Made more changes to the method, it's now even easier than before. Also updated page text to include useful information.
I've recently discovered a web site dedicated to global optimization: http://infinity77.net/global_optimization/
Now I'm using its guidelines. My test corpus includes 49 functions which can be successfully optimized by the method in 100 attempts, up to 2000 iterations each. This is only about 25% of all available functions, but I've included mostly harder functions into my test corpus. So, if I'm correct, my method can be considered as very robust (for stochastic method), and it can be called a global optimization method (which I was hesitant to do before).
Beside that, the method now also successfully optimizes 30-dimensional problems. Previously I thought it can't do that, but after adding dependence of the FanSize parameter on the number of dimensions, the thing just works.