Can a MetaGA solve timetabling problems

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Can a Meta-GA solve timetabling problems?

• Christian Blum, Sebastião Correia, Olivia
  Rossi-Doria, Marko Snoek,Marco Dorigo (team
  leader),
• Ben Paechter (problem leader)

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Contents

• Introduction
• The timetabling problem
• Solution directions
• Our approach
• Preliminary results
• Conclusions and future research directions

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Introduction

• Background of participants
• Christian mathematics
• Marko technology management
• Olivia mathematics
• Sebastião physics
• Lets do timetabling!

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The timetabling problem

• Goal assignment of classes to rooms and
  timeslots,
• while respecting the hard constraints,
• and taking into consideration the soft
  constraints.

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Problem hardness

• NP-hard problem
• Problem is highly constrained
• Difficult to build feasible solutions

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Solution directions

• Direct representationgenotype is the solution
• Indirect representationgenotype ?
  phenotypephenotype is the solution

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Solution directions II

• Characteristics of direct representationcrossove
  r is more likely to be disruptivemost solutions
  are infeasible
• Characteristics of indirect representationneed
  timetable builder to construct solution

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Summer School Problem

• Data
• Classes (type of room required)
• Rooms (type, size)
• Timeslots (45 in a week)
• Students (class attendance)

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Summer School Problem

• Hard constraints
• Each class in a suitable room
• One class per room / timeslot
• Each student can follow all his / her classes
• Soft constraints
• Students should not have only 1 class / day
• Students should not have more than 2 classes in a
  row

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Our approach

• Indirect representation
• Toolbox of heuristics is given
• Use heuristics to build timetable step-by-step
• Let GA evolve which heuristics to use in every
  step

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Our approach II

• Individual

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Our approach III

• Choose next class to insert in timetablee.g.
  pick class with most students
• Choose which room to assigne.g. pick smallest
  possible room
• Choose timeslote.g. pick timeslot with most
  parallel events

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Our approach IV
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Preliminary results
(yet!)

• NO RESULTS

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Room for improvement

• Extend set of heuristics
• Use other assignment orders,e.g. choose
  timeslot, followed by event, and room
• Change assignment order during timetable building
• Apply local search

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Conclusions

• Advantage of methodadaptation to problem
  instances
• Disadvantage of methodphenotype -/-gt genotype
• Presented method is new in the field of
  timetabling
• Approach can be improved in various ways