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

This problem is tougher than it seems.

As others have alluded to, this is a NP-complete problem, but let's analyse what that means.

Basically, it means you have to look at all possible combinations.

But "look at" doesn't tell you much what you need to do.

Generating all possible combinations is easy. It might produce a huge amount of data, but you shouldn't have much problems understanding the concepts of this part of the problem.

The second problem is the one of judging whether a given possible combination is good, bad, or better than the previous "good" solution.

For this you need more than just "is it a possible solution".

For instance, is the same teacher working 5 days a week for X weeks straight? Even if that is a working solution, it might not be a better solution than alternating between two people so that each teacher does one week each. Oh, you didn't think about that? Remember, this is people you're dealing with, not just a resource allocation problem.

Even if one teacher could work full-time for 16 weeks straight, that might be a sub-optimal solution compared to a solution where you try to alternate between teachers, and this kind of balancing is very hard to build into software.

To summarize, producing a good solution to this problem will be worth a lot, to many many people. Hence, it's not an easy problem to break down and solve. Be prepared to stake out some goals that aren't 100% and calling them "good enough".

Answer 2

Genetic algorithms are often used for such scheduling.

Found this example (Making Class Schedule Using Genetic Algorithm) which matches your requirement pretty well.

Answer 3

This paper describes the school timetable problem and their approach to the algorithm pretty well: "The Development of SYLLABUS—An Interactive, Constraint-Based Scheduler for Schools and Colleges."[PDF]

The author informs me the SYLLABUS software is still being used/developed here: http://www.scientia.com/uk/

Answer 4

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.

Answer 5

I have designed commercial algorithms for both class timetabling and examination timetabling. For the first I used integer programming; for the second a heuristic based on maximizing an objective function by choosing slot swaps, very similar to the original manual process that had been evolved. They main things in getting such solutions accepted are the ability to represent all the real-world constraints; and for human timetablers to not be able to see ways to improve the solution. In the end the algorithmic part was quite straightforward and easy to implement compared with the preparation of the databases, the user interface, ability to report on statistics like room utilization, user education and so on.

Answer 6

The International Timetabling Competition 2007 had a lesson scheduling track and exam scheduling track. Many researchers participated in that competition. Lots of heuristics and metaheuristics were tried, but in the end the local search metaheuristics (such as Tabu Search and Simulated Annealing) clearly beat other algorithms (such as genetic algorithms).

Take a look at the 2 open source frameworks used by some of the finalists:

• JBoss OptaPlanner (Java, open source)
• Unitime (Java, open source) - more for universities