Algorithm for creating a school timetable

Question

I\'ve been wondering if there are known solutions for algorithm of creating a school timetable. Basically, it\'s about optimizing \"hour-dispersion\" (both in teachers and

Answer 1

My timetabling algorithm, implemented in FET (Free Timetabling Software, http://lalescu.ro/liviu/fet/ , a successful application):

The algorithm is heuristic. I named it "recursive swapping".

Input: a set of activities A_1...A_n and the constraints.

Output: a set of times TA_1...TA_n (the time slot of each activity. Rooms are excluded here, for simplicity). The algorithm must put each activity at a time slot, respecting constraints. Each TA_i is between 0 (T_1) and max_time_slots-1 (T_m).

Constraints:

C1) Basic: a list of pairs of activities which cannot be simultaneous (for instance, A_1 and A_2, because they have the same teacher or the same students);

C2) Lots of other constraints (excluded here, for simplicity).

The timetabling algorithm (which I named "recursive swapping"):

1. Sort activities, most difficult first. Not critical step, but speeds up the algorithm maybe 10 times or more.

2. Try to place each activity (A_i) in an allowed time slot, following the above order, one at a time. Search for an available slot (T_j) for A_i, in which this activity can be placed respecting the constraints. If more slots are available, choose a random one. If none is available, do recursive swapping:

   a. For each time slot T_j, consider what happens if you put A_i into T_j. There will be a list of other activities which don't agree with this move (for instance, activity A_k is on the same slot T_j and has the same teacher or same students as A_i). Keep a list of conflicting activities for each time slot T_j.

   b. Choose a slot (T_j) with lowest number of conflicting activities. Say the list of activities in this slot contains 3 activities: A_p, A_q, A_r.

   c. Place A_i at T_j and make A_p, A_q, A_r unallocated.

   d. Recursively try to place A_p, A_q, A_r (if the level of recursion is not too large, say 14, and if the total number of recursive calls counted since step 2) on A_i began is not too large, say 2*n), as in step 2).

   e. If successfully placed A_p, A_q, A_r, return with success, otherwise try other time slots (go to step 2 b) and choose the next best time slot).

   f. If all (or a reasonable number of) time slots were tried unsuccessfully, return without success.

   g. If we are at level 0, and we had no success in placing A_i, place it like in steps 2 b) and 2 c), but without recursion. We have now 3 - 1 = 2 more activities to place. Go to step 2) (some methods to avoid cycling are used here).