MATLAB: How to get intlinprog to stop when the answer is good enough

Question

The code below finds an maximum independent set of the graph whose adjacency matrix is A. I would like to pass an option to intlinprog that says stop and return an answer if you get an objective value of -5 or less (meaning an independent set of size 5 or more has been found). This should be much more efficient than finding an independent set of maximum size.

If there is no option to pass to intlinprog that can accomplish my goal, then is there another approach that will?

n = 20;
A = rand(n, n) < 0.1;
A = A | A.';
[r, c] = find(A);
m      = numel(r);
B      = zeros(m, n);
for eI = 1 : m
B(eI, [r(eI), c(eI)]) = 1;
end
b = ones(m, 1);
c = -ones(n, 1);
% min cost.' * x subject to A * x <= b, x(i) is 0 or 1 for all i.
lb      = zeros(n, 1);
ub      = lb + 1;
intvars = 1 : n;
options                     = optimoptions('intlinprog','Display','off');
[x, fval, exitflag, output] = intlinprog(c, intvars, B, b, [], [], lb, ub, options);

Answer 1

You can create an intlinprog output function to stop the optimizaiton when the objective function value goes below a set limit such as -5. Ensure that the phase is not 'rootlp' when you check the objective function value.

Alan Weiss

MATLAB mathematical toolbox documentation