FINAL EXAM SCHEDULER FES

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FINAL EXAM SCHEDULER(FES)

• By
• Ersan ERSOY
• (Engineering Project)
• Advisor Assist.Prof.Dr. Ender ÖZCAN

• Department of Computer Engineering
• Faculty of Engineering Architecture
• Yeditepe University

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Outline

• Timetabling Problem
• Timetabling Markup Language (TTML)
• Genetic Algorithms (GAs)
• Implementation
• Experiments
• Conclusion Future Work

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Timetabling Problem

• Assignment of variables (courses, exams etc.) to
  some specific domains (time slots, rooms, etc)
  based on various constraints.
• NP-complete problem.
• Hard and soft constraints.

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Examination Timetabling

• Represented as (V, D, C)
• V contains variables (exams),
• D contains domains (time slots , rooms),
• C contains constraints.
• Constraint classifications
• Edges.
• Preset and exclusions.
• Ordering.
• Event-spread.
• Capacity.
• Aim in this project is to assign exams to time
  slots.

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Solution Approaches

• Human based techniques.
• Random search.
• Simulated annealing.
• Tabu search.
• Evolutionary algorithms.

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Timetabling Markup Language (TTML)

• Standard representation for timetabling problems.
• Based on XML and MathML
• Consists of three parts.
• Input-data.
• Output.
• Test-results.

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TTML (Cntd.)

• Input-data
• Author.
• Description.
• References.
• Variables.
• Domains.
• Constraints.
• Classifiers
• Hard
• Soft

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TTML (Cntd.)

• Classifiers
• Base
• Parent
• Projection
• Self
• Child
• Single

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TTML (Continues)

• Supports 11 different constraint functions.
• notsame
• nooverlap
• preset
• exclude
• ordering
• eventspr
• fullspr
• freespr
• chksum
• attrcomp
• resnoclash

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Genetic Algorithms (GAs)

• GAs were introduced by J. Holland.
• Member of Evolutionary Algorithms (EAs)
• Simply explained as
• Set i to 0 and randomly generate an initial
  population (P(i))
• Do until break criteria is satisfied
• Evaluate the fitness of each individual
• Select parents of the next generation from P(i)
  according to their fitness
• Produce new offspring by using crossover and
  mutation operators and put them into P(i1),set i
  to i1

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Components of GAs (Cntd.)

• Chromosomes.
• Gene.
• Population.
• Representation
• Binary encoding.
• Real value encoding.
• Initializing Population

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Components of GAs (Cntd.)

• Evaluating chromosomes
• Fitness function.
• Mate Selection.
• Fitness-based selection
• Rank-Based selection
• Tournament Selection

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Components of GAs (Cntd.)

• One-point Crossover

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Components of GAs (Cntd.)

• Two-point Crossover

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Components of GAs (Cntd.)

• Uniform Crossover

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Components of GAs (Cntd.)

• Mutation
• Randomly alters the values of genes of a
  chromosome after crossover.
• Replacement Strategy
• Trans-generational Genetic Algorithms.
• Steady-State Genetic Algorithms.
• Elitism

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Components of GAs (Cntd.)

• GA Parameters
• Crossover probability.
• Mutation probability.
• Population size.

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GAs (Cntd.)

• Memetic Algorithms (MAs)
• In GAs, crossover and mutation usually performs
  solutions near the local optima
• Memetic Algorithms (MAs) can be explained as
  hybridization of GA and local search algorithms.
• Gene in GAs is called meme in MAs.

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Implementation

• Three different programs are implemented.
• CONFETI generates examination problem data in
  TTML format.
• Final Exam Scheduler (FES) that takes problem
  input in TTML format and finds the optimum
  solution.
• FESViewer is implemented to view the output of
  FES

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Implementation (CONFETI)

• Java applet.
• Support generating TTML documents for examination
  timetabling problem.
• Consists
• Description
• Domain
• Variable
• Classifiers
• Students
• Curriculum
• Base Classifiers
• Constraints
• Capable of loading TTML documents

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Implementation (FES)

• Java application
• Solves examination problems.
• Deals with different types of constraints that
  can be converted to TTML form by CONFETI.

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FES

• Getting TTML Document and Basic Data Structures.
• Each course (variable) in TTML document stored in
  a class (Variable) that contains duration (length
  of the exam), number students, list of hard
  domain slots, list of soft domain slots.
• Hard domains are initialized according to hard
  preset and exclude constraints.
• Soft domains are initialized according to soft
  preset and exclude constraints.
• This class contains a function that returns
  random slots according to hard and soft domain
  for each course.

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FES

• Getting TTML Document and Basic Data Structures.
• Each student information, student id and courses
  that he takes, are stored in memory after reading
  from input in a array of array form with a length
  of student number.

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FES

• Getting TTML Document and Basic Data Structures..
• FES supports nine types of constraints that
  CONFETI supports. But it does not support every
  combination of these constraints. The set of
  constraints that FES generally does not support
  is
• Constraints with parent classifiers other than
  Students parent classifier.
• Constraints which take two base classifiers as
  arguments.
• For eventspr, constraints that have compare value
  other than lt .

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FES

• Getting TTML Document and Basic Data Structures..
• If a preset or exclude constraint is defined to a
  course than, modifications are implemented on the
  hard and soft domains of the courses.
• If two courses must have same slot, same slot
  references are given to them.

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FES

• Algorithm
• A Memetic algorthm is used.
• Representation
• Each meme contains assigned slot number of an
  exam.
• Evaluating chromosomes
• Fitness function
• 
  Where w i is the weight of the
  constraint ci.

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FES

• Algorithm
• Initializing Population
• Random
• With hill climbing.
• Mate Selection
• Fitness-based selection
• Rank based Selection
• Tournament Selection
• Crossover
• One-point
• Two-point
• Uniform

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FES

• Mutation
• Random
• Random Swap
• Hill Climbing
• Each constraint has an hill climbing function to
  improve its fitness except for eventspr and some
  combinations.

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FES

• Hill Climbing
• Pseudo code for hill climbing function of notsame
  
• If there exits a violation between course A and B
• Set counter to 0
• While counter is less than 10
• Get a random slot for B
• if violation is improved
• return
• Increment counter by one.
• Set counter to 0
• While counter is less than 10
• Get a random slot for A
• if violation is improved
• return
• Increment counter by one.

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FES

• Hill Climbing
• Two hill climbing algorithm is defined
• HCA1
• A chromosome is selected by using tournament
  selection. And hill climbing functions of all
  defined constraints is applied .

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FES

• Hill Climbing
• HCA2
• Select a chromosome by tournament selection
• Step1. Select a constraint
• Use hill climbing function to whole chromosome
• If individual is improved go to Step1.
• Step2. Select a constraint
• Use hill climbing function to a part of
  chromosome
• If individual is improved go to Step2.
• Step3. Select a constraint
• Use hill climbing function to one gene of
  chromosome
• If individual is improved go to Step3.

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FES

• Replacement strategy
• Steady-state
• Trans-generational
• Other Features User Interfaces
• GA parameters, operator types, weight of
  constraints can be entered.
• Any time, output ( examination schedule) can be
  viewed in student, department and faculty view
  and can be saved for examining later by FESViewer.

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Implementation(FESViewer)

• Java application.
• Displays the output of FES.

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Experiments

• Experimental data
• Yeditepe University, Faculty of Engineering and
  Architecture, 2004 second semester, final exam
  data are used in the experiments.It consists of
  443 courses, 1169 students
• Constraints
• No students must have two exams in one slot
  (hard).
• Students must have maximum 2 courses per day
  (hard).
• Each section of the courses has to be assigned on
  the same slot (Hard).
• Students have at least one free slot between two
  exams in a day (soft).
• Also there are many preset and exclude
  constraints (hard or soft).

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Experiments

• Experimental data
• Hard constraints have a weight value of one and
  soft constraints except for the fourth constraint
  have weight value of 0.01. Fourth constraints
  weight is 0.075.
• Constant parameters

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Experiments

• Variable parameters
• Total of 24 different configuration
• and 20 runs for each configuration is made.

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Experiments

• Results
• Results are grouped by the operator type to make
  compare between the types of each operator.

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Experiments

• Crossover

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Experiments

• Mutation

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Experiments

• Mate Selection

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Experiments

• Hill Climbing
• HCA1 with two-point crossover, random mutation,
  and tournament selection can be best
  configuration.

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Conclusion Future Work

• Experimental results show that hard constraints
  are easily solved. But few soft constraint
  violations remain.
• An early configuration is made for the algorithm
  by examining tests results
• In future, CONFETI and FES can be modified to
  support room assignments, and their constraints.

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Any Questions?