Nonlinear Constraints with gamultiobj

This Questionn has already been asked 1.5 years ago, there was no accepted answer. I hope there is a solution to this problem by now.

I am trying to find a global minimum for x values with the function gamultiobj. However i need to apply the constraint x(i+1) <= cos(asin(x(i)/b), b = const. Is it by now possible to apply such a nonlinear constraint to my problem? Is there a workaround?

Thanks for any help!

Answer 1

[Matt J]

Assuming all x(i)>=0, the constraints can be transformed to linear ones. Since cos(asin(z))=sqrt(1-z^2), the constraint

 x(i+1) <= cos(asin(x(i)/b))

is equivalent to

 x(i+1)^2+ x(i)^2/b^2<=1

If you make the change of variables y(i)=x(i)^2, and rewrite the problem in terms of the variables y(i), all the constraints become linear.

Answer 2

[Rahul Mishra]

gamultiobj of Global optimization toolbox now supports nonlinear constraints as well . [2014B onwards].

Answer 3

[Bruno Pop-Stefanov]

gamultiobj does not allow nonlinear constraints. Depending on your problem you might want to consider other solvers.

For example, ga does accept nonlinear constraints (defined by a function). If you can use a non-genetic algorithm, then consider the MultiStart and GlobalSearch classes. For example, fmincon can be specified as a solver with nonlinear constraints.

[Ben]

If it would not be necessary to use a genetic algorithm multiobjective solver, I would not try to use it ;) I am aware of other solvers like ga, fmincon or fgoalattain... Thank you for your input though!