checking the Benders decomposition

Problems with syntax of GAMS
Post Reply
Parisa
User
User
Posts: 14
Joined: 2 years ago

checking the Benders decomposition

Post by Parisa » 3 months ago

Hello,
I have coded the Benders decomposition for the following problem.
This is the subproblem;
Image
Image

And by assuming the following terminology and knowing that the subproblem does not need the feasibility cuts, the master is shown below;
Image
Image

And here is my code;

Code: Select all

** benders decomposition **
*** Hybrid Car (qless) ***
** sub version: primal **

Sets

         k               /1*25/

         r(k)            /1,2,4,5,7*14,16,17,19*23/

         l(k)            /2*10,12*21,23*25/

         n               /1*1000/
         onn(n)



alias(k,s,t);

Set
         j(s,t)
/
$ondelim
$include qlessPairs.csv
$offdelim
/;

Set
         a(s,t)
/
$ondelim
$include distance.csv
$offdelim
/;

********************************************************************************

Parameters
         f(s,t)
/
$ondelim
$include qlessPairs.csv
$offdelim
/;

Parameters
         d(s,t)
/
$ondelim
$include distance.csv
$offdelim
/;

Parameters
         p;
         p = 25;

Parameters
         mu(s,t,r,n)
         rho(s,t,n)
         phi(s,t,n)
         sigma(s,t,n);
********************************************************************************

scalar
         point1, elapsed
         etaUB   /21000000/;

********************************************************************************

variables
         master_objective, sub_objective, eta;

positive Variables
         y(s,t,r)
         z(s,t);
binary variable
         x(k);


********************************************************************************

equation masterObj, subObj
         Const1(s,t,r)
         Const2(s,t)
         Const3(s,t)
         const4(s,t)
         Const5, OptimalityCut, Consteta;

subObj..
         sub_objective =e= sum((s,t)$(j(s,t)),f(s,t)*d(s,t)*z(s,t))+ sum((s,t,r)$(a(s,t)),f(s,t)*d(s,t)*y(s,t,r));

Const1(s,t,r)$(ord(s)<>ord(r) and ord(s)<>ord(t))..
         y(s,t,r) =l= x.l(r);

Const2(s,t)$(ord(s)<>ord(t))..
         sum(r$(ord(r)> ord(s) and ord(r)< ord(t)),y(s,t,r)) =l= 1;

Const3(s,t)$(ord(s)<>ord(t))..
         z(s,t) =l= sum(l,x.l(l));

Const4(s,t)$(ord(s)<>ord(t))..
         z(s,t) =l= 1;


masterObj..
         master_objective =e= eta;

OptimalityCut(onn)..
         eta =l= sum((s,t,r)$(ord(s)<>ord(r) and ord(s)<>ord(t)),x(r)*mu(s,t,r,onn))+sum((s,t)$(ord(s)<>ord(t)),rho(s,t,onn)+sigma(s,t,onn))
                 +sum((s,t,l)$(ord(s)<>ord(t)),x(l)*phi(s,t,onn));

Const5..
         sum(k,x(k)) =e= p;

Consteta..
         eta =l= etaUB;


 option optcr = 0;
 option optca = 0;
 option MIP = CPLEX;
 option SYSOUT = ON
 option limrow = 200;


model firstMasterModel /masterObj, Const5, Consteta/
model masterModel /masterObj, Const5, OptimalityCut, Consteta/
model subModel /Const1, Const2, Const3, Const4, subObj/;

scalar
         UB      /inf/
         LB      /-inf/
         iter    /1/
         epsilon /0.01/;

point1 = jnow;

solve FirstMasterModel using MIP maximizing master_objective;
UB = master_objective.l;
display x.l, master_objective.l;

solve subModel using LP maximizing sub_objective;
onn(n)$(n.val=iter) = yes;

mu(s,t,r,n)$(n.val=iter) = Const1.m(s,t,r);
rho(s,t,n)$(n.val=iter) = Const2.m(s,t);
phi(s,t,n)$(n.val=iter) = Const3.m(s,t);
sigma(s,t,n)$(n.val=iter) = Const4.m(s,t);
display mu, rho, phi,sigma;


iter = iter+1;
LB = eta.l+sub_objective.l;

while (LB-UB>epsilon,

         solve masterModel using MIP maximizing master_objective;
         UB = master_objective.l;

         solve subModel using LP maximizing sub_objective;
         onn(n)$(n.val=iter) = yes;
         mu(s,t,r,n)$(n.val=iter) = Const1.m(s,t,r);
         rho(s,t,n)$(n.val=iter) = Const2.m(s,t);
         phi(s,t,n)$(n.val=iter) = Const3.m(s,t);
         sigma(s,t,n)$(n.val=iter) = Const4.m(s,t);

         iter = iter+1;
         LB = eta.l+sub_objective.l;
         display x.l, master_objective.l,  mu, rho, phi,sigma;
);

elapsed=(jnow-point1)*24*3600;

display master_objective.l, UB, LB, iter, elapsed, x.l;
I know that there must be a problem with it. I want you to help me find it.
Any help is appreciated. Thank you.
Attachments
master.JPG
ssss.JPG
sss.JPG
ss.JPG

Post Reply