I\'m currently working on a website that will allow students from my university to automatically generate valid schedules based on the courses they\'d like to take.
Scheduling is a very famous constraint satisfaction problem that is generally NP-Complete. A lot of work has been done on the subject, even in the same context as you: Solving the University Class Scheduling Problem Using Advanced ILP Techniques. There are even textbooks on the subject.
People have taken many approaches, including:
You need to reduce your problem-space and complexity. Make as many assumptions as possible (max amount of classes, block based timing, ect). There is no silver bullet for this problem but it should be possible to find a near-optimal solution.
Some semi-recent publications: