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:
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


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
Meta-heuristics
Choice Function
Ant Algorithm
Case-based Reasoning
…
Low level heuristics:


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different moving strategies,
constructive heuristics
…
Nam Pham
Hyper-heuristic Framework
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Graph Colouring Problem


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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
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Constructive hyper-heuristics
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Search for sequence of heuristics [Ross 2002]
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Each heuristic is applied for colouring one vertex
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Evaluation function is defined as the number of
required colours when applying heuristic sequence
Nam Pham
Graph Example
1
Heuristic 1 (H1)
Heuristic 2 (H2)
Heuristic 3 (H3)
2
8
3
7
4
6
5
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Search Space of Heuristic Sequences

We are looking for a heuristic sequence that
produces smallest number of used colours

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Decisions
H1
H2
H3
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Sequence
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1
2
3
Nam Pham
4
5
6
7
8
Ant Colony Hyper-heuristics
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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:

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

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
LD
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
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