Originally posted by: Rym

Hi

 

Always the CPlex can't generate the prod expression in the model

 

 

int V=1..5;

int D=1..3;

inr P=1..4;

 

  dvar boolean lumda[V][P];
    dexpr int O = sum( i in V, j in P) lumda[i][j];
    dvar int R[P][D] in 0..1000;
    dexpr int RWx[j in P]=prod (l in D) R[j][l];
    dexpr int  RW = sum (j in P) RWx[j] ;
    maximize RW;

ubject to{ 

//une machine virtuelle est hébergée par au plus une seule pm
  limit:
   forall( i in V)
     sum( j in P ) lumda[i][j] <= 1;
 
   
//la quantité de cpu consommée par les vms ne depasse pas la quantité de cpu de la pm j
   cpur:
      forall( j in P)
       sum( i in V) cpui[i]*lumda[i][j] <= cpuj[j];
        

//la quantité de ram consommée par les vms ne depasse pas la quantité de ram de la pm j
    ramr:
     forall( j in P)
       sum( i in V) rami[i]*lumda[i][j] <= ramj[j];

//la quantité de disk consommée par les vms ne depasse pas la quantité de disk de la pm 

    diskr: 
     forall( j in P)
       sum( i in V) diski[i]*lumda[i][j] <= diskj[j];  
       

forall(j in P) 
{cv:

R[j][1]==sum(i in V) lumda[i][j]*cpui[i];
R[j][2]==sum(i in V) lumda[i][j]*rami[i];
 R[j][3]==sum(i in V) lumda[i][j]*diski[i];

} 
  

}

 

thanks

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

prod leads to a non linear model so you should try CPO:

using CP;
 
 range D=1..3;

range P=1..4;   
 
  dvar int R[P][D] in 0..100;
 
 
 dexpr int RWx[j in P]=prod (l in D) R[j][l];
  dexpr int  RW = sum (j in P) RWx[j] ;
    maximize RW;

works

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Rym

Thanks but i must use an ILP model. SO can i remplace the prod by an other expression without using CP ??

 

If i modify the constraint  "cv" by

 

int V=1..5;

int D=1..3;

inr P=1..4;

 

  dvar boolean lumda[V][P];
    dexpr int O = sum( i in V, j in P) lumda[i][j];
    dvar int R[P];
    dexpr int  RW = sum (j in P) R[j] ;
    maximize RW;

subject to 

{

.......

forall(j in P) 
{cv:

R[j]==((sum(i in V) lumda[i][j]*cpui[i])*(sum(i in V) lumda[i][j]*rami[i])*(sum(i in V) lumda[i][j]*diski[i]));

} 
  }

 

 CPLEX can't generate the constraint

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

I would recommend you to try CPO:

using CP;
 
range V=1..5;

range D=1..3;

range  P=1..4;

int cpui[i in V]=i;
int rami[i in V]=i;
int diski[i in V]=i;

 

  dvar boolean lumda[V][P];
  dvar int R[P];
    dexpr int O = sum( i in V, j in P) lumda[i][j];
    dvar int RWx[P];
    dexpr int  RW = sum (j in P) RWx[j] ;
    maximize RW;

subject to

{

forall(j in P)
{cv:

R[j]==((sum(i in V) lumda[i][j]*cpui[i])*(sum(i in V) lumda[i][j]*rami[i])*(sum(i in V) lumda[i][j]*diski[i]));

}
  }
   

but if you are very reluctant, you may also write your constraint in ILP and develop the product:

forall(j in P)
{cv:

R[j] == sum(i1,i2,i3 in V) cpui[i1]*rami[i2]*diski[i3]*(lumda[i1][j]==1)*(lumda[i2][j]==1)*(lumda[i3][j]==1);

 

}

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Rym

I developped the product function but the probelm becomes no convex

 

my .mod file

 

 

int mySeed;
execute{
        var now = new Date();
        mySeed = Opl.srand(Math.round(now.getTime()/1000));
}  

int v = 2;
range V = 1..v;
int p=2;
int d=3;
range P = 1..p;
range D = 1..d;
int cpui[V];
int rami[V];
int diski[V];
int cpuj[P];
int ramj[P];
int diskj[P];
int VMmin=1;
int VMmax=4;
int cpum=24;
int ramm=48;
int diskm=900;
string S[VMmin..VMmax]=["s","m","l","xl"];
{string} VMTypes={S[v] | v in VMmin..VMmax};
int VM[i in V]=1+(rand() % (VMmax - VMmin+ 1));
string vms[i in V] =S[VM[i]];
  
    
tuple PM
{
  int npm;
  string nvm;
  }

 
{PM} indexes={<i,j> | i in P,j in VMTypes}; 

int countPVX[indexes];
execute VMS
{
var ofilevms = new IloOplOutputFile("resvmss.txt");
 writeln("vms=",vms);
for (var i in vms)
{ ofilevms.write("'",vms[i],"',");

if(vms[i]=="s")

  {
   cpui[i]=1;
   rami[i]=2;
   diski[i]=50;

   }
   
 else if(vms[i]=="m")
 {
   cpui[i]=2;
   rami[i]=4;
   diski[i]=100;
 
    
    }
    
  else if(vms[i]=="l")
  
  { cpui[i]=4;
   rami[i]=8;
   diski[i]=150;

 }   
   else
   
  {
   cpui[i]=8;

   rami[i]=16;
   diski[i]=250 ;

   
   } 
   
   
}
writeln(cpui);
writeln(rami);
writeln(diski);

};

execute PMS
{
 

for (var i in P)
{ 

   cpuj[i]=cpum;
   ramj[i]=ramm;
   diskj[i]=diskm;
   
   }

   

writeln(cpuj);
writeln(ramj);
writeln(diskj);

};
 

 
//the model/problem definition
    dvar boolean lumda[V][P];
    dexpr int O = sum( i in V, j in P) lumda[i][j];
    dvar int R[P];
    dexpr int  RW = sum (j in P) R[j] ;
    maximize RW;

//constraint

subject to{ 

//une machine virtuelle est hébergée par au plus une seule pm
  limit:
   forall( i in V)
     sum( j in P ) lumda[i][j] <= 1;
 

 

 

   
//la quantité de cpu consommée par les vms ne depasse pas la quantité de cpu de la pm j
   cpur:
      forall( j in P)
       sum( i in V) cpui[i]*lumda[i][j] <= cpuj[j];
        

//la quantité de ram consommée par les vms ne depasse pas la quantité de ram de la pm j
    ramr:
     forall( j in P)
       sum( i in V) rami[i]*lumda[i][j] <= ramj[j];

//la quantité de disk consommée par les vms ne depasse pas la quantité de disk de la pm 

    diskr: 
     forall( j in P)
       sum( i in V) diski[i]*lumda[i][j] <= diskj[j];  
       
forall(j in P) cps:R[j] == sum(i1 in V,i2 in V,i3 in V) cpui[i1]*rami[i2]*(lumda[i1][j]==1)*(lumda[i2][j]==1)*(lumda[i3][j]==1);
 

 

}
execute
{

writeln("lumda= ",lumda);
//writeln("minx",minx);
//writeln("mini",ro);
writeln("R =",R);
writeln("RW=",RW);
writeln("VMs= ",O);
//writeln("PMs= ",pm);

}

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

you may try with

forall(j in P) cps:R[j] == sum(i1 in V,i2 in V,i3 in V) cpui[i1]*rami[i2]*
((lumda[i1][j]==1) && (lumda[i2][j]==1) && (lumda[i3][j]==1));

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer