Constraint with Loop

[Raouf]

Hi,

I'm new with the yalmip, so i want to to solve a in binary problem (the fixed charge location problem/warehouse location problem see the annex for the cplex model of this problem) The question is : is it possible to use a loop on variable when constructing identical constraints to simplify the constraint construction ? (see constraint 3)

this example is my first try with yalmip i hope it's easy to understand...

All comments are welcome to improve my model

Example :

Parameters:

 fj = [5 6]; %Cost of server

 cj = [12 13];%capacity of server

 cj1 = diag(cj);%diagonal of server capacity 

 dij=[1 4;2 4;3 1;5 2];%distance from server  j to client i

 

 hi=[2;4;2;4];%client i demand

 hi1=diag(hi);%diagonal of the demand 

 alpha=1;%travel cost

a1=ones(1,2); 

b1=ones(4,1);

%variables 

y = binvar(4,2); %client i is served by server j 

x = binvar(2);  %locate a server at  j then  x=1 else 0 

%constraint

Contraints = [y*b1==b1, y'*hi1-cj1*x<=0, y(i,j)-x(j) <=0];

%constraint 1: y*b1==b1 cover all the point of demand

%constraint 2: y'*hi1-cj1*x<=0 contraint of capacity limitation

%constraint 3: y(i,j)-x(j) for each i and j 

obj=fj*cj+alpha*sum(sum((hi1*y)'*dij));

solvesdp(Contraints,obj);

Cplex version:

int Fixed = ...;
{string} Warehouses = ...;
int NbStores = ...;
range Stores = 0..NbStores-1;
int Capacity[Warehouses] = ...;
int SupplyCost[Stores][Warehouses] = ...;
dvar boolean Open[Warehouses];
dvar boolean Supply[Stores][Warehouses];


minimize
  sum( w in Warehouses ) 
    Fixed * Open[w] +
  sum( w in Warehouses , s in Stores ) 
    SupplyCost[s][w] * Supply[s][w];
    

subject to{
  forall( s in Stores )
    ctEachStoreHasOneWarehouse:
      sum( w in  Warehouses ) 
        Supply[s][w] == 1;
  forall( w in Warehouses, s in Stores )
    ctUseOpenWarehouses:
      Supply[s][w] <= Open[w];
  forall( w in Warehouses )
    ctMaxUseOfWarehouse:         
      sum( s in Stores ) 
        Supply[s][w] <= Capacity[w];
}

[Johan Löfberg]

First, I think you want x = binvar(2,2,'full'); As you have defined it now, it is symmetric
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Basics

Concerning loops, I am not sure what it is you want to do, but the general rule is that YALMIP is MATLAB consistent, so if if can do it in MATLAB with numerical variables, you can do it in YALMIP

Something like this, although there are some strange things here as your notation was unclear

%constraint

Constraints = [y*b1==b1];
obj = 0;
for j = 1:2
 for i = 1:4
  Constraints = [Constraints, y(i,j)-x(j)<=0];
 end
 Constraints = [Constraints, y'*hi1-cj1*x<=0];??

 obj=obj + f(j)*c(j)+alpha*sum(sum((hi1*y)'*d(i,j));??

end

Your code can probably be simplified a lot by using standard MATLAB code. For instance, your first constraint is simply

sum(y,2) == 1

In a similar way, you don't have to introduce those diagonal matrices you create etc.

[Raouf]

First, Thank for your fast answers, i'll try to simplify my model with your advices and repost it to see if am on the right direction.

[Raouf]

I have considered your comment and I changed my model. Here is the new version and the message listed by matlab (i used CPLEX and the default solver)

%Parameters:

 fj = [5;6]; %location cost j

 cj = [25;27];%capacity of server j

 dij=[1 4;2 4;3 1;5 2];%distance from server j to client i

 

 hi=[1 1;2 2;3 3;4 4];%demand of client i

 

 %alpha=1;%

%variables 

y = binvar(4,2); 

x = binvar(2,1); 

%x = binvar(2,1,'full');%what what a full bring to  a binary variable of

%2 lines and one collumn

%constraints

Constraints = [sum(y,2)==1,sum(y)'-x<=0];

for j = 1:2

 for i = 1:4

  Constraints = [Constraints, y(i,j)-x(j)<=0];

  

 end

end

obj=sum(fj.*x) + sum(sum((hi.*y.*dij))) ;

%solvesdp(Constraints,obj);

options = sdpsettings('verbose',1,'solver','cplex');

sol = solvesdp(Constraints,obj,options);

Row 'c1' infeasible, all entries at implied bounds.

Presolve time =    0.00 sec.

[Johan Löfberg]

cplex says the problem is infeasible, which it trivially is

Constraints = [sum(y,2)==1,sum(y)'-x<=0];

Here you say there has to be exactly one 1 on every row of y, and then that the sum of every column should be at most 1 (since x can be at most 1). That is totally inconsistent since at least one column will have at least 2 1s.

[1 0
 1 0
 1 0
 1 0]

one columns sums to 4, so obviously not feasible

[1 0
 0 1
 0 0
 0 1]

both columns sum to 2, so obviously not feasible

etc etc.

[Johan Löfberg]

Siunce you seem to struggle with vectorization of MATLAB code, it might be useful to go with a direct line-by-line translation of the code. Something like this

Open   = binvar(nWarehouses,1);
Supply = binvar(nStores, nWarehouses,'full');

obj = 0;
for w = 1:nWarehouses
    obj = obj + Fixed*Open(w);
    for s = 1:nStores
        obj = obj +  SupplyCost(s,w)*Supply(s,w);
    end
end

Constraints = [];
for s = 1:nStores
    Constraints = [Constraints, sum(Supply(s,;))==1];
end
for s = 1:nStores
    for w = 1:nWarehouses
        Constraints = [Constraints,Supply(s,w) <= Open(w)];
    end
end
for w = 1:nWarehouses
    Constraints = [Constraints, sum(Supply(:,w))<= Capacity(w)];
end

[Raouf]

Thank you for your help, i just realized the errors with my model :) so i  rebuild it with matlab vectorization and some of your advice and it's ok. I will pass YALMIP to my colleague and  the student of our lab.