It seems the amount of change was a large problem. Was it attempted to minimize either number of student start times changed or total delta of minutes changed? Was it discussed how this could be done incrementally to slowly move towards more optimal start times?
Yes incremental changes looks like a good solution. I think it is hard to do it with the delta minutes changed, as you could have dramatic consequences on the costs (the ripples on the transportation systems can be quite surprising, in that changing the time of one school can have a big impact on the number of buses needed). As to the number of student start time, the main question is how do you choose the schools that change first? How do you make sure that your changes are not interrupted in the middle for political reasons, which would be unfair for the first schools and maybe the whole system.
Also, it is an algorithmic challenge to find a "path" of good solutions that go step by step to the good final start times.
