This document was written by Liviu Lalescu. Fair use of this document is allowed/encouraged/expected.
Begin: 2007.
Last modified on: 26 December 2019.
Added on 19 January 2009: the implementation of the algorithm is good now, I changed it in 2008.
Some words about the algorithm:
FET uses a heuristic algorithm, placing the activities in turn, starting with the most difficult ones. If it cannot find a solution it points you to the potential impossible activities, so you can correct errors. The algorithm swaps activities recursively if that is possible in order to make space for a new activity, or, in extreme cases, backtracks and switches order of evaluation. The important code is in src/engine/generate.cpp. The algorithm mimics the operation of a human timetabler, I think.
When placing an activity, I choose the place with lowest number of conflicting activities and recursively replace them. I use a tabu list to avoid cycles.
The maximum depth (level) of recursion is 14.
The maximum number of recursive calls is 2*nInternalActivities (found practically - modified 18 Aug. 2007). I tried with variable number, more precisely the 2*(number of already placed activities+1). I am not sure about the results, it might be better with variable number, but not sure.
The recursion chooses only one variant from depth 5 (modified 15 Aug. 2007) above, then it returns.
How to respect the students gaps (possible in combination with early)? Compute the number of total hours per week for each subgroup, then when generating, the total span of lessons should not exceed the total number of hours per week for the subgroup. The span is computed differently if you have no gaps or if you have no gaps+early
Added on 16 Aug 2007, modified 22 Aug 2007:
The structure of the solution is an array of times[MAX_ACTIVITIES] and rooms[MAX_ACTIVITIES], I hope you understand why. I begin with unallocated. I sort the activities, most difficult ones first. Sorting is done in generate_pre.cpp. In generate_pre.cpp I also compute various matrices which are faster to use than the internal constraints list. Generation is recursive. Suppose we are at activity no. permutation[added_act] (added_act from 0 to gt.rules.nInternalActivities - permutation[i] keeps the activities in order, most difficult ones first, and this order will possibly change in allocation). We scan each slot and for each slot record the activities which conflict with permutation[added_act]. We then order them, the emptiest slots first. Then, for the first, second, ... last slot: unallocate the activities in this slot, place permutation[added_act] and try to place the remaining activities recursively with the same procedure. The max level of recursion is 14 (humans use 10, but I found that sometimes 14 is better) and the total number of calls for this routine, random_swap(act, level) is 2*nInternalActivities (found practically - might not be the best).
If I cannot place activity permutation[added_act] this way (the 2*nInternalActivities limit is reached), then I choose the best slot, place permutation[added_act] in this slot and pull out the other conflicting activities from this slot and add them to the list of unallocated activities. added_act might decrease this way. Now I keep track of old tried removals and avoid them (they are in the tabu list - with size tabu_size (nInternalActivities*nHoursPerWeek for now)) - to avoid cycles.
The routine random_swap will only search (recursively) the first (best) slot if level>=5. That is, we search at level 0 all slots, at level 1 the same, ..., at level 4 the same, at level 5 only the first (best) slot, at level 6 only the first (best) slot, etc., we reach level 13, then we go back to level 4 and choose the next slot, etc. This is to allow FET more liberty, I think. This trick was found practically to be good. It might not always be good.