I will try to help with your problem.
The problems that SCE-UA focused is mainly on the constrained problems, which have a fixed parameter bounds,such as [2,54]. To solve your problem, i think it is able to set a very small number (10e-7) as the fixed lower bound for both a and b. Same way to deal with the upper bound. It might need to play with the algorithm parameter (Number of complexes or simplexes) to improve the computation efficiency. Hope this can help.
I have to use this optimization algorithm to minimizing a objective function like this:
error = ((((a./(a+b))-mean).^2)./(mean.^2))+(((((a.*b)./((a+b+1).*((a+b).^2)))-variance).^2)./(variance.^2))+(((((2.*(b-a).*(sqrt(a+b+1)))./((a+b+2).*(sqrt(a.*b))))-skewness).^2)./(skewness.^2))
This is a function beta with parameters a and b. I want to calculate a and b minimizing this fuction error.
I dont know how I can impose the limits of a and b in the algorithm. The limits are, a>0,b>0 and b>0.