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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