# How to input mixed positive integer variable to "gamultiobj" fitness function?

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AKHILESH BARNWAL on 27 Mar 2022
Answered: Alan Weiss on 28 Mar 2022
Hello all, I am using the "gamultiobj" optimization function.
I have two variable(nvars=2) in my problem. That is each function takes the two variable x(1) and x(2). The problem solves well for contineuos variable lying between 2 to 10 and 1.5 to 5.
Now I want to modify the first variable as positive integer i.e. the first variable must be a positive integer number between 2 to 10 (1, 2, 3, 4,5, 6, 7, 8, 9 or 10 only) while the second one is a contineous. My problem is when I am setting lb=[2 1.5]; ub=[10 5]; the second variable is still continous number. So how can I fix the first variable to vary as integer number in between 2 to 5?
fn = @(x)[fn1(x),fn2(x),fn3(x),];
nvars=2;
A=[];
b=[];
Aeq = [];
beq = [];
lb=[2 1.5];
ub=[10 5];
rng default % for reproducibility
[x,fval] = gamultiobj(fn,nvar,A,b,Aeq,beq,lb,ub);

Alan Weiss on 28 Mar 2022
If your MATLAB version is R2021b or later, you can use integer constraints in gamultiobj. For details, see the function reference page.
Alan Weiss
MATLAB mathematical toolbox documentation