What is a good optimization algorithm for a binary constraints function?

I'm using fmincon at the moment but one of the equality constraints functions that I have can only output a logical array. This means that fmincon cannot know in which direction to continue its search (right?) so I often get an infeasible point as a result. My question is whether there's an interesting MATLAB algorithm that can deal with this type of nonlinear optimization. Global optimization toolbox perhaps?

To visualize, I'm looking for a solution of n points that each contain 3 variables, so the solution is n by 3 and the logical array is n x 1, indicating whether the solution is possible at all. If any of the logicals is true, the solution is useless. I have no knowledge at all of this constraints function so I cannot adjust the upper/lower bound meaningfully.

[Matt J]

ga and surrogateopt in the Global Optimization Toolbox support integer (and therefore also binary) constraints. However, it would probably be advisable to show us a more detailed problem description. I've never heard of a case where the output (not the inputs) of a constraint function needed to be integer-valued.

[Walter Roberson]

In my youth, I sometimes wrote constraint functions that returned logicals, not having understood that the information returned by the constraint functions was used to locate the boundary better.

[Daniele Sonaglioni]

You can try to use Global Search with fmincon as routine and put all your constraints inside GlobalSearch. I think that this is a very good way to deal with your problem.

Alternatively, you can use the genetic algorithm which works very well.

[Steven H]

Thanks guys! I will try the trial license and run the suggestions.

@Walter Roberson I'm not sure whether I understood your.. retrospect? Are you saying that it's actually good for the optimization to have such a constraint function? I do actually update the boundaries before running fmincon such that the boundaries satisfy that constraint function, but apparently solutions within the boundaries can also cause trouble.