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Ant Colony Hyper-heuristics for Graph Colouring. Nam Pham ASAP Group, Computer Science School University of Nottingham. Overview. Hyper-heuristic Framework Problem Description Hyper-heuristic design for the problem An ant colony hyper-heuristic approach and experimental results

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Ant Colony Hyper-heuristics for Graph Colouring


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ant colony hyper heuristics for graph colouring

Ant Colony Hyper-heuristics for Graph Colouring

Nam Pham

ASAP Group, Computer Science School

University of Nottingham

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

Nam Pham

hyper heuristic
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

Nam Pham

graph colouring problem
Graph Colouring Problem
  • Assignment of “colours” to vertices in a graph
  • Adjacent vertices have different colours
  • Objective: minimise the number of required colours

Nam Pham

hyper heuristic design
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

Nam Pham

graph example
Graph Example

Heuristic 1 (H1)

Heuristic 2 (H2)

Heuristic 3 (H3)

1

2

8

3

7

4

6

5

Nam Pham

search space of heuristic sequences
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

1

2

3

4

5

6

7

8

Nam Pham

ant colony hyper heuristics
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)

Nam Pham

ant colony hyper heuristics1
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)

Nam Pham

ant colony hyper heuristics2
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)

Nam Pham

ant colony hyper heuristics3
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)

Nam Pham

experiment
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

Nam Pham

results
Results

Nam Pham

future works
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

Nam Pham

reference
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.

Nam Pham