nonlinear integer(boolean) programming problem

can we solve this using MATLAB?

cost function is known.

thanks

Answer 1

[Alan Weiss]

Is the cost linear in the decision variables? If so, use intlinprog. I assume that you have other constraints that you did not list, such as all variables are positive. All Optimization Toolbox™ solvers minimize; to maximize, use the negative of your cost function.

If the cost cannot be made linear, you can try ga or surrogateopt, which try to minimize nonlinear functions over integer variables.

Alan Weiss

MATLAB mathematical toolbox documentation

[R yan]

Thank you for your answer. The cost function is already computed and stored in a matrix. The decision variables are binary.

[R yan]

Also the objective function is non-linear.

[Alan Weiss]

I am not at all sure how to solve this problem efficiently, sorry. I didn't read carefully your problem description at first. Our nonlinear integer solvers do not allow equality constraints, so while you can represent equality constraints as two inequalities, I doubt that the solvers would perform well.

I hope that someone else has better ideas for you.

I could imagine that a greedy search would give a bound that might be not too bad, but this would not be optimal, and would not generalize to an iterative algorithm.

Alan Weiss

MATLAB mathematical toolbox documentation