I have a bounded non-convex function in 10-dimensional space. The function is quasi-smooth, you can imagine a histogram, here is an illustration, it just shows the idea and not related to my particular function:
The function value is obtained by time consuming simulation (it takes about 10 seconds). Obviously if I want compute gradients, I need to approximate them by difference quotients. If you need more details about the function, I might be able to say more.
I have read the article of L.M. Rios and N.V. Sahinidis, Derivative-free optimization: A review of algorithms and comparison of software implementations
So I've tried all of TOMLAB solvers, proposed in article and also MCS method, also mentioned in the article as one of the best. But neither of them could not overperform simple Brent method accompanied by hand picked initial guess (well, I hardly believe I can produce such great guesses).
I've also heard about surrogate modeling, is it worth trying?
So which other global optimization methods should I consider?