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)8

1 2

7

6

4

3

5

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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

1 2 3 4 5 6 7 8

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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)

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)

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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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ResultsLD LCD SD Ant Algorithm HH Best known

Car91 37 35 31 29 28

Car92 32 33 33 29 28

Ear83 26 25 23 22 22

Hec92 19 20 19 17 17

Kfu93 20 21 20 19 19

Lse91 17 18 17 17 17

Pur93 36 40 35 32 35

Rye93 22 23 22 21 21

Sta83 13 13 13 13 13

Tre92 23 26 23 20 20

Uta92 32 33 32 30 30

Ute92 10 10 10 10 10

Yor83 22 24 22 19 19

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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.