I have an existing given schedule for a hospital department. I use supervised learning from historical data to predict the reservation durations providing determined process times. A requirement is not to change the original schedule 'too much'. So I will include a cost in respect to time for distance from the original schedule. I believe a local search approach (Tabu, SA, GA) will work well, where I always start from the original schedule. Are there any other algorithms or approaches that may better suit this problem?