I heard that computation results can be very sensitive to choice of random number generator.
I wonder whether it is relevant to program own Mersenne-Twister or other pseudo-random routines to get a good number generator. Also, I don't see why I should not trust native or library generators as random.uniform() in numpy, rand() in C++. I understand that I can build generators on my own for distributions other than uniform (inverse repartition function methor, polar method). But is it evil to use one built-in generator for uniform sampling?
What is wrong with the default 'time' seed? Should one re-seed and how frequently in a code sample (and why)?
Maybe you have some good links on these topics!
--edit More precisely, I need random numbers for multistart optimization routines, and for uniform space sample to initialize some other optimization routine parameters. I also need random numbers for Monte Carlo methods (sensibility analysis). I hope the precisions help figure out the scope of question.