Originally posted by: Srihitha Reddy B

Hi,

I would like to know how to give a matrix as an input to the optimization problem.

Also, how to use the outputs from other mod file into the current mod file? Are there any options like importing? 

Please help me out.

Thanks,

Srihitha.

Hi,

about matrix input , have a look at the example in CPLEX_Studio128\opl\examples\opl\foodmanufact

In the .mod you ll see

float Cost[Months][Products] = ...;

and in the .dat

Cost = [[110.0, 120.0, 130.0, 110.0, 115.0],
[130.0, 130.0, 110.0,  90.0, 115.0],
[110.0, 140.0, 130.0, 100.0,  95.0],
[120.0, 110.0, 120.0, 120.0, 125.0],
[100.0, 120.0, 150.0, 110.0, 105.0],
[90.0, 100.0, 140.0,  80.0, 135.0]];

For using the result of a first model in a second model, have a look at https://www.ibm.com/developerworks/community/forums/html/topic?id=471cc451-9dc2-44d8-a0e9-5f146fb14765&ps=25

regards

PS: Many how to at https://www.linkedin.com/pulse/how-opl-alex-fleischer/

Originally posted by: Srihitha Reddy B

Hi, Alex!!

Thanks for the reply.

We are having a set of constraints in which we are getting syntax errors. Please have a look at it.

ERROR:  Cannot use the type int with "in"

Thanks in advance,

Srihitha.

Hi,

I guess m1 is an int and you should use a range such as 1..m1 instead of m1!

regards

Originally posted by: Srihitha Reddy B

Hi,

Thank you. We corrected m1 to 1..m1.

And, in the code q is an array of integers. Can't we use q itself or should we change the syntax?

Regards,

Srihitha.

Hi

for q you should maybe use the index. Write q[i] for instance.

Regards

Originally posted by: Srihitha Reddy B

Thank you, Alex!

I tried writing the algorithm, but still, I couldn't figure it out.Am getting errors.

Please help me out.

Algorithm is:

Please find attached the CPLEX files.

Thanks in advance.

Please solve this issue.

Regards,

Srihitha.

Originally posted by: Srihitha Reddy B

Hi,

I founded out the error. It occurs at z[i][j][k].

Actually, z[i][j][k] is the bivalent variable expressing migration of VM_k from server i to server j. 

But, declaring as shown above (z[i][j][k]) is incorrect. Please provide me an answer to proceed with.

Thanks in advance,

Srihitha. 

Hi,

if you rewrite cons1 and cons2 into

cons1:forall(i,j,l in 1..m1, k in 1..q[i],k1 in 1..q[j])         
       //cons1:
          z[i][j][k] + z[j][l][k1] <= 1;
       
   
       cons2:forall(i,j in 1..m1, k in 1..q[i])
          //cons2:
          sum(j in 1..m1) (z[i][j][k]) <= 1;

your model will work better.

See

https://www.ibm.com/support/knowledgecenter/en/SSSA5P_12.6.1/ilog.odms.ide.help/OPL_Studio/opllangref/topics/opl_langref_constraints_labels_limit.html

for limits with labeling constraints

regards

PS:

What you try to do is linked with https://www.linkedin.com/pulse/best-kept-secret-can-help-alex-fleischer/

?

Originally posted by: Srihitha Reddy B

Hi, Alex!
Thanks for the reply. The errors got resolved.

But, suggest me a way to declare the bivalent variable z_ijk, which expresses migration of VM_k from server i to server j. It should be a 2-dimensional matrix. But, by declaring z _ijk, as z[i][j][k], we are getting a 3-dimensional matrix.

Please help me with this issue.

Thanks in advance,

Srihitha.

Hi,

what would be the indexes for your  2-dimensional matrix ?

regards

Originally posted by: Srihitha Reddy B

Hi,

In z_ijk , i and j values are from the number of non-idle servers out of available servers (4) and k values are from number of VMs(5).

Thanks,

Srihitha.

which make z a 3D array

Originally posted by: Srihitha Reddy B

Hi,

Whatever the values of inputs may be, we are not getting the dvar z matrix values. We are getting all values as zero.

 //parameters
 int n=...; //no. of requested VMs
 int m=...; //no. of servers
 
 range VMs=1..n;
 range servers=1..m;
 
 float maxpower=...;   //max power consumed by server
 float idlepower=...;
 float power[VMs]=...; //power consumption of VMs
 float currentpower[servers]=...; //current power consumption of servers
 int x[VMs][servers]=...;
 int e[servers]=...;
 int y[servers]=...;
 
 //variables
   
 //dvar boolean y[servers];
 dvar boolean z[servers][servers][VMs];

 //int count;
 int m1=0;
 float p;
 int q[servers];
 float pk=...;
  
 execute
{
  for(var j=1;j<=m;j++)
  {
     //if(e[j]==1) y[j]==0;
     //else y[j]==1;
     p=0;  
     q[j]=0;
     for (var i=1;i<=n;i++)
     {
       if(x[i][j]==1) 
       {
         p=p+power[i];
         q[j]=q[j]+1;      
       }    
       writeln(q[j]);
     }  
     if(p<maxpower && p>0)
     {
       m1=m1+1;     
     }
  }
  writeln("#non-idle servers=",m1);
  //writeln("#VMs hosted on server i=",q[j]);
}

 //expression
 maximize sum(i in 1..m1) (idlepower*y[i]) - sum(i in 1..m1)sum(j in 1..m1)sum(k in 1..q[i]) (pk*z[i][j][k]);  //Objective: Min used no. of servers
  
 //constraints
 subject to{
        cons1:
          forall(i,j,l in 1..m1) forall(k,k1 in 1..q[i]) 
          z[i][j][k] + z[j][l][k1] <= 1;
       
       cons2:
          forall(i in 1..m1) forall(k in 1..q[i]) 
          sum(j in 1..m1) (z[i][j][k]) <= 1;
       
       cons3:
          forall(j in servers )
          sum(i in 1..m1)sum(k in 1..q[i]) (pk*z[i][j][k]) <= (maxpower - currentpower[j])*(1-y[j]);  
          
       cons4:
          forall(i in 1..m1)
          sum(j in 1..m1) sum(k in 1..q[i]) (z[i][j][k]) == q[i]*y[i];
                   
       cons5:
       sum(i in 1..m1) y[i] <= m1 - ceil ((sum(j in 1..m1) currentpower[j])/maxpower);   
        }

output: 

z = [[[0
                 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]]
             [[0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]]
             [[0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]]
             [[0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]
                 [0 0 0 0 0]]];

Also, we are getting 57 warnings as:

Decision variable "z[1][1][4]" has never been used by the engine.

Decision variable "z[1][1][5]" has never been used by the engine.

....

Thanks in advance,

Srihitha.

Hi,

can you attach .dat ?

regards

Originally posted by: Srihitha Reddy B

Hi,

PFA the files.

Thanks,

Srihitha

Hi

have a look at

cons4:
          forall(i in 1..m1)
          sum(j in 1..m1) sum(k in 1..q[i]) (z[i][j][k]) == q[i]*y[i];

If you realize that y is [ 0 0 0 1] and q is [2 2 1 0]

you ll understand that for all i in 1..m1

sum(j in 1..m1) sum(k in 1..q[i]) (z[i][j][k])

needs to be 0 which explains why all z are 0

regards

Originally posted by: Srihitha Reddy B

Hi,

Please have a look at eq-25 which is cons4 in our code. Neglecting eq-27, the rest (22-26) are our 5 constraints.

Also, what do those warnings mean?

And, how should we include i !=j (i not equal to j) in some of the constraints?

Thanks,

Srihitha.

Hi,

let me  comment the first one:

Instead of

cons1:
          forall(i,j,l in 1..m1) forall(k,k1 in 1..q[i])
          z[i][j][k] + z[j][l][k1] <= 1;

you could try

cons1:
          forall(i,j,l in 1..m1:i!=j && l!=j) forall(k,k1 in 1..q[i]:k!=k1)
          z[i][j][k] + z[j][l][k1] <= 1;

The warning meant that the decision variable was not used in any constraint.

Are you a student ?

regards

Originally posted by: Srihitha Reddy B

Yes, Alex.

I am a student.

I will replace the cons1 and I will try that.

Thanks,

Srihitha.

Originally posted by: Srihitha Reddy B

 Hi,

For this algorithm, the inputs are x _ij  matrix and e_j matrix.  

Decision variables are z _ijk and y_j , in which, the 'y' values depend on 'e' values like if e[j] = 0(server j is not being used i.e idle server), then y[j]=1(idle server)  and vice-versa.

But, in this algorithm, if we are declaring y as a decision variable and giving this condition on "e[j]", then we are not getting the values of 'y' exactly as opposite as 'e.' We are getting some random stuff for 'y' by which q*y may not become zero.

Unless, if we directly feed in the exact opposite values of 'e' as the matrix 'y', then obviously q*y values become zero and we are getting z values as zeroes.

So could you suggest us something that works..

Thanks in advance,

Srihitha.

Originally posted by: Srihitha Reddy B

Hi,

This is the explanation for cons4.

y=0,if server is non-idle

y=1, if idle

Thanks,

Srihitha.

Originally posted by: Srihitha Reddy B

Hi,

We would like to know how to include the lifetime of VMs in the migration algorithm discussed above.

For eg. : We have a set of incoming VMs, with a uniform incoming rate(say 1 second) and uniform lifetime (say 10 secs). Suppose, 5th VM take 5 secs to enter the pipeline, similarly 10th  VM take 10 sec to enter. By the time 11th VM enters, which takes 11 secs, the 1st VM should complete its job and that memory should be released such that re-arrangement (migration)  takes place. 

Could you suggest a way to implement this kind of algorithm?

Thanks in advance,

Srihitha.