This problem occurs when I use the Kriging and QMC methods in the RBDO module:
" Starting Quantile Monte Carlo (QMC) optimization approach…
Initial point is not feasible. Searching for a new one by random uniform sample on the search space
Warning: No feasible point could be found after 100*nvars^2 trials "
At this time, Kriging uses the Gaussian kernel function.
When I change it to Matern-5_2, I get the correct answer.
Why does this happen?
The warning you get is due to the optimization solver that is used (constrained (1+1)-CMA-ES). It requires a feasible starting point. When the initial design (either user provided, or the default one) is not feasible, a new one is sought by randomly sampling the design space. If no feasible design is found after a predefined number of samples are tried, the warning is printed but the algorithm contiues.
If it works when you switch from Gaussian to Matérn kernel, it may be that the Kriging model with the Gaussian kernel is not accurate enoough to capture the failure domain. I would suggest, you start with an initial experimental design of larger size.
Note that you can also change your solver to something that does not require an initial feasible design. While this will remove the warning, it does not solve your problem if the underlying surrogate model is not accurate.
Thank you @moustapha . It is really useful.
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