l;
y1.l=uniform(0,10);
y1par(i)=y1.l;
y2.l=uniform(0,10);
y2par(i)=y2.l;
*solve the problem
solve bilinear minimizing func using NLP;
*store the value
);
display x1par,x2par,y1par,y2par;

*solve Exercise minimizing func using nlp;

sonuclar: