Dear all

I have a question about creating integer variables and equations with

special features in GAMS.

Consider the following optimization problem:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0=<yi=<10

xi is integer xi=0 or 10

xi=<yi

Is there anyway to define xi as a two-state variable in GAMS while the

programming remains linear?

(When we use the following codes the accepted domain for xi will be

all integers between 0 and 10 rather than 0 and 10 themselves:

integer variable x;

x.lo(i)=0;

x.up(i)=0;)

As a trick, I tried to declare the optimization in a nonlinear form,

using binary variables qi:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0=<yi=<10

xi is integer 0=<xi=<10

qi is binary

xi=qi*yi

xi=<yi

I tried to solve this programming by MIQCP. In GAMS’ output all

variables turned out to be zero. However it is easy to track that the

following solution is better than the solution with all variables

zero:

x1=10;

x2=10;

x3=0;

y1=10;

y2=10;

y3=0;

z=90;

Is there a better way to solve this quadratic problem? (For example by

changing the problem types or solvers )?

THNAKS A LOT

\

Dear Milad

Replace variable X by term Y1 + 2.Y2 + 4.Y3 + 8.Y4 and add the

following constraints:

Y1 + 2.Y2 + 4.Y3 + 8 Y4 wrote:

Dear all

I have a question about creating integer variables and equations with

special features in GAMS.

Consider the following optimization problem:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0= > xi is integer xi=0 or 10

xi= > Is there anyway to define xi as a two-state variable in GAMS while the

programming remains linear?

(When we use the following codes the accepted domain for xi will be

all integers between 0 and 10 rather than 0 and 10 themselves:

integer variable x;

x.lo(i)=0;

x.up(i)=0;)

As a trick, I tried to declare the optimization in a nonlinear form,

using binary variables qi:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0= > xi is integer 0= > qi is binary

xi=qi*yi

xi= > I tried to solve this programming by MIQCP. In GAMS’ output all

variables turned out to be zero. However it is easy to track that the

following solution is better than the solution with all variables

zero:

x1=10;

x2=10;

x3=0;

y1=10;

y2=10;

y3=0;

z=90;

Is there a better way to solve this quadratic problem? (For example by

changing the problem types or solvers )?

THNAKS A LOT

\

Dear Milad,

The following model is a good way to solve your problem (GAMS code):

- Min(z=-5x1-7x2-6x3+y1+2y2+8y3)
- yi is integer 0=<yi=<10
- xi is integer xi=0 or 10
- xi=<yi

binary variables x1,x2,x3; integer variables y1,y2,y3; variable z;

equation obj,le1,le2,le3;

obj… z =e= -50*x1-70*x2-60*x3+y1+2*y2+8*y3;

le1… 10*x1 =l= y1; le2… 10*x2 =l= y2; le3… 10*x3 =l= y3;

y1.up=10;y2.up=10;y3.up=10;

model m / all / solve m us mip min z;

Regards,

Timo

\

2011/4/30 milad ziai

Dear all

I have a question about creating integer variables and equations with

special features in GAMS.

Consider the following optimization problem:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0=<yi=<10

xi is integer xi=0 or 10

xi=<yi

Is there anyway to define xi as a two-state variable in GAMS while the

programming remains linear?

(When we use the following codes the accepted domain for xi will be

all integers between 0 and 10 rather than 0 and 10 themselves:

integer variable x;

x.lo(i)=0;

x.up(i)=0;)

As a trick, I tried to declare the optimization in a nonlinear form,

using binary variables qi:

Min(z=-5x1-7x2-6x3+y1+2y2+8y3)

yi is integer 0=<yi=<10

xi is integer 0=<xi=<10

qi is binary

xi=qi*yi

xi=<yi

I tried to solve this programming by MIQCP. In GAMS’ output all

variables turned out to be zero. However it is easy to track that the

following solution is better than the solution with all variables

zero:

x1=10;

x2=10;

x3=0;

y1=10;

y2=10;

y3=0;

z=90;

Is there a better way to solve this quadratic problem? (For example by

changing the problem types or solvers )?

THNAKS A LOT

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