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Development of University Timetabling System By
Using Evolution Strategies and Simulated Annealing
Endi Wu
EDS PLM Solutions Troy, MI USA Endi.wu@ugs.com
Submitted to Dr. Chan-Jin Chung, LTU/MCS Department, in partial fulfillment of the requirements for MCS 7033 Collaborative Research Project II class in Fall 2001
1. System Input Format
There are two files needed to create for scheduling. One is teacher schedule file that includes time slots, room available, and teacher’s preference for the class. The other is student survey data that includes time preferred by student for classes. The structure of two files as follows:
Teacher schedule file:
T0 T1 T2 T
C0 *
C1 *
C2 *
C3 T
C4 T
Class taught time, * means can be taught at any time, otherwise, this class can be taught at only that specific time
Rooms available at one time slot
Time slots available
Student survey file:
0 C1 T
1 C1 T
2 C1 T
3 C1 T
4 C2 T
5 C3 T
6 C4 T
Class ID
Preferable Time
Student ID
2. Algorithm
Timetabling is the assignment of time slots to a set of events, subject to constraints on these assignments. The NP-complete classes and time slots that bring highest score is a constraint satisfaction problem after evaluating student preferable time. Here I introduce two algorithms with different kinds of constraints to optimize the score.
2.1 Evolutionary Algorithm, 1 plus 1 Basic algorithm is initialize one schedule, using this schedule to generate another schedule by random method, compare two schedule, higher score schedule will survive and generate next schedule until no generate can be produced. During the reproducing, a legal schedule needs to be found such that no room is expected to accommodate more than one class at a time. The constraints for this problem can be hard (strict) or generous.
2.1.1 Strict rule Strict constraints are usually constraints that physically cannot be violated. This includes events that must not overlap in time, such as: Class must be taught by the specified time appointed by professor One class taught by only one time
Algorithm
Schedule(parent)=Initialize schedule (init file )
For gen=1 to Maximum generation do Schedule(child) = generate(Schedule(parent)) While HardConstraint(Schedule(child) return ture If ( Score(Schedule(child) ) < Score(Schedule(parent)) ) Schedule(parent) = Schdule(child) End for
2.1.2 Generous rule Generous constraints are usually constraints that can be violated in certain range. Because sometime illegal schedule will be adjusted to good result
Algorithm
Schedule(parent) = Initialize schedule (init file )
For gen=1 to Maximum generation
Schedule(child)=generate(Schedule(parent))
if (GeneralConstraint(Schedule(child))
2.2.1 Strict rule
Algorithm
Initialize T
Generate random configuration X (^) old
WHILE T > T (^) min DO FOR i = 1 to Nc DO
generate new configuration, X (^) new
IF (! HighContraint(X (^) new ) ) IF (inRange) X (^) old = X (^) new ENDIF ELSE continues
ENDIF ELSE
calculate new score, E (^) new
calculate E = E (^) new – E (^) old IF E < 0 or random < prob = e - E/T^ THEN
X (^) old = X (^) new E (^) old = E (^) new END IF END FOR
reduce T END WHILE
2.2.2 Generous rule
Algorithm
Initialize T
Generate random configuration X (^) old
WHILE T > T (^) min DO FOR i = 1 to Nc DO
generate new configuration, X (^) new
IF (! HighContraint(X (^) new ) ) Break; ENDIF ELSE
calculate new score, E (^) new
calculate E = E (^) new – E (^) old IF E < 0 or random < prob = e - E/T^ THEN
X (^) old = X (^) new E (^) old = E (^) new END IF END FOR
reduce T END WHILE
3. Sample Result
Sample Result Include
Large number of classes
- EC Strict with 150 classes, 2760 preferable time 2. EC Generous with 150 classes, 2760 preferable time
- SA Strict with 150 classes, 2760 preferable time
- SA Generous with 150 classes, 2760 preferable time (Picture only)
Medium number of classes
- SA Strict with 150 classes, 1337 preferable time
- SA Generous with 150 classes, 1337 preferable time
- EC Strict with 150 classes, 1337 preferable time 8. EC Generous with 150 classes, 1337 preferable time (Picture only)
Small number of classes
- EC Strict with 2 classes, 43 preferable time 10. EC Generous with 2 classes, 43 preferable time
- SA Strict with 2 classes, 43 preferable time
- SA Generous with 2 classes, 43 preferable time (Picture, final class assignment using program and manpower)
Class Assignment using program:
- EC Strict with 2 classes, 43 preferable time Result:
C0 T C1 T Score: 20
2. EC Generous with 2 classes, 43 preferable time Result:
C0 T C1 T Score: 20
- SA Strict with 2 classes, 43 preferable time Result:
C0 T C1 T Score: 20
- SA Generous with 2 classes, 43 preferable time Result:
C0 T C1 T Score: 20
Class assignment using manual calculation
C0 C
T0 T0 6+5 = T0 T1 6+10= T0 T2 6+7= T1 T0 5+5= T1 T1 5+10= T1 T2 5+7 = T2 T0 10+5= T2 T1 10+10= T2 T2 10+7=
So result:
C0 T C1 T Maximum Score = 20
4. Summary Results 1. Evolution Strategies (ES) with 1/5 rule performs better than Simulated Annealing (SA) according to the graph result from large to medium size of classes. 2. Generous rule is approach to handle illegal schedules, which works fine with both ES and SA. 3. ES with Generous rule once gave the best result ever found before while I was testing the system. For 150 classes, it gave about 460.
