The Course Timetabling Problem

Presented by Ben PaechterNapier University

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.

Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 3

Goal

We want to produce:

Feasible Timetables Good Timetables

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

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

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 108000

The vast majority of these are infeasible.

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

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

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 classThe heuristics to use at various stages of the

buildThe order of considering the classes

Course Timetabling by Ben Paechter, Napier University, for the EvoNet Summer School 2001 10

Other ways you might solve it:

Decreasing UniverseAssume an infinite number of rooms and

eventsMany more timetables are feasibleGradually reduce the size of the universe

Graph TheoryE.g. find sets of things that can happen at

the same time

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!

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.

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