Constraint Handling

[rrraaaccc]

Hello and huge thank for your development of this great library.
I am just starting to use it for CFD Parameter optimization.

I was wondering if you have a best practice for handling constraints in the optimization loop.

Specifically we have to deal with two different cases. The first case is simply non convergence of the simulation and the second is a constraint violation in the cost function.

I would be very happy about any tips how to handle this as good as possible.

Many thanks and best regards
Nils

[nomuramasahir0]

Hello Nils,
thank you for your interest.

It depends on the type of constraints.
In our library, handling of box constraints is already implemented.
For example, the default CMA-ES implements resampling and repair, while CatCMA-ESwM uses a penalty method.

On the other hand, handling of more complex constraints is currently not supported.
One general and relatively simple approach is the one introduced in DX-NES-IC (Eq. 14).
In this method, when comparing two infeasible solutions, a preference is given to the solution with the smaller z-norm (||z||), i.e., Mahalanobis distance, which helps stabilize the distribution update.
When implementing this, the function value of an infeasible solution can be defined, for example, as (maximum function value among feasible solutions) + ||z||.

Constraint handling is something we would like to improve in the future, but there is no concrete timeline at the moment.

[nomuramasahir0]

@ha-mano if you have anything to add, please feel free!