Originally posted by: Rym

Did you have a proposition in modifying some constraints in order to have a feasible submodel, without a relaxed solution

 

 

themodel is:

 

 

int M=10000000000;
int n=1;
int p=4;
range N=1..n;
int nd=8;
range ND=1..nd;

int PDCBW[ND][ND];
int PDC[1..nd][1..nd]=[ 
                         [0,0,0,0,1,0,0,0],
                         [0,0,0,0,1,0,0,0],
                         [0,0,0,0,0,1,0,0],
                         [0,0,0,0,0,1,0,0],
                         [1,1,0,0,0,0,1,1],
                         [0,0,1,1,0,0,1,1],
                         [0,0,0,0,1,1,0,0],
                         [0,0,0,0,1,1,0,0]
                        
                                   
                   ];
                   
                   
                   ;
int PDCBWx=10;
execute xc
{
for (var x=1;x<=nd;x++)
  {
   for(var y=1;y<=nd;y++)
    {
     if(PDC[x][y]==1)
     {
       PDCBW[x][y]= PDCBWx;
      }        
    
   }    
  

}
//writeln("P=",PDCBW);
}

tuple edge // link definition
{
int i;
int j;
}
{edge} liaisonp = { <i,j> | i in 1..p,j in 1..p:i!=j};

int LR[N][liaisonp]=[[0, 0, 48, 0, 0, 0, 0, 0, 0, 48, 0, 0]];
int LRb[N][liaisonp]=[[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]];

 

//Definition of the model
dvar boolean lumdabw[N][liaisonp][ND][ND];
dvar boolean Vd[N];
dexpr int lumdij[i in ND][j in ND]=sum(f in N,l in liaisonp)lumdabw[f][l][i][j]*LR[f][l];
dexpr int maxbw=max(i,j in ND)lumdij[i][j];
dexpr int o= sum(f in N) Vd[f];
dvar boolean vdf[N];
maximize o;;

subject to
{

 

//capacity link constraint

clc:
forall (i in ND, j in ND)
sum(f in N,l in liaisonp)(lumdabw[f][l][i][j])*LR[f][l]<=PDCBW[i][j];
//flow constraint

flc:

forall(f in N,l in liaisonp,i in ND)
 {(i==l.i) => ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==LRb[f][l]);
(i==l.j) => ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==-LRb[f][l]);
((i!=l.i)&&(i!=l.j)) => ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==0);     
}
 //A virtual link can be embedded into one physical path(a set of physical links)
    rgv:
   forall(f in N,l in liaisonp,i in ND)
     sum(j in ND)(lumdabw[f][l][i][j])<=1; 
   
 // a virtual link can be embedded into only  a existing  physical link  
   thn:
  forall(f in N, l in liaisonp,i,j in ND) 
    lumdabw[f][l][i][j]<=PDC[i][j];

//lumdaBw existe si seulement si LR existe
yhj:
  forall(f in N,l in liaisonp,i,j in ND) 
     lumdabw[f][l][i][j]<=LRb[f][l];

   
   forall(f in N)
  (1/M)*(sum(i,j in ND,l in liaisonp)lumdabw[f][l][i][j])<=Vd[f];
       
}

 

Thanks

#CPLEXOptimizers
#DecisionOptimization

Hi,

at

https://www.ibm.com/developerworks/community/forums/html/topic?id=8dcfe05c-e35f-4997-ab26-777fffc2861c&ps=25

I suggested

clc:
forall (i in ND, j in ND)
sum(f in N,l in liaisonp)(lumdabw[f][l][i][j])*LR[f][l]<=PDCBW[i][j]+100;

But you said we should not relax that one. Which one could we relax a bit ?

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: Rym

Hi,

 

Yes i can't add 100 to  PDCBW[i][j] in :

lc:
forall (i in ND, j in ND)
sum(f in N,l in liaisonp)(lumdabw[f][l][i][j])*LR[f][l]<=PDCBW[i][j]

 

I can relax only this constraint: 

 //A virtual link can be embedded into one physical path(a set of physical links)
    rgv:
   forall(f in N,l in liaisonp,i in ND)
     sum(j in ND)(lumdabw[f][l][i][j])<=1; 
   

 

#CPLEXOptimizers
#DecisionOptimization

ok then

int M=10000000000;
int n=1;
int p=4;
range N=1..n;
int nd=8;
range ND=1..nd;

int PDCBW[ND][ND];
int PDC[1..nd][1..nd]=[
                         [0,0,0,0,1,0,0,0],
                         [0,0,0,0,1,0,0,0],
                         [0,0,0,0,0,1,0,0],
                         [0,0,0,0,0,1,0,0],
                         [1,1,0,0,0,0,1,1],
                         [0,0,1,1,0,0,1,1],
                         [0,0,0,0,1,1,0,0],
                         [0,0,0,0,1,1,0,0]
                        
                                   
                   ];
                   
                   
                   ;
int PDCBWx=10;
execute xc
{
for (var x=1;x<=nd;x++)
  {
   for(var y=1;y<=nd;y++)
    {
     if(PDC[x][y]==1)
     {
       PDCBW[x][y]= PDCBWx;
      }        
    
   }    
 

}
//writeln("P=",PDCBW);
}

tuple edge // link definition
{
int i;
int j;
}
{edge} liaisonp = { <i,j> | i in 1..p,j in 1..p:i!=j};

int LR[N][liaisonp]=[[0, 0, 48, 0, 0, 0, 0, 0, 0, 48, 0, 0]];
int LRb[N][liaisonp]=[[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]];

 

//Definition of the model
dvar boolean lumdabw[N][liaisonp][ND][ND];
dvar boolean Vd[N];
dexpr int lumdij[i in ND][j in ND]=sum(f in N,l in liaisonp)lumdabw[f][l][i][j]*LR[f][l];
dexpr int maxbw=max(i,j in ND)lumdij[i][j];
dexpr int o= sum(f in N) Vd[f];
dvar boolean vdf[N];
maximize o;;

subject to
{

 

//capacity link constraint

//clc:
forall (i in ND, j in ND)
sum(f in N,l in liaisonp)(lumdabw[f][l][i][j])*LR[f][l]<=PDCBW[i][j];
//flow constraint

flc:

forall(f in N,l in liaisonp,i in ND)
 {ct1:(i==l.i) <= ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==LRb[f][l]);
ct2:(i==l.j) <= ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==-LRb[f][l]);
ct3:((i!=l.i)&&(i!=l.j)) <= ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==0);     
}
 //A virtual link can be embedded into one physical path(a set of physical links)
    
   forall(f in N,l in liaisonp,i in ND)
     rgv:sum(j in ND)(lumdabw[f][l][i][j])<=1;
   
 // a virtual link can be embedded into only  a existing  physical link  
   
  forall(f in N, l in liaisonp,i,j in ND)
    thn:lumdabw[f][l][i][j]<=PDC[i][j];

//lumdaBw existe si seulement si LR existe
yhj:
  forall(f in N,l in liaisonp,i,j in ND)
     lumdabw[f][l][i][j]<=LRb[f][l];

   
   forall(f in N)
  (1/M)*(sum(i,j in ND,l in liaisonp)lumdabw[f][l][i][j])<=Vd[f];
       
}

gives the following relaxation:

Line    Original    Relaxed    Element (8)
78    [-Infinity,-1]    [-Infinity,0]    ct1[1][<1,4>][1]
78    [-Infinity,-1]    [-Infinity,0]    ct1[1][<4,1>][4]
78    [-Infinity,-1]    [-Infinity,0]    ct2[1][<1,4>][4]
78    [-Infinity,-1]    [-Infinity,0]    ct2[1][<4,1>][1]
78    [-Infinity,-1]    [-Infinity,0]    ct1[1][<1,4>][1]
78    [-Infinity,-1]    [-Infinity,0]    ct2[1][<1,4>][4]
78    [-Infinity,-1]    [-Infinity,0]    ct2[1][<4,1>][1]
78    [-Infinity,-1]    [-Infinity,0]    ct1[1][<4,1>][4]

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: Rym

if i relax both constraints a the following

 

forall (i in ND, j in ND)
clc:sum(f in N,l in liaisonp)(lumdabw[f][l][i][j])*LR[f][l]<=PDCBW[i][j];
//flow constraint

 

forall(f in N,l in liaisonp,i in ND)
 {ct1:(i==l.i) => ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==LRb[f][l]);
ct2:(i==l.j) =>((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==-LRb[f][l]);
ct3:((i!=l.i)&&(i!=l.j))=> ((sum(j in ND) (lumdabw[f][l][i][j])-  sum(j in ND) (lumdabw[f][l][j][i]))==0);     
}

I obtained as conflict theses lines, what does it mean ?

 

#CPLEXOptimizers
#DecisionOptimization

Hi

In the documentation you may read

plus do not hesitate to have a look at

http://www-01.ibm.com/support/docview.wss?uid=swg27044521&aid=1

regards

 

#DecisionOptimization