For Robert Gu, real creativity most often came after a good night's sleep, just as he roused himself to wakefulness. That moment was such a reliable source of inspiration that when he was having problems with writing he would often go the pedestrian route in the evening, stock up his mind with the intransigencies of the moment ... and then the next morning, drowsing, review what he knew. There in the labile freshness of new consciousness, answers would drift into view.
I use a similar technique to get an insight into most difficult problems. During the evening, or several evenings in a row, I do a lot of background work on analyzing the problem, exploring its system aspects, trade-offs, dilemmas, etc. often, when I wake up in the morning, I go over my analysis again and discover a new idea that was not there before.
This experience is consistent with the earlier Lunch Talk video in my blog where neuroscience professor Vincent Walsh recommends to become obsessed with a problem in order to come up with a creative solution. I would add that system analysis techniques really help with getting obsessed in a right way, especially when you have to do it for an inter-disciplinary group of creative people.