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

One of my half-term assignments was an genetic-algorithm school table generation.

Whole table is one "organism". There were some changes and caveats to the generic genetic algorithms approach:

• Rules were made for "illegal tables": two classes in the same classroom, one teacher teaching two groups at the same time etc. These mutations were deemed lethal immediately and a new "organism" was sprouted in place of the "deceased" immediately. The initial one was generated by a series of random tries to get a legal (if senseless) one. Lethal mutation wasn't counted towards count of mutations in iteration.

• "Exchange" mutations were much more common than "Modify" mutations. Changes were only between parts of the gene that made sense - no substituting a teacher with a classroom.

• Small bonuses were assigned for bundling certain 2 hours together, for assigning same generic classroom in sequence for the same group, for keeping teacher's work hours and class' load continuous. Moderate bonuses were assigned for giving correct classrooms for given subject, keeping class hours within bonds (morning or afternoon), and such. Big bonuses were for assigning correct number of given subject, given workload for a teacher etc.

• Teachers could create their workload schedules of "want to work then", "okay to work then", "doesn't like to work then", "can't work then", with proper weights assigned. Whole 24h were legal work hours except night time was very undesired.

• The weight function... oh yeah. The weight function was huge, monstrous product (as in multiplication) of weights assigned to selected features and properties. It was extremely steep, one property easily able to change it by an order of magnitude up or down - and there were hundreds or thousands of properties in one organism. This resulted in absolutely HUGE numbers as the weights, and as a direct result, need to use a bignum library (gmp) to perform the calculations. For a small testcase of some 10 groups, 10 teachers and 10 classrooms, the initial set started with note of 10^-200something and finished with 10^+300something. It was totally inefficient when it was more flat. Also, the values grew a lot wider distance with bigger "schools".

• Computation time wise, there was little difference between a small population (100) over a long time and a big population (10k+) over less generations. The computation over the same time produced about the same quality.

• The calculation (on some 1GHz CPU) would take some 1h to stabilize near 10^+300, generating schedules that looked quite nice, for said 10x10x10 test case.

• The problem is easily paralellizable by providing networking facility that would exchange best specimens between computers running the computation.

The resulting program never saw daylight outside getting me a good grade for the semester. It showed some promise but I never got enough motivation to add any GUI and make it usable to general public.