Ant Colony Hyperheuristics for Graph Colouring

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Ant Colony Hyper-heuristics for Graph Colouring

• Nam Pham
• ASAP Group, Computer Science School
• University of Nottingham

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Overview

• Hyper-heuristic Framework
• Problem Description
• Hyper-heuristic design for the problem
• An ant colony hyper-heuristic approach and
  experimental results
• Future works

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Hyper-heuristic

• Heuristics that choose heuristics
• High level heuristics
• Meta-heuristics
• Choice Function
• Ant Algorithm
• Case-based Reasoning
• Low level heuristics
• different moving strategies,
• constructive heuristics

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Hyper-heuristic Framework
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Graph Colouring Problem

• Assignment of colours to vertices in a graph
• Adjacent vertices have different colours
• Objective minimise the number of required
  colours

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Hyper-heuristic Design

• Constructive hyper-heuristics
• Search for sequence of heuristics Ross 2002
• Each heuristic is applied for colouring one
  vertex
• Evaluation function is defined as the number of
  required colours when applying heuristic sequence

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Graph Example

• 
  Heuristic 1 (H1)
• 
  Heuristic 2 (H2)
• 
  Heuristic 3 (H3)

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Search Space of Heuristic Sequences

• We are looking for a heuristic sequence that
  produces smallest number of used colours
• Decisions
• H 1
• H 2
• H 3
• Sequence

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2
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Ant Colony Hyper-heuristics

• Ant algorithms are well-known if used as low
  level heuristics
• There are only two papers using ant algorithms as
  hyper-heuristics so far (reference at the end)

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Ant Colony Hyper-heuristics

• Ant algorithm is well-known if used as a low
  level heuristic
• There are only two papers using ant algorithm as
  hyper-heuristic so far (reference at the end)

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Ant Colony Hyper-heuristics

• Ant algorithm is well-known if used as a low
  level heuristic
• There are only two papers using ant algorithm as
  hyper-heuristic so far (reference at the end)

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Ant Colony Hyper-heuristics

• Ant algorithm is well-known if used as a low
  level heuristic
• There are only two papers using ant algorithm as
  hyper-heuristic so far (reference at the end)

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Experiment

• Heuristics employed include
• Largest Degree First (LD)
• Largest Colour Degree First (LCD)
• Least Saturation Degree First (SD)
• University of Toronto Benchmark Data
  ftp//ftp.mie.utoronto.ca/pub/carter/testprob

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Results
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Future works

• Compare ant colony hyper-heuristic with other
  population based hyper-heuristics evolutionary
  algorithms, genetic algorithm, swarm
  intelligence
• Do research on characteristics of heuristic
  search space
• Expand to exam timetabling problem

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Reference

• Burke, E.K., Kendall, G., Landa Silva, J.D.,
  O'Brien, R.F.J., Soubeiga, E. An ant algorithm
  hyperheuristic for the project presentation
  scheduling problem.
• Cuesta-Cañada, A., Garrido, L., Terashima-Marín,
  H. Building Hyper-heuristics Through Ant Colony
  Optimization for the 2D Bin Packing Problem.