Decision Optimization

Attachment 1 is the algorithm that I am trying to solve.
Attachment 2 and 3 contain the problem (McCormick relaxation is applied to linearized the product of continuous variables)
4th is the initial feasible solution
5th is the result of bounds improvement
I am trying to reproduce the results.
I am having issues.
I don't know how to provide initial solution to cplex particularly in this case and also how to add a constraint that x has to be between bounds provided in the iteration.
following is the code.
I will be thankful if you can help


float l1 = ...;
float l2 = ...;
float l3 = ...;

float u1 = ...;
float u2 = ...;
float u3 =...;

float zf = 967.5207101;

dvar float x1;
dvar float x2;
dvar float x3;

dvar float w11;
dvar float w22;
dvar float w33;
dvar float w12;
dvar float w13;


minimize
x1;



subject to{

1000- w11 - 2*w22 - w33 - w12 - w13 <= zf;

8*x1 +14*x2 +7*x3 == 56;
w11 + w22 + w33 == 25;

w11 >= - u1*u1 + 2*u1*x1;
w11 >= - l1*l1 + 2*l1*x1;
w11 <= - u1*l1 + 5*x1 + l1*x1;

w22 >= - u2*u2 + 2*u2*x2;
w22 >= - l2*l2 + 2*l2*x2;
w22 <= - u2*l2 + 4*x2 + l2*x2;

w33 >= - u3*u3 + 2*u3*x3;
w33 >= -l3*l3 + 2*l3*x3;
w33 <= - u3*l3 + 5*x3 + l3*x3;

w12 >= - u1*u2 + u2*x1 + u1*x2;
w12 >= - l1*l2 + l2*x1 + l1*x2;
w12 <= - u1*l2 + l2*x1 + u1*x2;
w12 <= - l1*u2 + u2*x1 + l1*x2;

w13 >= - u1*u3 + u3*x1 + u1*x3;
w13 >= - l1*l3 + l3*x1 + l1*x3;
w13 <= - u1*l3 + l3*x1 + u1*x3;
w13 <= - l1*u3 + u3*x1 + l1*x3;

x1 >= l1;
x2 >= l2;
x3 >= l3;

x1 <= u1;
x2 <= u2;
x3 <= u3;


}


main {
thisOplModel.generate();
var produce = thisOplModel;

var L1 = produce.l1;

var tol = 0.0001;

var xl1iter = 0;

while (1){

xl1iter = L1;
writeln("Solve with L1 = ",L1);

if ( cplex.solve() ) {


xl1iter = cplex.getObjValue();
writeln();

writeln("OBJECTIVE: ",xl1iter);
}
else {
writeln("No Sloution");
break;

}

if ((Opl.abs(L1 - xl1iter)) < tol) break;

L1 = xl1iter;

     }
}

------------------------------
Tooba Binte Asif
------------------------------

#DecisionOptimization

Did you look at the various examples that ship with CPLEX? There are examples for how to solve models iteratively and how to specify an initial solution. Look for example at the warmstart.mod example for starting solutions. For the other aspect look for .mod files that contain a 'main' block with a loop.

------------------------------
Daniel Junglas
------------------------------

Original Message:
Sent: Thu June 25, 2020 03:29 AM
From: Tooba Binte Asif
Subject: Trying to solve bound tightening algorithm

Attachment 1 is the algorithm that I am trying to solve.
Attachment 2 and 3 contain the problem (McCormick relaxation is applied to linearized the product of continuous variables)
4th is the initial feasible solution
5th is the result of bounds improvement
I am trying to reproduce the results.
I am having issues.
I don't know how to provide initial solution to cplex particularly in this case and also how to add a constraint that x has to be between bounds provided in the iteration.
following is the code.
I will be thankful if you can help


float l1 = ...;
float l2 = ...;
float l3 = ...;

float u1 = ...;
float u2 = ...;
float u3 =...;

float zf = 967.5207101;

dvar float x1;
dvar float x2;
dvar float x3;

dvar float w11;
dvar float w22;
dvar float w33;
dvar float w12;
dvar float w13;


minimize
x1;



subject to{

1000- w11 - 2*w22 - w33 - w12 - w13 <= zf;

8*x1 +14*x2 +7*x3 == 56;
w11 + w22 + w33 == 25;

w11 >= - u1*u1 + 2*u1*x1;
w11 >= - l1*l1 + 2*l1*x1;
w11 <= - u1*l1 + 5*x1 + l1*x1;

w22 >= - u2*u2 + 2*u2*x2;
w22 >= - l2*l2 + 2*l2*x2;
w22 <= - u2*l2 + 4*x2 + l2*x2;

w33 >= - u3*u3 + 2*u3*x3;
w33 >= -l3*l3 + 2*l3*x3;
w33 <= - u3*l3 + 5*x3 + l3*x3;

w12 >= - u1*u2 + u2*x1 + u1*x2;
w12 >= - l1*l2 + l2*x1 + l1*x2;
w12 <= - u1*l2 + l2*x1 + u1*x2;
w12 <= - l1*u2 + u2*x1 + l1*x2;

w13 >= - u1*u3 + u3*x1 + u1*x3;
w13 >= - l1*l3 + l3*x1 + l1*x3;
w13 <= - u1*l3 + l3*x1 + u1*x3;
w13 <= - l1*u3 + u3*x1 + l1*x3;

x1 >= l1;
x2 >= l2;
x3 >= l3;

x1 <= u1;
x2 <= u2;
x3 <= u3;


}


main {
thisOplModel.generate();
var produce = thisOplModel;

var L1 = produce.l1;

var tol = 0.0001;

var xl1iter = 0;

while (1){

xl1iter = L1;
writeln("Solve with L1 = ",L1);

if ( cplex.solve() ) {


xl1iter = cplex.getObjValue();
writeln();

writeln("OBJECTIVE: ",xl1iter);
}
else {
writeln("No Sloution");
break;

}

if ((Opl.abs(L1 - xl1iter)) < tol) break;

L1 = xl1iter;

     }
}

------------------------------
Tooba Binte Asif
------------------------------

#DecisionOptimization

Yeah

I have tried but not succeeded.

Can you help me write the code for this algorithm?

------------------------------
Tooba Binte Asif
------------------------------

Original Message:
Sent: Fri June 26, 2020 12:23 AM
From: Daniel Junglas
Subject: Trying to solve bound tightening algorithm

Did you look at the various examples that ship with CPLEX? There are examples for how to solve models iteratively and how to specify an initial solution. Look for example at the warmstart.mod example for starting solutions. For the other aspect look for .mod files that contain a 'main' block with a loop.

------------------------------
Daniel Junglas

Original Message:
Sent: Thu June 25, 2020 03:29 AM
From: Tooba Binte Asif
Subject: Trying to solve bound tightening algorithm

Attachment 1 is the algorithm that I am trying to solve.
Attachment 2 and 3 contain the problem (McCormick relaxation is applied to linearized the product of continuous variables)
4th is the initial feasible solution
5th is the result of bounds improvement
I am trying to reproduce the results.
I am having issues.
I don't know how to provide initial solution to cplex particularly in this case and also how to add a constraint that x has to be between bounds provided in the iteration.
following is the code.
I will be thankful if you can help


float l1 = ...;
float l2 = ...;
float l3 = ...;

float u1 = ...;
float u2 = ...;
float u3 =...;

float zf = 967.5207101;

dvar float x1;
dvar float x2;
dvar float x3;

dvar float w11;
dvar float w22;
dvar float w33;
dvar float w12;
dvar float w13;


minimize
x1;



subject to{

1000- w11 - 2*w22 - w33 - w12 - w13 <= zf;

8*x1 +14*x2 +7*x3 == 56;
w11 + w22 + w33 == 25;

w11 >= - u1*u1 + 2*u1*x1;
w11 >= - l1*l1 + 2*l1*x1;
w11 <= - u1*l1 + 5*x1 + l1*x1;

w22 >= - u2*u2 + 2*u2*x2;
w22 >= - l2*l2 + 2*l2*x2;
w22 <= - u2*l2 + 4*x2 + l2*x2;

w33 >= - u3*u3 + 2*u3*x3;
w33 >= -l3*l3 + 2*l3*x3;
w33 <= - u3*l3 + 5*x3 + l3*x3;

w12 >= - u1*u2 + u2*x1 + u1*x2;
w12 >= - l1*l2 + l2*x1 + l1*x2;
w12 <= - u1*l2 + l2*x1 + u1*x2;
w12 <= - l1*u2 + u2*x1 + l1*x2;

w13 >= - u1*u3 + u3*x1 + u1*x3;
w13 >= - l1*l3 + l3*x1 + l1*x3;
w13 <= - u1*l3 + l3*x1 + u1*x3;
w13 <= - l1*u3 + u3*x1 + l1*x3;

x1 >= l1;
x2 >= l2;
x3 >= l3;

x1 <= u1;
x2 <= u2;
x3 <= u3;


}


main {
thisOplModel.generate();
var produce = thisOplModel;

var L1 = produce.l1;

var tol = 0.0001;

var xl1iter = 0;

while (1){

xl1iter = L1;
writeln("Solve with L1 = ",L1);

if ( cplex.solve() ) {


xl1iter = cplex.getObjValue();
writeln();

writeln("OBJECTIVE: ",xl1iter);
}
else {
writeln("No Sloution");
break;

}

if ((Opl.abs(L1 - xl1iter)) < tol) break;

L1 = xl1iter;

     }
}

------------------------------
Tooba Binte Asif
------------------------------

#DecisionOptimization

Hi,

you may also rely on 

How to multiply two float decision variables ?

in

https://www.linkedin.com/pulse/how-opl-alex-fleischer/

and then you can skip the flow control part

regards

------------------------------
ALEX FLEISCHER
------------------------------

Original Message:
Sent: Thu July 09, 2020 06:14 AM
From: Tooba Binte Asif
Subject: Trying to solve bound tightening algorithm

Yeah

I have tried but not succeeded.

Can you help me write the code for this algorithm?

------------------------------
Tooba Binte Asif

Original Message:
Sent: Fri June 26, 2020 12:23 AM
From: Daniel Junglas
Subject: Trying to solve bound tightening algorithm

Did you look at the various examples that ship with CPLEX? There are examples for how to solve models iteratively and how to specify an initial solution. Look for example at the warmstart.mod example for starting solutions. For the other aspect look for .mod files that contain a 'main' block with a loop.

------------------------------
Daniel Junglas

Original Message:
Sent: Thu June 25, 2020 03:29 AM
From: Tooba Binte Asif
Subject: Trying to solve bound tightening algorithm

Attachment 1 is the algorithm that I am trying to solve.
Attachment 2 and 3 contain the problem (McCormick relaxation is applied to linearized the product of continuous variables)
4th is the initial feasible solution
5th is the result of bounds improvement
I am trying to reproduce the results.
I am having issues.
I don't know how to provide initial solution to cplex particularly in this case and also how to add a constraint that x has to be between bounds provided in the iteration.
following is the code.
I will be thankful if you can help


float l1 = ...;
float l2 = ...;
float l3 = ...;

float u1 = ...;
float u2 = ...;
float u3 =...;

float zf = 967.5207101;

dvar float x1;
dvar float x2;
dvar float x3;

dvar float w11;
dvar float w22;
dvar float w33;
dvar float w12;
dvar float w13;


minimize
x1;



subject to{

1000- w11 - 2*w22 - w33 - w12 - w13 <= zf;

8*x1 +14*x2 +7*x3 == 56;
w11 + w22 + w33 == 25;

w11 >= - u1*u1 + 2*u1*x1;
w11 >= - l1*l1 + 2*l1*x1;
w11 <= - u1*l1 + 5*x1 + l1*x1;

w22 >= - u2*u2 + 2*u2*x2;
w22 >= - l2*l2 + 2*l2*x2;
w22 <= - u2*l2 + 4*x2 + l2*x2;

w33 >= - u3*u3 + 2*u3*x3;
w33 >= -l3*l3 + 2*l3*x3;
w33 <= - u3*l3 + 5*x3 + l3*x3;

w12 >= - u1*u2 + u2*x1 + u1*x2;
w12 >= - l1*l2 + l2*x1 + l1*x2;
w12 <= - u1*l2 + l2*x1 + u1*x2;
w12 <= - l1*u2 + u2*x1 + l1*x2;

w13 >= - u1*u3 + u3*x1 + u1*x3;
w13 >= - l1*l3 + l3*x1 + l1*x3;
w13 <= - u1*l3 + l3*x1 + u1*x3;
w13 <= - l1*u3 + u3*x1 + l1*x3;

x1 >= l1;
x2 >= l2;
x3 >= l3;

x1 <= u1;
x2 <= u2;
x3 <= u3;


}


main {
thisOplModel.generate();
var produce = thisOplModel;

var L1 = produce.l1;

var tol = 0.0001;

var xl1iter = 0;

while (1){

xl1iter = L1;
writeln("Solve with L1 = ",L1);

if ( cplex.solve() ) {


xl1iter = cplex.getObjValue();
writeln();

writeln("OBJECTIVE: ",xl1iter);
}
else {
writeln("No Sloution");
break;

}

if ((Opl.abs(L1 - xl1iter)) < tol) break;

L1 = xl1iter;

     }
}

------------------------------
Tooba Binte Asif
------------------------------

#DecisionOptimization