Nonlinear Constraints with gamultiobj

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Ben
Ben am 9 Mai 2014
Beantwortet: Rahul Mishra am 13 Mär. 2015
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!

Akzeptierte Antwort

Matt J
Matt J am 9 Mai 2014
Bearbeitet: Matt J am 10 Mai 2014
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.

Weitere Antworten (2)

Rahul Mishra
Rahul Mishra am 13 Mär. 2015
gamultiobj of Global optimization toolbox now supports nonlinear constraints as well . [2014B onwards].

Bruno Pop-Stefanov
Bruno Pop-Stefanov am 9 Mai 2014
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.
  1 Kommentar
Ben
Ben am 9 Mai 2014
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!

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