Ant Colony Hyper-heuristics for Graph Colouring

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# Ant Colony Hyper-heuristics for Graph Colouring - PowerPoint PPT Presentation

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

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
• Future works

Nam Pham

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
• 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
• 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

Heuristic 1 (H1)

Heuristic 2 (H2)

Heuristic 3 (H3)

1

2

8

3

7

4

6

5

Nam Pham

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 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-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-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-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
• 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

Nam Pham

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
• 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