Faculty Scheduling Using Genetic Algorithms

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Faculty Scheduling Using Genetic Algorithms

• By Kevin Soule
• April 17, 2006

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Problem Defined

• Many classes to schedule.
• Limited resources (professors, rooms ..).
• Unhappy professors, students.
• Successful solution may not exist.
• Very large search space.

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Search Space

• Assume a small problem of 10 courses, 5 rooms, 3
  professors and 10 time periods
• Search space becomes
• 150 choices for first class (5x3x10)
• 149 choices are then left for second, and so on
• Final number of total search space
• 150! / 140! Or 6.0 x 1023
• You can imagine a large problem would be huge

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Needed to Represent an Individual Class

• Class name
• Section number (multiplies of same class)
• Professor name
• Starting time
• Location
• Days of the week
• Hours of class time per week

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Inputs Required

• Courses to schedule-all sections
• Room availability and restrictions
• Professor availability and preferences

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Input Creation and Organization

• Random and Manually Entered
• Program created to handle each
• Data Stored in Three Integer Files
• Course
• Professor
• Room
• Random Input Data created based on actual
  values/trends noticed on college schedules

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Random Input Proportions Used

• Number of different courses ½ total number of
  sections offered
• Number of professors 1/5 total sections
• Number of rooms ½ total number of professors
• 50 chance a room can hold a given course
• 33 chance a professor has a preference on when
  they teach

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Course Input Data
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Professor Input Data
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Main Problems - Conflicts

• Room
• Certain rooms unavailable for certain classes
• (I.E. Computer lab needed and no computers in
  room)
• Professor
• Professor not trained to teach certain courses
• Time
• Some classes should not be taught at same time
• (Calculus 101 and CS 101)
• Combinations of the above
• Professor cant be in two places at once
• Rooms cant hold two classes at same time

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Minor Problems

• Professor Preferences
• No early/late classes
• Teach many of same class to limit prep time
• Doesnt like certain classes
• Wants to teach certain number/ Cant teach too
  many
• Student Needs
• Different sections of same class should be at
  different times
• Most classes in prime time of day

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Schedule Representation

• Each class stores 7 unique parameters
• A programming object is created
• Each schedule has potentially hundreds of classes
• An array of class objects is formed
• Each trial run will create a population of
  schedules
• An array of arrays is set up
• Usually about 50 schedules worth

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Determining a Good Schedule

• A list of constraints to our solution is decided
  up front
• These constraints are weighted on how important
  they are to the final solution
• Two basic constraint categories
• Hard constraints
• Soft constraints
• Hard constraints are impossible situations
• Soft constraints are usually preferences and
  annoying schedule quirks

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Comparing Schedules in Population

• Each created schedule is searched to find any
  failed constraints
• Each failed constraint found will give that
  schedule a weighted demerit value
• The sum of all demerits for each schedule is
  called its fitness.
• The fitness value can be used to compare
  schedules with one another

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GA Programming Steps

• Load in all input data
• Build initial population of schedules
• Hold tournaments to find good genetic material
• Creation of new schedule with crossover
  techniques
• Mutation of schedules to infuse new genetic
  material
• Replace tournament losers with newly created
  schedules.
• Hold next tournament and repeat until solved

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Genetic Programs Attempted

• Base program as explained (control)
• Base program with greedy procedure
• Ordered Greed Program
• Ordered Greed/Base Hybrid
• Mutation only

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Base with Greedy Procedure

• Greedier attempt at building the population
• Placing classes into the schedule is still
  random, but multiple random attempts are tried
  and only the best is placed
• Gives a much better initial population with only
  slightly more processing time

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Ordered Greed Program

• Instead of a population of schedules, a
  population of permutations is created instead
• To place each course into a schedule, lists of
  possible professors and viable rooms are created
  and methodically tested for every time slot
• Courses are only placed into the schedule once a
  location is found that breaks no hard constraints

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Ordered Greed Continued

• Since this is a population of permutations,
  regular crossovers can not be done
• Crossovers that generate new permutations were
  tried and tested amongst each other
• Partially-Matched
• Ordered
• Merging
• Mutations were also different- a small swap of
  values inside the permutation

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Hybrid Program

• Born out of the tendencies of Ordered Greed to
  solve all hard constraints, and the basic program
  doing better with most soft constraints
• Starts Ordered Greed
• Ends Base program

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Mutation Only Program

• Generational type program
• Mutation seemingly had such a powerful effect in
  the results of the other programs
• Discarding tournaments and crossover procedures
  altogether

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Optimizing Parameters

• Crossover (both base and OG)
• Population Size
• Tournament Size
• Mutation Rates (both base and OG)
• Greedy Parameter

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Final Comparison of Programs

• All five programs were then set up with best set
  of parameters
• Hundreds of trials were done comparing each of
  them on many sets of inputs.
• Results were a little misleading

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Summary of Final Results
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Possible Improvements

• Retest parameters for longer times with same sets
  of input data.
• Adding seniority of Faculty to the Mix
• Using more efficient pre-built GAs
• Such as GA-LIB
• Using Bit Streams to store schedules
• Inputting a real world example
• Fixing the sharing of resources problem

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Questions?

• Thanks for coming

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Hard Constraints

• Professor signed up for two classes at the same
  time
• Room scheduled for two classes at the same time
• Professor teaching a class they are not trained
  for
• Professor teaching more classes then their
  maximum load
• Room holding a class that it can not accommodate

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Soft Constraints

• Professor preferences for evening or morning
  classes
• Professor teaching both on same day
• Professor teaching class they do not wish to
  teach
• Professor teaching more or less credits then they
  wish
• Different sections of the same class being held
  the same time
• Different section of the same class being taught
  by different professors

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Build Initial Population of Schedules

• Decide on Random Build or Ordered Greed
• Random Build creates each schedule by randomly
  picking all needed information for every class
  with no regard to constraints
• Ordered Greed attempts to place classes into
  schedules only if they do not violate constraints
• Ordered Greed gives a much better initial
  population while Random Build is much quicker

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Tournaments

• Randomly pick a handful of schedules from the
  array
• Pick the two best and two worst from this
  selection
• Use the two best to create new schedules using
  crossover
• The two worst will be replaced with the newly
  created ones

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Crossover

• Method that takes parts from two schedules in
  order to create new ones, much like a child is
  formed by taking DNA pieces from both parents.
• Regular Crossover types
• Uniform
• One-point
• Two-point
• Ordered Greed Crossover types
• Partially-Matched
• Ordered
• Merging

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Mutations

• Regular mutations are needed on newly created
  schedules in order to introduce genetic diversity
• When mutation is done one class is randomly
  given a new room, professor, and time
• Experimentation was done to determine rate of
  mutation for both how often a schedule is
  mutated and how many classes of that schedule are
  changed