Mixed Integer (binary) Non-linear problem

Dear all,

I am working on intger (binary) nonlinear problem which is only (0-1) variable, with equality constraint. I am using Genetic Algorithm in order to solve this problem but I got the this error ("GA does not solve problems with integer and equality constraints"), because I have two constraints, the variables solution should be integer and at the same time I have equality constraints.

I got an answer for this question before on the following link:

https://de.mathworks.com/help/gads/mixed-integer-optimization.html#bs1clc2

I reformulated the equality constraints to be as nonequality constraints as the following example, but the result I got is not accurate. Knowing that I have around 10 000 variables in my problem:

3x1 – 2x2 = 5,

create two inequality constraints:

3x1 – 2x2 ≤ 5

3x1 – 2x2 ≥ 5.

To write these constraints in the form A x ≤ b, multiply the second inequality by -1:

–3x1 + 2x2 ≤ –5.

How can I solve this problem, and is there any other functions in matlab can help or support this kind of problem (integer nonlinear problem with equality constraint)

Thanks,

Answer 1

[Alan Weiss]

That is way too many variables for ga even if it handled integer equality constraints. I suggest that you would probably be best served by an iterative approach using intlinprog as a subproblem solver. See Mixed-Integer Quadratic Programming Portfolio Optimization: Solver-Based for an example.

Good luck,

Alan Weiss

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