1. The Course Timetabling Problem Presented by Ben Paechter Napier University

2. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 2 Introduction In order to produce the timetable for a University, we have to place the classes into: Timeslots (e.g. Wednesday 3.00-4.00pm) Rooms (e.g. Room 115) Let’s assume people (students, lecturers) are already assigned.

3. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 3 Goal We want to produce: Feasible Timetables Good Timetables

4. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 4 Feasible Timetables Every person can attend every class. Not at two classes at once Travel time OK Time for lunch, etc Each class is assigned a suitable room Big enough Right equipment Disabled access, etc

5. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 5 Good Timetables People and the institution like the timetable. Efficient use of rooms Minimal movement Not too many classes in a row Lecturers have days with no teaching No large gaps in a day Unpopular times avoided

6. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 6 Size of the Problem A typical institution (Napier University) has 2000 classes 200 rooms 45 timeslots Number of different timetables is (200*45) 2000 – about 10 8000 The vast majority of these are infeasible.

7. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 7 Summer School Problem Scaled down (but still big) You must find a good feasible timetable in a short amount of time. Feasible means Students don’t have any clashes Rooms are big enough and of the right type Best means: Minimum occurrences of three classes in a row Minimum occurrences of a single class in a day

8. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 8 Ways you might solve it: Direct Representation Each event has a timeslot and room encoded in the chromosome Might have problems with the large number of infeasible timetables

9. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 9 Ways you might solve it: Indirect Representation The chromosome tells us something about how to build the timetable. There is a separate timetable builder parameterised by the chromosome. Parameters might be: A suggested time (and room?) for each class The heuristics to use at various stages of the build The order of considering the classes

10. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 10 Other ways you might solve it: Decreasing Universe Assume an infinite number of rooms and events Many more timetables are feasible Gradually reduce the size of the universe Graph Theory E.g. find sets of things that can happen at the same time

11. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 11 Ways you might solve it: Something Else It doesn’t matter so long as it works!

12. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 12 You will be given A windows program to produce (text based) problem file instances of varying hardness. Each instance has at least one perfect solution. A windows program to check each (text based) problem solution. More detailed instructions about the problem.

13. Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 13 You will produce A program (Windows or Linux) that takes the text input file and produces the text output file Comments on what your program seems to be good at, and what it seems not so good at Ideas for further research