How to define Binary Variable?

Hi, I'm trying to solve an obtimization problem which includes constraints with binary variables

My question is how can i write these constraints and how can i define the binary variable in Matlab (oij) ?

Thanks so much

Answer 1

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/60099

http://www.mathworks.com/help/optim/ug/bintprog.html

[Walter Roberson]

If you know the value of the binary variables ahead of time, then you would just go ahead and construct the constraint matrix

A = zeros(2*N, N);
B = zeros(2*N, 1);
R = 0;
for I = 1 : N
  for J = I+1 : N
    R = R + 1;
    A(R, I) = +1;
    A(R, J) = -1;
    B(R) = O(I,J);
    R = R + 1;
    A(R, I) = -1;
    A(R, J) = +1;
    B(R) = ~O(I,J);
  end
end

B = B .* L;

Note: your constraints appear to be inconsistent with regards to O(i,i). If O(I,I) = 1 - O(I,I) then the solution is O(I,I) = 1/2, but the O(I,I) is constrained to be 0 or 1.

Answer 2

[ada]

Thanks for your answer but the problem is what i'm trying to optimize is not depending on the binary variable oij. It's added in the constraints just to partition the problem into convex sets. So this is not a binary integer programing. It's a mixed integer nonlinear programming which includes a binary variable in the constraints.

[Alan Weiss]

There is currently only one solver for MINLP in MATLAB toolboxes: GA. See the documentation on integer constraints. You represent binary constraints by setting the variables to integer, and putting lower bounds of 0 and upper bounds of 1 for those variables.

Alan Weiss

MATLAB mathematical toolbox documentation

[ate kasa]

Dear this best help