# How to get intlinprog to stop when the answer is good enough?

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Jonathan on 28 Mar 2020
Commented: Alan Weiss on 31 Mar 2020
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);

Alan Weiss on 29 Mar 2020
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

Jonathan on 30 Mar 2020
Alan,
Thank you; this does what I was looking for.
Since you are part of the documentation team, I will share why I did not look at this option in the first place. The documentation for the OutputFcn option for intlinprog states the following.
"Specify one or more functions that an optimization function calls at events as 'savemilpsolutions', a function handle, or a cell array of function handles. For custom output functions, pass function handles.
• 'savemilpsolutions' collects the integer-feasible points in the xIntSol matrix in your workspace, where each column is one integer feasible point.
For information on writing a custom output function, see intlinprog Output Function and Plot Function Syntax."
This suggested to me that the OutputFcn option was for storing feasible solutions and such, not for exiting early. I recommend updating the documentation to highlight the versatility of this option.
Kind regards,
Jonathan
Alan Weiss on 31 Mar 2020
Thank you for the suggestion. I will consider putting this in the next documentation release.
Alan Weiss
MATLAB mathematical toolbox documentation