[Coin-discuss] How to make SBB force variables to be integers

[Izhar Wallach]

Hi All,
I'm trying to use the Sbb module in order to solve the below integer 
problem.
However, I would like to force the variable to be integers and not only 
only the solution.
Currently, the value of the variables are not integers since the 
constrain: X belongs to {0,1} is relaxed to 0<=X<=1.
Is there a way to configure the Sbb module to seek an integer solution 
for the variables and not only for the objective function?
(The linear program is defined in an MPS file supplier the Sbb module).

The problem:
**********
Consider all the binary vectors of size 4 (vector4) and size 3 (vector3).
There are 2^4 and 2^3 sets of vectors respectively.
The objective is to find a minimal set of vector4  such that it covers 
all the vectors in the vector3 set.
For instance, the vector:    0100 covers the following vector3 vectors:
                                        010
                                        01 0
                                        0 00
                                         100

I assign each vector4's vector  a variable Xi where  1<=i<=2^4 and 
define the objective function and the constrains  to be:
minimize: Z=X1+X2+...+X16
s.t.      for each vector i in vector3:
                      A1X1+A2X2+...+A16X16 >= 1 // for each vector3 
there is at least one vector4 which covers it
                      where Ai = 1 if Xi covers vector i and  0 otherwise.
           
           where:  0<=Xi<=1 // this should be Xi belongs to {0,1} in 
order to be able to obtain not only the size of the minimal set
                                        // but the vectors in that set 
as well.


                     
Thanks,
Izhar.