teacher assignment program
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Teacher Assignment Program. Maria Lizarraga Project Defense Master of Computer Science Tuesday June 29, 2010 Department of Computer Science University of Colorado, Colorado Springs. Agenda. Introduction Background Information Solution Test Results Lessons Learned Future Research - PowerPoint PPT PresentationTRANSCRIPT
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Teacher Assignment Program
Maria LizarragaProject Defense
Master of Computer ScienceTuesday June 29, 2010
Department of Computer ScienceUniversity of Colorado, Colorado Springs
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Agenda Introduction Background Information Solution Test Results Lessons Learned Future Research Summary
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Introduction High School Timetabling Problem Scheduling Problem
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Scheduling Models
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School Timetabling Problem
Find: xijk (i = 1,….,m; j = 1,…,n; k= 1,…,p)
Where:
xijk = 0 or 1 (i = 1,…,m; j=1,…,n; k=1,…,p)
Such that:p
xijk = rij (i = 1,…,n; j=1,…,n)k=1
n
xijk = 1 (i = 1,…,m; k=1,…,p)j=1
m
xijk = 1 (j = 1,…,n; k=1,…,p)i=1
Scheduling Component - Class
Course
Teacher
Period
Objective Function: m n p
min wijkxijk i = 1 j = 1 k = 1
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Local SearchNeighborhood
Neighborhood Selection
0200400600800
100012001400160018002000
1 201 401 601 801 1001 1201 1401
Iteration
Ob
ec
tiv
e F
un
cti
on
Va
lue
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Genetic Algorithms
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Ant Colony Optimization
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Related Research Michael Clark, Martin Henz, Bruce Love, QuikFix A Repair-based Timetable
Solver, In Proceedings of the 7 th PATAT Conference, (2008) Defu Zhang, Yongkai Liu, Stephen C.H. Leung, A simulated annealing with a
new neighborhood based algorithm for high school timetabling problems, Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary
Computation, pp 381-386 Aldy Gunawan, K. M. Ng, H. L. Ong, A Genetic Algorithm for the Teacher
Assignment Problem for a University in Indonesia, Information and Management Sciences, Vol. 19 No. 1. pp 1-16, 2008
Djasli Djamarus, Ku Ruhana Ku-Mahamud, Heuristic Factors in Ant System Algorithm for Course Timetabling Problem, isda, pp.232-236, 2009 Ninth International Conference on Intelligent Systems Design and Applications,
2009
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Problem Definition Machine
Environment Flexible Flow Shop
Constraints Objective
Function total weight of all
violated constraints
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Solution Teacher Assignment Program
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Strategic Tabu Search Algorithm
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Neighborhood Selection
Barney PE Pebbles PE 9
Barney Health Betty PE 9
Barney Weights
Dino PE 9
Barney Fred PE 9
Barney Bamm Bamm
PE 9
Select class to swap Switch teacher with classes
within same period Switch with unassigned
teachers within same period
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Mutation
Tabu List
Mutation 1
Mutation 2
Mutation 3
Mutation 4
Mutation 5
New Period 1 Barney PE Pebbles PE 9
X Period 1 Barney PE 9 Pebbles PE
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Speed Test
#Teachers Time
Weight
#Iteration
s
5< 1 sec 0 29
10< 1 sec 0 381
25< 1 sec 0 334
500:00:0
3 0 497
600:00:0
3 0 226
700:00:0
3 0 165
800:00:0
6 0 241
900:00:0
8 0 212
1000:00:1
5 0 316
#Constrain
ts Time Weight
#Iteration
s
2 < 1 sec 0 60
5 < 1 sec 0 463
10 0:00:02 0 1844
15 0:00:04 0 2030
20 0:00:08 0 4486
24 0:00:32 0 16870
30 0:00:36 0 16562
36 0:01:51 30 38882
42 0:03:19 80 41515
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Random vs Strategic
Random vs StrategicQuality Comparison
1300300
33004200
1200200
24003300
13002300
010002000300040005000
1 2 3 4 5 6 7 8 9 10
Run
We
igh
t
Random Strategic
Random vs StrategicSpeed Comparison
0:00
0:28
0:57
1:26
1:55
2:24
2:52
3:21
1 2 3 4 5 6 7 8 9 10
Run
Min
ute
sRandom Strategic
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Tabu List Size
Strategic Tabu
Size Comparison
5 7 9Weight 20 10 20
# Iterations
29161
36773 43688
Time 0:29 0:29 0:34
# Violations 0.2 0.1 0.2
Random Tabu
Size Comparison
5 7 9Weight 1980 1910 1170
# Iterations 5551 3638 4187
Time 3:06 3:08 3:09
# Violations 4.5 4.7 3.6
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Equalized Weights
Iterations Strategic Neighborhood SelectionWeight Change Comparison
0
50000
100000
150000
1 2 3 4 5 6 7 8 9 10
Run
# Ite
ratio
ns
Unequal Weights Equal Weights
Iteration Random Neighborhood SelectionWeight Change Comparison
0
50000
100000
150000
1 2 3 4 5 6 7 8 9 10
Run
# Ite
ratio
ns
Unequal Weights Equal Weights
Strategic Neighborhood SelectionRandom Neighborhood Selection
Violations Random Neighborhood SelectionWeight Change Comparison
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10
Run
# V
iola
tio
ns
Unequal Weights Equal Weights
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Lessons Learned Application requirement versus
constraint Tailoring solution to problem Remove concept of hard and soft
constraints
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Further Research Tabu list for each period Dynamically changing the weights
when stuck in a local minimum Dynamically changing to Random
Neighborhood Selection when stuck in local minimum
Investigate how to have multiple course sections
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Summary Sensitive to the number of constraints Strategic Neighborhood selection
performs better than Random Neighborhood select, (speed and quality)
Size of Tabu List made little difference Equalizing weights can help escape
local minimum
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Questions
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Supplemental Slides
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Tabu Search Candidate Selection
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Simulated Annealing Candidate Selection Acceptance
Probability Functione (-/T) Where: = selectedNeighbor.OFV
– candidate.OFV
T = current temperature
Cool RateTn = a * Tn-1
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Neighborhood Examples