nonlinear integer(boolean) programming problem

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R yan
R yan 2020-7-30
评论： Alan Weiss 2020-7-30
can we solve this using MATLAB?
cost function is known.
thanks

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Alan Weiss
Alan Weiss 2020-7-30
编辑：Alan Weiss 2020-7-30
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
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Alan Weiss
Alan Weiss 2020-7-30
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

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