Multi-Objective Hyper-heuristics and their Application to Water Distribution Network Design

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University of Exeter

College of Engineering, Mathematics and Physical Sciences









Multi
-
Objective Hyper
-
heuristics

and their Application to

Water Distribution Network Design



Kent

M
c
Clymont


September 2012









Supervised by Dr. Edward C. Keedwell and Prof. Dragan Savi
ć


Submitted by Kent M
c
Clymont to the

University of Exeter as a thesis

for the degree of Doctor of
Philosophy in Computer Science, September 2012.

This the
sis

is available for Library use on the understanding that it is copyright material and that no
quotation from the thesis may be published without proper acknowledgement.

I certify that all material in this thesis which is not my own work has been identified
and that no material
has previously been submitted and approved for the award of a degree by this or any other University.




(signature) ….……………………....................................



Abstract


2


Abstract


Hyper
-
heuristics is a new field of optimisation which has recently emerged and is receiving
growing exposure in the research community and literature. Hyper
-
heuristics are optimisation methods
which are designed with a high level of abstraction from any on
e specific problem or class of problems
and therefore are more generally applicable than specialised meta
-
heuristic and heuristic methods. Instead
of being designed to solve a specific real
-
world problem, hyper
-
heuristics are designed to solve the
problem
of heuristic generation and selection. As such, hyper
-
heuristics can be thought of as methods for
optimising the operations of an optimisation process which finds good solutions to a problem as a
by
-
product
. This approach has been shown to be very
e
ffectiv
e and in some cases provides improvement in
search performance as well as reducing the burden
associated with
tailoring meta
-
heuristics

which is
often
required when
solving new problems.

In this thesis, the hypothesis that

hyper
-
heuristics can be competiti
vely applied to real
-
world multi
-
objective optimisation problems such as the wa
ter distribution design problem is tested. Although many
single
-
objective hyper
-
heuristics have been proposed in the literature, only a few multi
-
objective methods
have been pro
posed. This thesis e
xplores two different novel mult
i
-
objective hyper
-
heuristics: one
designed for generating new specialised heuristics; and one designed for solving the online selection of
heuristics. Firstly, the behaviour of a set of heuristics is expl
ored to create a base understanding of
different heuristic behavioural traits in order to better understand the hyper
-
heuristic behaviours and
dynamics later in the study. Both approaches are tested on a range of benchmark optimisation problems
and finally

applied to real
-
world instances of the water distribution network design problem where the
selective hyper
-
heuristics is demonstrated as being very effective at solving this difficult problem.
Furthermore, the thesis demonstrates how heuristic selection c
an be improved by incorporating a greater
level of information about heuristic performance, namely the historical joint performance of different
heuristics, and shows that exploiting this sequencing information in heuristic selection can produce highly
com
petitive results.



Abstract


3





I would like to thank my supervisors Dr. Edward Keedwell and Professor
Dragan Savi
ć

for their continued patience and the support and guidance that
they have given me throughout my PhD
;

for which I will always be very
grateful.

I would also like to thank Mark Randall
-
Smith who provided an
invaluable real
-
world perspective.

Thank you also to
Prof. Sanja Petrovic and
Dr Guangtao Fu

for kindly agreeing to be my examiners
and
their valueable
comments and considered corrrections.

I w
ould especially like to thank Rosalyn for without whom I would not have
had the courage to embark on this expedition
.
Thank you.

Thank you to my
parents,
family and friends for t
heir guidance and amity,

and for being there at every celebration along the way. A special thanks goes
to
Andy,
Carlos,
David
, Elizabeth
,
Jacqueline,
Maryam,
Max
, P
hilip

and

Zena

who
were

the spark for so many new ideas and to the Exe
-
calibre
Drago
n Boat club who kept me reaching
, all the way to the finish line.




In honour of Professor Peter Brown who

opened to me the doors to academia.



Abstract


4











“We can do better, and we must do better, and we will do better!”

President
Josiah Edward

Jed


Bartlet



Contents


5


Contents


Abstract

................................
................................
................................
................................
.............

2

Contents

................................
................................
................................
................................
............

5

List of Tables

................................
................................
................................
................................
....

9

List of Figures

................................
................................
................................
................................
.

10

Publications

................................
................................
................................
................................
.....

17

Chapter 1: Introduction

................................
................................
................................
...................

19

1.1

Aims

................................
................................
................................
................................
.

21

1.2

Novelties

................................
................................
................................
..........................

21

1.3

Thesis Structure

................................
................................
................................
................

22

Chapter 2: Background

................................
................................
................................
...................

24

2.1

Water Distribution Networks and Design

................................
................................
........

24

2.2

Discolouration

................................
................................
................................
..................

25

2.2.1

Causes of Discolouration

................................
................................
.........................

26

2.2.2

Modelling Discolouration

................................
................................
........................

27

2.2.3

Applications of Discolouration Propensity Modelling

................................
............

28

2.3

Optimisation

................................
................................
................................
.....................

29

2.4

Heuristi
c Methods

................................
................................
................................
............

30

2.4.1

Meta
-
heuristics

................................
................................
................................
........

31

2.4.2

Evolutionary Algorithms

................................
................................
.........................

32

2.5

Multi
-
objective Optimisation

................................
................................
...........................

35

2.5.1

Pareto Optimality
................................
................................
................................
.....

36

2.5.2

Multi
-
objective Evolutionary Algorithms

................................
...............................

38

2.6

Meta
-
level Optimisation

................................
................................
................................
...

38

2.6.1

Adaptive Methods

................................
................................
................................
...

39

2.6.2

Hyper
-
heuristics

................................
................................
................................
......

40

2.6.3

Selective Hyper
-
heuristics

................................
................................
.......................

44

2.6.4

Hyper
-
heuristics Summary

................................
................................
......................

49

2.6.5

Multi
-
method Algorithms

................................
................................
........................

50

2.6.6

Memetic Algorithms

................................
................................
................................

51

Contents


6

2.7

WDN Design Optimisation

................................
................................
..............................

52

2.7.1

Approaches to Solving the WDN Design Problem

................................
.................

53

2.8

Conclusion

................................
................................
................................
.......................

54

Chapter 3: Ana
lysing Heuristics
................................
................................
................................
......

56

3.1

Heuristic Performance

................................
................................
................................
......

57

3.1.1

Variance between Heuristics

................................
................................
...................

57

3.1.2

Variance in Range

................................
................................
................................
...

60

3.1.
3

Variance between Problems

................................
................................
....................

61

3.1.4

Summary

................................
................................
................................
.................

62

3.2

Heuristics from Evolutionary Computation

................................
................................
.....

63

3.2.1

Constructive Heuristics

................................
................................
...........................

63

3.2.2

Perturbing Heuristics

................................
................................
...............................

63

3.3

Biaxial Box Plot

................................
................................
................................
...............

69

3.3.1

Existing Visualisation Methods

................................
................................
...............

69

3.3.2

The Biaxial Box Plot Visualisation

................................
................................
.........

71

3.3.3

Ordered Trial Rank

................................
................................
................................
..

73

3.4

Experimental Setup

................................
................................
................................
..........

75

3.4.1

Quality Measures for Comparison

................................
................................
...........

75

3.4.2

Figures for Comparison

................................
................................
...........................

75

3.4.3

Heuristics

................................
................................
................................
.................

76

3.4.4

Benchmark Problems

................................
................................
...............................

76

3.5

Results

................................
................................
................................
..............................

77

3.5.1

Generational Distance Results

................................
................................
.................

77

3.5.2

Hypervolume Results

................................
................................
..............................

80

3.5.3

Final Generation Distributions

................................
................................
................

82

3.5.4

Performance Trends

................................
................................
................................
.

83

3.5.5

Summary of Novel Heuristics’ Performance

................................
...........................

83

3.5.6

Mean and Attraction Heuristics

................................
................................
...............

83

3.5.7

Uniform and Gaussian Heuristics

................................
................................
............

83

3.5.8

Variance across Problems

................................
................................
........................

86

3.5.9

Variance between Phases
................................
................................
.........................

86

3.6

Conclusion

................................
................................
................................
.......................

87

Chapter 4: Generative Hyper
-
heuristics

................................
................................
..........................

89

Contents


7

4.1

Optimal Heuristics

................................
................................
................................
...........

91

4.1.1

Mutation Perturbation Distribution
................................
................................
..........

92

4.2

Method

................................
................................
................................
.............................

94

4.2.1

Generative Framework

................................
................................
............................

94

4.2.2

Optimisation Method

................................
................................
...............................

95

4.3

Experiment 1: Single
-
Objective Approach

................................
................................
....

102

4.3.1

Experimental Setup

................................
................................
...............................

103

4.3.2

Tests and Results

................................
................................
................................
...

103

4.3.3

Summary

................................
................................
................................
...............

126

4.4

Experiment 2: Multi
-
Objective Approach

................................
................................
......

128

4.4.1

Experimental Setup

................................
................................
...............................

128

4.4.2

Results

................................
................................
................................
...................

131

4.5

Conclusion

................................
................................
................................
.....................

145

Chapter 5: Selective Hyper
-
heuristic

................................
................................
............................

147

5.1

Modes of Operation

................................
................................
................................
........

148

5.2

Evaluating Heuristic Performance

................................
................................
..................

149

5.2.1

Existing Performance Measures

................................
................................
............

150

5.2.2

Novel Performance Measures

................................
................................
................

152

5.2.3

Comparing Performance Measures
................................
................................
........

156

5.3

Heuristic Selection Mechanisms

................................
................................
....................

182

5.3.1

Deterministic Methods

................................
................................
..........................

182

5.3.2

Learning Methods

................................
................................
................................
..

183

5.3.
3

Proposed Selection Mechanism: Markov
-
chain Hyper
-
heuristic (MCHH)

...........

185

5.3.4

Comparing selection mechanisms

................................
................................
.........

191

5.4

Conclusion

................................
................................
................................
.....................

208

5.4.1

Heuristic Performance Measures

................................
................................
...........

208

5.4.2

Heuristic Selection Mechanisms
................................
................................
............

209

Chapter 6: Application

................................
................................
................................
..................

211

6.1

Method

................................
................................
................................
...........................

212

6.1.1

Multi
-
objective WDN Design Problem

................................
................................
.

212

6.2

Experimental Setup

................................
................................
................................
........

213

6.2.1

Experimental Data

................................
................................
................................
.

213

6.2.2

Optimisers

................................
................................
................................
.............

214

Contents


8

6.2.3

Performance Measure

................................
................................
............................

216

6.
3

Results

................................
................................
................................
............................

216

6.3.1

The MCHH on WDN Problems

................................
................................
............

217

6.3.2

Discolouration Propensity in WDN Problems

................................
.......................

220

6.4

Conclusion

................................
................................
................................
.....................

222

Chapter 7: C
onclusion

................................
................................
................................
...................

224

7.1

Aims and Achievements

................................
................................
................................
.

224

7.1.1

Variability of Heuristic Performance

................................
................................
.....

224

7.1.2

Multi
-
objective Generative Hyper
-
heuristic

................................
..........................

225

7.1.3

Multi
-
objective Online Selective Hyper
-
heuristic

................................
.................

226

7.1.4

Discolouration Propensity

................................
................................
.....................

227

Chapter 8: Future Work
................................
................................
................................
.................

229

8.1

Classifications

................................
................................
................................
................

229

8.2

Heur
istic Understanding

................................
................................
................................
.

229

8.3

Generative Framework

................................
................................
................................
...

230

8.4

Heuristic Selection

................................
................................
................................
.........

230

8.5

Sequence Based Approaches

................................
................................
..........................

231

Bibliography

................................
................................
................................
................................
..

232





List of Tables


9


List of Tables


Table 1. Parameter settings for the DTLZ, WFG and LZ09
benchmark problems

................................
....

76

Table 2. GHH objective results for the single
-
parameter, single
-
objective linear problems used for testing.
The values range from 0 to 2 where 0 is the best value and 2 the worst. Each objective value is
given with the standard deviation of individual evolved distributions objective values used to
calculate the averaged objective values.

................................
................................
........................

108

Table 3. Single
-
parameter, single
-
objective cosine test problem results.

................................
.................

112

Table 4. Single
-
parameter, single
-
objective cosine problem with central optima for training.

................

115

Table 5. Single
-
parameter, single
-
objective cosine problem with varying wavelengths.

.........................

117

Table 6. S
ingle
-
parameter, single
-
objective cosine problem with central optima for training.

................

118

Table 7. Single
-
parameter, single
-
objectiv
e cosine problem with central optima for training.

................

121

Table 8. Single
-
parameter, single
-
objective cosine problem with central op
tima for training.

................

123

Table 9. Parameter Settings for the DTLZ Benchmark Problems

................................
............................

157

Table 10. Parameter Settings for the DTLZ, WFG and LZ09 Benchmark Problems

...............................

172

Table 11. Results from two meta
-
heuristics and two MCHH variants on the six test networks


best result
shown in
bold
. Each algorithm is broken down into the best value obtained for each of the three
objectives on each net
work; Cost, Discolouration Propensity (Disc.) and Cumulative Head Excess
(H.)

Cost is given in USD ($), Discolouration Propensity in expressed in Nephelometric Turbidity
Units (NTU) and Head Excess in meters (m).

................................
................................
...............

216




List of Figures


10


List of Figures


Figure 1 Illustration of the interaction of information between the problem independent hyper
-
heuristic
and the problem s
pecific heuristics in the context of the domain barrier. In this example the hyper
-
heuristic selects one solution that generates a number solutions that are evaluated by the current
problem being solved


highlighted in blue.

................................
................................
...................

40

Figure 2. Line plot of a single objective problem with one parameter


f(x) = 1


x.

................................

55

Figure 3. Samples from two probability distribution functions used in EA mutation operators.

...............

56

Figure 4. Results of two (1+1)
-
ESs with Uniform and Gaussian mutation shown in two plots: objective
value against generation (left) and distribution of final
generation objective value (right).

...........

57

Figure 5. Illustration of the likely range of values a uniform distribution will perturb t
o.

.........................

57

Figure 6. Illustration of the likely range of values a Gaussian distribution will perturb to.

.......................

58

Figure 8. Cosine descent problem with four deceptive local minima.

................................
........................

59

Figure 10. Taxonomy of heuristics

................................
................................
................................
.............

61

Figure 11. Diagram illustrating the application of
the uniform random mutation heuristic on randomly
selected real
-
valued parameters.
................................
................................
................................
......

64

Figure 12. Diagram illustrating the applicat
ion of the Gaussian mutation heuristic on a randomly selected
real
-
valued parameter.

................................
................................
................................
.....................

64

Figure 14. Diagram illustrating the applic
ation of the attraction heuristic on two randomly selected real
-
valued parameters.

................................
................................
................................
...........................

65

Figure 15. Diagram illustrating the applicat
ion of the repulsion heuristic on two randomly selected real
-
valued parameters.

................................
................................
................................
...........................

66

Figure 16. Diagram illustrating the applicatio
n of the replication heuristic on two randomly selected
parameters with the same encoding type.

................................
................................
........................

66

Figure 17. Diagram illustratin
g the application of the transposition heuristic on two randomly selected
parameters with the same encoding type.

................................
................................
........................

67

Figure 18.
Illustration of a heatmap of multiple algorithm results on a set of problems

............................

68

Figure 19. Illustration of a box plot of multiple
algorithm results on a single problems

............................

68

Figure 20. Illustration of the Biaxial Box Plot of multiple algorithm results on multipl
e of problems

......

69

Figure 21. Biaxial Box Plot with ranges.

................................
................................
................................
....

70

Figure 22. Illustration of the Ordered Trial Rank (OTR) and average OTR.

................................
.............

72

Figure 23. Biaxial box plot of ordered trial ranks for the Generational Distance measure.

.......................

76

List of Figures


11

Figure 24. Biaxial box plot of
ordered trial ranks for the Hypervolume indicator.

................................
....

79

Figure 25. Box plots showing the distribution of hypervolume and generationa
l distance results of the
final generation over all trials of each heuristic on the seven DTLZ problems.

..............................

82

Figure 26. Line plots
shown average generational distance and hypervolume results over generations.

...

83

Figure 27. Generational and final generation obj
ective value results for the cosine descent problem.

......

90

Figure 28. Samples from a tri
-
modal probability distribution function for
use in EA mutation operators.

91

Figure 30. General Generative Framework. Blue shaded elements indicate generative optimisation a
ctions
and green shaded elements indicate interaction underlying problem class.

................................
....

93

Figure 31. Samples from two variations of the
tri
-
modal GMM distribution function with means at {
-
0.2,
0, 0.2} and {
-
0.1, 0, 0.1} and weights of {0.455, 0.09, 0.455} and {0.425, 0.15, 0.425}
respectively.

................................
................................
................................
................................
....

95

Figure 32. Illustration of the sampling of solutions and sorting into three sets for evaluating GMM PDFs.
................................
................................
................................
................................
.........................

97

Figure 33. Single
-
parameter, single
-
objective linear problem with 5 test variants.

................................
.

102

Figure 34. Nine evolved distri
butions illustrating the variety of shapes.

................................
.................

103

Figure 35. Pareto front of evolved GMMs (blue circles) on the Linear training prob
lem (two views)
compared to 10 Gaussians (red triangles)

................................
................................
.....................

104

Figure 36. Plots showing objective value over generations and the di
stribution of final generation results.
Solid blue lines represent the average evolved GMM objective values over generations and the
dashed black lines the tuned Gaussians.

................................
................................
........................

105

Figure 38. Final generation results
-

comparison with Gaussians on test problems.

................................

107

Figure 39. Single
-
parameter, single
-
objective cosine problem with 5 test variants.

................................

108

Figure 40. Six selected distributions evolved on the cosine problem.

................................
......................

109

Figure 41. Final generation results
-

comparison with Gaussians on cosine training problem.

................

110

Figure 43. Single
-
parameter, singl
e
-
objective cosine problem with central optima for training.

.............

111

Figure 44. Selected distributions from the x =0.5 cosine
training problem.

................................
.............

112

Figure 45. Objective value results
-

comparison with Gaussians on training problem.

............................

113

Figure 47. Variants of the cosine problem with varying wavelengths for testing.

................................
...

114

Figure 48. Objective value results
-

comparison of training and test problems.

................................
.......

115

Figure 50. Two
-
parameter, single
-
objective plane problem.

................................
................................
....

117

Figure 51. Four variants of th
e two
-
parameter, single
-
objective plane problem for testing.

....................

118

Figure 52. Example distributions from the Pareto front.

................................
................................
..........

119

List of Figures


12

Figure 53. Two plots comparing the objective values on the training and test problems and comparing
objective values of the evolved
GMM distributions against the Gaussians on the training problem.
................................
................................
................................
................................
.......................

119

Figure 54. Two
-
parameter, single
-
objective cosine2 problem f
or training.

................................
.............

120

Figure 55. Variants of two
-
parameter, single
-
objective cosine2 problem for testing.

..............................

12
1

Figure 57. Variants of the two
-
parameter, single
-
objective cosine2 problem for testing.

........................

123

Figure 58. Final generation results
-

comparison with Gaussians on test problems.

................................

123

Figure 59. Two plots comparing the objective values on the training and test problems and comparing
objective values of the evolved GMM distributions against the Gaussians on the training problem.
................................
................................
................................
................................
.......................

124

Figure 60. Two
-
objective Pareto fronts for the DTLZ1 to 6 optimisation problems.

...............................

128

Figure 61. Two
-
objective Pareto fronts for the WFG1, 2 and 3 optimisation problems.

.........................

128

Figure 62. Example Distributions Evolved on DTLZ1

................................
................................
............

130

Figure 63. Objective

values
-

comparison against tuned Gaussians

................................
.........................

131

Figure 64. Optimisation run
-

comparison against tuned Gaussians
................................
.........................

132

Figure 66. Optimisation run results on test problem 1


DTLZ1 with 10 parameters.

.............................

133

Figure 67. Optimisation run results on test problem 2


DTLZ1 with 14 parameters.

.............................

133

Figure 68. Test 2


varying objective dimensionality


objective values

................................
.................

134

Figure 69 .Optimisation run results on test problem 1


DTLZ1 with 3 objectives.

................................

134

Figure 70. Optimisation run results on test problem 2


DTLZ1 with 4 objectives.

................................

135

Figure 71. Generative framework objective va
lues for evolved distributions on DTLZ1 to DTLZ6.

......

136

Figure 72. Generational distance results for the evolved distributions on DT
LZ2

................................
...

136

Figure 73. Generational distance results for the evolved distributions on DTLZ3

................................
...

136

Figure 74. Generational distance results for the evolved distributions on DTLZ4

................................
...

137

Figure 75. Generational distance results for the evolved distributions on DTLZ5

................................
...

137

Figure 76. Generational distance results for the evolved distributions on DTLZ6

................................
...

137

Figure 77. Generative framework
objective values for evolved distributions on WFG1, 2 and 3.

...........

139

Figure 78. Generational distance results for the evolved distrib
utions on WFG1

................................
....

139

Figure 79. Generational distance results for the evolved distributions on WFG2

................................
....

139

Figure 80. Generational distance results for the evolved distributions on WFG3

................................
....

140

Figure 81. Contour plots of perturbation values for GMM distributions.

................................
.................

140

Figure 82. Contour plots of dominance scores for GMM distributions.

................................
...................

142

List of Figures


13

Figure 83. Illustration of performance assessment measure
given in Equation (12), showing three cases:
good performance, average performance, and poor performance.

................................
................

152

Figure 85. Two plots

showing average performance score assigned to each heuristic over generations for
the optimistic and pessimistic binary dominance performance measures.

................................
....

158

Figure 86. Two plots showing average performance score assigned to each heuristic over generations for
the binary problem decomposition and max objective improvement problem decomposition
measures.

................................
................................
................................
................................
.......

1
58

Figure 87. Two plots showing average performance score assigned to each heuristic over generations for
the average dominance count and dominance score p
erformance measures.

................................

159

Figure 88. Two plots showing average performance score assigned to each heuristic over generations for
t
he hypervolume comparison and change in archive hypervolume comparison performance
measures.

................................
................................
................................
................................
.......

160

Figure 89. Generational distance

and hypervolume results over generations for each heuristic applied to
the DTLZ2 problem. Averaged over 50 trial runs.

................................
................................
........

161

Figure

90. Two plots showing average performance score assigned to each heuristic over generations for
the optimistic and pessimistic binary dominance performance measures.

................................
....

162

Figure 91. Two plots showing average performance score assigned to each heuristic over generations for
the binary problem decomposition and max objective improvement problem decomposition
measures.

................................
................................
................................
................................
.......

163

Figure 92. Two plots showing average performance score assigned to each heuristic over generations for
the average dominance count and
dominance score performance measures.

................................

163

Figure 93. Two plots showing average performance score assigned to each heuristic over g
enerations for
the hypervolume comparison and change in archive hypervolume comparison performance
measures.

................................
................................
................................
................................
.......

164

Figure 94. Gener
ational distance and hypervolume results over generations for each heuristic applied to
the DTLZ1 (6 objective) problem. Averaged over 50 trial runs.

................................
...................

165

Figure 96. Four plots showing average performance score assigned to each heuristic over generations for
the optimistic and pessimistic binary dominance performance measures for the 6 (top) and 12
(bottom) objective instances of DTLZ
1.

................................
................................
.......................

167

Figure 97. Four plots showing average performance score assigned to each heuristic over generations for
the binary problem

decomposition and max objective improvement problem decomposition
measures for the 6 (top) and 12 (bottom) objective instances of DTLZ1.
................................
.....

168

Figure 98. Four plots showing average performance score assigned to each heuristic over generations for
the average dominance count and dominance score performance measures for the 6 (top) and 12
(bottom) objective instances of DTLZ1.

................................
................................
.......................

168

List of Figures


14

Figure 99. Four plots showing average performance score assigned to each heuristic over generations for
the hypervolume comparison and

change in archive hypervolume comparison performance
measures for the 6 (top) and 12 (bottom) objective instances of DTLZ1.
................................
.....

169

Figure 101. Generational distance and hypervolume results over generations for each binary heuristic
performance measure embedded in credit assignment hyper
-
heuristics applied to the DTLZ1
problem.

................................
................................
................................
................................
........

175

Figure 102. Generational distance and hypervolume results over generations for each binary heuristic
performance measure embedded in credit assignment hyper
-
heuristics applied to the D
TLZ2
problem.

................................
................................
................................
................................
........

175

Figure 104. Generational distance and hypervolume results over generations for each scalar heuristic
performance

measure embedded in credit assignment hyper
-
heuristics applied to the DTLZ1
problem.

................................
................................
................................
................................
........

179

Figure 105. Generational distance and hy
pervolume results over generations for each scalar heuristic
performance measure embedded in credit assignment hyper
-
heuristics applied to the DTLZ2
problem.

................................
................................
................................
................................
........

179

Figure 106. Example Markov chain with 3 states representing three heuristics.

................................
......

184

Figure 107.
Transition Weight Matrix for Example Markov chain with 3 states representing three
heuristics.

................................
................................
................................
................................
......

185

Figure 108. Schematic represen
tation of an EA with embedded online selective hyper
-
heuristic processes
(shaded).

................................
................................
................................
................................
........

188

Figure 109. Ordered trial rank and generat
ional distance and hypervolume results for each hyper
-
heuristic
selection mechanism on all benchmark problems.

................................
................................
........

191

Figure 110.
Two plots showing average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on DTLZ1.

................................
..........

192

Figure 111. Two plots showing average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on DTLZ7.

................................
..........

193

Figure 112. Two plots showing average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on WFG8.

................................
...........

193

Figure 113. Two plots showing average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on
LZ09 F2.

................................
........

193

Figure 114. Plots showing the cumulative use of each heuristic by the Simple Random and Tabu Search
hyper
-
heuristics

on DTLZ1 and DTLZ2.

................................
................................
......................

195

Figure 115. Plots showing the cumulative use of each heuristic by both Credit Assignment hyper
-
heuristic
s on DTLZ1 and DTLZ2.

................................
................................
................................

196

Figure 117. Three heatmaps showing the weights assigned to each edge in the four heuristic Markov
chain
in the MCHH hyper
-
heuristic from one example run on DTLZ2.

................................
.......

198

List of Figures


15

Figure 118. Eight plots showing generational distance (left) and h
ypervolume (right) for Simple Random
and three variants of TSRoulWheel on DTLZ1 and 7, and WFG1, 2 and 9, each averaged over 30
trial runs.

................................
................................
................................
................................
.......

200

Figure 119. OTR results for generational distance and hypervolume for each hyper
-
heuristic selection
mechanism on all benchmark problems using the increased heuristic sets.

................................
..

202

Figure 120. Two plots showing average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on DTLZ1 when supplied with the larger
heuristic set.

................................
................................
................................
................................
..

204

Figure 121. Two plots showing average generational distance (left) and hypervolume (right) over
generations fo
r all hyper
-
heuristic selection mechanisms on DTLZ7 when supplied with the larger
heuristic set.

................................
................................
................................
................................
..

204

Figure 122. Two plots showin
g average generational distance (left) and hypervolume (right) over
generations for all hyper
-
heuristic selection mechanisms on WF8 when supplied with the larger
heuristic set.

................................
................................
................................
................................
..

204

Figure 123. Plots showing the cumulative use of each heuristic by the Credit Assignment (Dominance
Score) and MCHH hyper
-
heuristics on DTLZ1, DTLZ7 and WFG8.

................................
..........

205

Figure 124. Schematic view of the experimental design.

................................
................................
.........

212

Figure 126. Two plots showing hypervolume results NSGA
-
II, SPEA2, both MCHH variants, Simple
Random and TSRoulWheel on the Anytown benchmark network. Again, the left plot shows
hypervolume over generations (averaged over all trial runs), righ
t plot shows distribution of final
generation hypervolume for all trial runs.

................................
................................
.....................

216

Figure 127. Two plots showing hypervolume
results NSGA
-
II, SPEA2, both MCHH variants, Simple
Random and TSRoulWheel on real
-
world network 2.

................................
................................
..

217

Figure 128. Two plots of n
ormalised total weights (sum of all weights for moving to each heuristics) over
generations assigned to each heuristic by the MCHH during the optimisation search process from
two different trial runs on the Hanoi benchmark water network.

................................
..................

218




Publications


16


Publications


Some of the material presented in this thesis has previously been published in the following:

Journals:



Kent M
c
Clymont, Ed Keedwell, Dragan Savi
ć

and Mark Randall
-
Smith (2012): A General
Multi
-
objective Hyper
-
Heuristic for Water Distribution Network Design with Discolouration
Risk
,
Journal of Hydroinformatics
,
doi:10.2166/hydro.2012.022
,

(
To Appear
).



K. M
c
Clymont and E. C. Keedwell (2011): Deductiv
e Sort and Climbing Sort: New Methods for
Non
-
Dominated Sorting,
Evolutionary Computation
. Spring 2012, Vol. 20, No. 1, Pages 1
-
26.

Conferences:



K. M
c
Clymont, E. C. Keedwell and D. Savi
ć

(2012): Automated Construction of Fast Heuristics
for the Water Dist
ribution Network Design Problem,
Proceedings of the

10th International
Conference on Hydroinformatics
(
HIC 2012
)
,
July 14
-
18,
Hamburg,
Germany
.



K. M
c
Clymont and E. C. Keedwell (2011): Markov chain Hyper
-
heuristic (MCHH): an Online
Selective Hyper
-
heuristic

for Multi
-
objective Continuous

Problems,
Proceedings of the 13th
annual conference on Genetic and evolutionary computation (
GECCO 2011
)
,

Pages
2003
-
2010
,
Dublin,

Ireland
,
ACM
:

New York, USA
.



K. McClymont and E. C. Keedwell (2011): Benchmark Multi
-
objectiv
e Optimisation Test
Problems with Mixed Encodings,
IEEE Congress on Evolutionary Computation

(
CEC 2011
)
,

Pages 2131
-
2138
,
5
-
8 June
,

USA.



K. M
c
Clymont, E. C. Keedwell, D.
Savić

and M. Randall
-
Smith (2011): A Hyper
-
heuristic
Approach to Water Distribution Network Design,
Urban Water Management: Challenges and
Oppurtunities
-

Computing and Control for the Water Industry

(
CCWI 2011
)
,
5
-
7 September,

Exeter
, UK
.



K. M
c
Clymont, D. Walk
er, E. C. Keedwell, R. Everson, J. Fieldsend, D.
Savić

and M. Randall
-
Smith (2011): Novel Methods for Ranking District Metered Areas for Water Distribution
Network Maintenance

Scheduling,
Urban Water Management: Challenges and Oppurtunities
-

Computing and

Control for the Water Industry

(
CCWI 2011
)
,
5
-
7 September,

Exeter
, UK
.



M. Randall
-
Smith, J. Collingbourne, J. Harvey and K. M
c
Clymont (2011): Targeting Water
Distribution Network Interventions for the Cost
-
Effective Mitigation of Discolouration Risk: a
Ca
se Study,
Urban Water Management: Challenges and Oppurtunities
-

Computing and Control
for the Water Industry

(
CCWI 2011
)
,
5
-
7 September,

Exeter
, UK
.

Publications


17



K. M
c
Clymont, E. C. Keedwell, D.
Savić

and M. Randall
-
Smith (2010): Mitigating
Discolouration Risk with Optimised Network Design,
The 9th International Conference on
Hydroinformatics

(
HIC 2010
)
,
Tianjin,
China.



K. M
c
Clymont and E. C. Keedwell (2010): Optimising Multi
-
Modal Polynomial Mutation
Operators for Multi
-
Objective Problem Classes,
IEEE
Congress on Evolutionary Computation

(
CEC 2010
)
,
18
-
23 July
,

Barcelona.



K. M
c
Clymont and Z. Wood (2011): A Classificati
on of Heuristics,
The Postgraduate
Conference for Computing:

Applications and Theory
(
PCCAT
)
, Exeter.



Introduction


18

Chapter 1:

Introduction

The world is full of problems. People encounter and solve problems every day in practically every
aspect of their lives, be that at home when arranging furniture in a new house or at work when organising
their daily activiti
es. Many of these tasks are trivial or, at least, to humans appear simple to complete.
Through natural evolution, people have evolved to be very good at performing certain types of tasks
efficiently by using, often subconsciously, rough methods for solving

difficult

problems. These

rules of
thumb


are called heuristics and they are used to quickly produce solutions to problems with some degree
of satisfaction.

Consider, for example, the task of walking to work. For one person travelling a short distance wi
th
only a limited number of different roads or pathways available to them, the task is easy to complete. That
is to say,

in this instance

the problem of designing a suitable route is easy to solve. However, as the length
of the journey increases and the nu
mber of different routes available to the traveller increases the task
becomes more difficult and the likelihood of finding the best or even close to the best route becomes less
likely. If the person were to be travelling from Exeter to, say, a specific st
reet in Newcastle it would take
considerably greater effort to find the best, i.e., optimal, route than it would for a journey from one street
in Exeter to another.

The larger, more difficult tasks are sometimes solvable using simple heuristic approaches,
such as
always picking the road that gets you closest to your destination in the shortest distance, but rarely
guarantee an optimal result. In computer science, the field of optimisation is concerned with developing
good automatic methods for solving diffi
cult tasks using algorithms which can systematically search the
space of possible solutions.

The
se

automated methods are able to consider many more possible solutions to a problem and
therefore often find better solutions than those designed by experts. Again, considering route planning,
contemporary computers have the capacity to create and evaluate m
any millions of different routes from a
given origin and destination and therefore
are
more likely to find a shorter, more efficient route than a
person studying a map. In addition, by provi
di
ng
fast
algorithms for solving problems, such as route
planning,

it becomes possible to solve far more complex instances, such as planning distribution routes
for an entire fleet of haulage lorries.

These algorithms can themselves be simple heuristics, such as programming the procedure for
selecting the next sectio
n of

the route which ends closest

to the destination. Alterna
tively, more complex
algorithms called meta
-
heuristics

can

be

used which are built from a combination of heuristics.
Evolutionary Algorithms (EAs), for example, use the conceptual basis of evolution
through natural
selection as the inspiration for an optimisation meta
-
heuristic. EAs use a combination of two heuristics,
mutation and crossover, to

evolve


new solutions to a problem by iteratively mutating and combining
different sections of individual
solutions and selecting the
better, more

optimal solution (shorter path) to
automatically search through the space of solutions to the problem.

Int
roduction


19

Meta
-
heuristics provide more generalised methods for solving a range of problems compared to
specialised individ
ual heuristics. For example, EAs can be applied to route planning problems, space
allocation, jet engine design, personnel timetabling and many more. Meta
-
heuristics, like EAs, have been
applied many times and demonstrated through numerous studies as being

effective at solving a very wide
range of problems.

In addition to solving more difficult and varied problems, meta
-
heuristics methods like EAs are
well suited to solving problems with multiple objectives. That is to say, the meta
-
heuristic can solve
mult
iple objective
s

simultaneously in the same optimisation run. So far the route planning problem has
been discussed in terms of a single objective


the shortest route


but many other factors could affect
the

d
ecision of which route to take;

which is

optima
l. Consider, for example, that when travelling on certain
types of roads such as motorways a car emits less carbon emissions per mile and uses less fuel per mile
then on a slower road with more turns and junctions. A driver may wish to reduce their carbon
emissions
for ecological reasons or reduce fuel con
sumption

for economic reasons and so when optimising their
route would like to consider both distance and fuel consumption. Meta
-
heuristics like EAs are able to,
through methods like Pareto efficiency, evo
lve populations of solutions which provide a trade
-
off
between more than one objective, providing the decision maker with a
varied
set of possible solutions to a
problem and allowing the decision maker to select the solution which best matches their trade
-
off
preference.

Despite being applicable to a number of problems, meta
-
heuristics require tailoring and tuning to
each problem in order to effectiv
ely solve each specific problem
. Setting the amount of mutation and the
type of crossover, for example. This
process of tailoring meta
-
heuristics requires a careful consideration
of the features present in the problem or class of problems which requires specialist skills.
As such, t
his
process of
manually

optimising the optimiser


a priori

is both time consuming

and knowledge intensive.

To overcome th
e

problem of generalising but also tailoring meta
-
heuristics, researchers
have

recently
been
exploring the concept of prov
id
ing heuristics built specifically with the purpose of
optimising the
creation
, tailor
ing and

selection of heuristics: optimisers to optimise the optimiser.

These
approaches, called
hyper
-
heuristic
s,

aim to remove much of the burden associated with heuristic
selection, tuning and tailoring to specific problems and th
erefore provide a more general

and easily
applicable optimisation method.

There are two primary branches of hyper
-
heuristic
:
generative

and
selective
.
Generative

hyper
-
heuristics use optimisation techniques to create or evolve new heuristic
algorithms which are tailored to specific pro
blem classes.
Selective

hyper
-
heuristics optimise the selection
of heuristics, which may or may not be problem specific, to improve the quality and/or efficiency of the
optimisation search.

This thesis explores the development of both
generative

and
selec
tive

hyper
-
heuristics
for solving

multi
-
objective optimisation problems.

The selective hyper
-
heuristic and automatically generated
heuristics are firstly tested using benchmark numerical optimisation problems in order to understand the
behavioural traits a
nd performance limits of the heuristics.
The proposed approaches are then
demonstrated on the real
-
world optimisation problem of water distribution network design from the field
of hydroinformatics.

Introduction


20

1.1

Aims

The aims of this thesis are to:



prove that
the

performance
of a heuristic
can vary both on different optimisation problems and at
different locations in a single problem;



provide a base understanding of the behavioural traits of a set of heuristics to further enable
analysis of hyper
-
heuristics;



explo
re the potential validity of generative hyper
-
heuristics for multi
-
objective optimisation
problems;



propose a novel approach to evolving real
-
valued mutation heuristics which draw perturbation
values from probability distribution

functions tailored to spec
ific problems or classes of
problems
;



demonstrate

through experimental study

the validity of the proposed generative hyper
-
heuristic
approach;



examine through experimentation the efficacy of a range of multi
-
objective heuristic
performance measures for use

in online selective hyper
-
heuristics;



propose a novel selective hyper
-
heuristic selection mechanism for multi
-
objective optimisation
problems;



demonstrate using experimental results, the relative quality and performance attributes of the
novel selective h
yper
-
heuristic on multi
-
objective benchmark optimisation problems against
state
-
of
-
the
-
art multi
-
objective selective hyper
-
heuristics from the literature;



apply and demonstrate the validity of the proposed online selective hyper
-
heuristic on a set of
real
-
world instances of the multi
-
objective water distribution network design problem.

1.2

Novelties

Within the limits of the author’s understanding, the following aspects of this thesis are believed to
be novel:



Biaxial Box Plot (
3.3
)


a novel visualisation method for displaying large sets of grouped multi
-
sampled results, such as multiple optimisation runs on multiple problems from multiple
heuristics.



Ordered Trial Rank (
3.3.3
)


a method for ranking and comparing the relative performance of
multi
-
sampled results from multiple heuristics on a sin
gle problem.



Generative Hyper
-
heuristic (
4.2
)


a method for evolving

heuristics for multi
-
objective
optimisation problems which is demonstrated by
producing

tailored probability distribution
functions for mutation heuristics.

The framework
, the first of its kind,

is designed generically to
enable to generation of new heuristics for multi
-
objective problems through EA, GP or other
optimisation methods
, although EA optimisation of mutation distributions is used in this study.
The framework utilises Pareto dominance to rate candidate heuristics, optimising their
performance for three different stages of the optimisation search process: initial random
Introduction


21

pop
ulation, mid search and end of the search exploring the Pareto front. The approach produces
a novel distribution which is found to be very effective on a wide range of problems.



Heuristic Performance Measures (
5.2.2
)


four novel approaches to measure heuristic
performance for use in selective hyper
-
heuristics.

The performance measures are constructed
with
multi
-
objective methods such as Pareto domin
ance and hypervolume and designed to rate
heuristic performance to inform the selection of heuristics in future iterations.



Selective Hyper
-
heuristic (
5.3.3
)


the Markov
-
chain Hyper
-
heuristic (MCHH) selection
mechanism for use on multi
-
objective optimisation problems.

The proposed approach records
and takes advantage of heuristic interaction information represented by a weighted Markov
-
chain to contr
ol the selection of heuristics. The MCHH utilises the best heuristic performance
measure


dominance performance


proposed in
5.2.2
. The approach d
emonstrates the benefits
of including heuristic interactions in the selection process and demonstrated as outperforming
the multi
-
objective hyper
-
heuristics from the literature.



Formulation of the Water Distribution Network Design Problem
which includes di
scolouration
propensity

(
6.1
)


a novel multi
-
objective formulation of the water distribution network design
problem which includes discolouration
propensity

as an objective of the design problem.

The
formulation is test
ed on a range of be
nchmark and real
-
world networks. The results provide
interesting new network designs which for a minimal increase in cost greatly reduce the
propensity

of discolouration events and, through self
-
cleaning properties, would result in long
term reduction in maintenance and flushing costs.

1.3

Thesis Structure

The thesis is split into
eight

chapters, including this introductory chapter and a concluding
and
future work
chapter. The main contributions of the thesis are organised in the five main ch
apters, which
are briefly summarised below.

Chapter 2 provides a background to both main aspects of the thesis: hyper
-
heuristics, and
discolouration
propensity

modelling for water distribution design. Each of the subjects are introduced to
give a context t
o the remaining chapters through a literature survey.

Chapter 3 examines the behavioural features of a set of heuristics design
ed

for use in Evolutionary
Algorithms and demonstrates through experimental results how heuristic performance varies between
prob
lems and at different stages of the optimisation search process.

The conclusions of this chapter form
the basis
for
the

argument
that in order
to
obtain the best possible performance there is a need for
(a)
heuristics tailored to problem classes and (b) on
line selective hyper
-
heuristics for selecting the most
apposite heuristic at each stage in the optimisation search.

Chapter

4 explores the potential for automatically generating tailored real
-
value mutation
heuristics through the process of evolving optimi
sed probability distribution functions. The chapter
presents a novel generative hyper
-
heuristic framework for evolving heuristics for multi
-
objective
optimisation problems. The framework is used to evolve the tailored mutation distributions and shown to
Introduction


22

ou
tperform the traditional Gaussian distribution. One distribution in particular, a tri
-
modal distribution, is
shown to be very effective at optimising the
benchmark optimisation problems and is used
in
the
following study of online selective hyper
-
heuristic
s for multi
-
objective problems.

Chapter 5 studies the two
core
aspects of a multi
-
objective online selective hyper
-
heuristic:
heuristic performance measures

and

heuristic selection mechanisms. Four novel performance measures
are proposed and compared again
st performance measures from the literature. The dominance score
performance measure proposed in

5.2.2.2

is then used in the examination of selection mechanisms from
the literature and incorporat
ed

within a novel hyper
-
heuristic selection mechanism called the Markov
-
chain Hyper
-
heuristic (
MCHH). The MCHH is shown in the

chapter
,

through experimental results
,

to
be
an effective online selective hyper
-
heuristic with the capacity to learn the behavioural links between
different heuristics.

The MCHH proposed in Chapter 6

is then applied to real
-
world instances of a novel multi
-
objective formulation of the water d
istribution network design problem. The
design problem is
formulated to take into account the
propensity

of discolouration
events

in addition to the traditional
objectives of cost and pressure. The use of discolouration
propensity

in network design represe
nts an
important step towards considering the long term maintenance and cleaning requirements of a water
distribution network which, through experiments, is shown to provide new trade
-
off solutions to the
decision maker.

An overarching conclusion to the th
esis is given in Chapter
7

which
is followed by Chapter 8
which

gives

a description of potential further study in the areas of multi
-
objective hyper
-
heuristics and
water distribution network design.



Background


23

Chapter 2:

Background

In this chapter a review of the relevant literature is conducted relating to
d
iscolouration

modelling,
the
Water Distribution Network

(
WDN
) design optimization problem as well as a review of optimization
methods from traditional
heuristic

methods through t
o
the
recently emerged fields of
hyper
-
heuristics
,
Memetic Algorithms

and
m
ulti
-
method algorithms
. The literature review is organized as follows:



review of the origins and recent advancements in the
water distribution network design

optimization problem;



introduction to
discolouration

modelling in potable
water distribution networks
;



summary of traditional optimization techniques including a short description of the genesis of
multi
-
objective optimization in the context of
Evolutionary Computing
;



descripti
on of modern abstracted optimization techniques, specifically focusing on the field of
hyper
-
heuristics

in relation to
Memetic Algorithms

and multi
-
method algorithms;



a
review of optimisation methods applied to the
water distribution network design

optimiz
ation
problem.

2.1

Water Distribution Networks and Design

Water distribution networks are built by water companies in order to provide water services to end
users with the aim of satisfying their demand. A
water distribution network

(
WDN
) is comprised of
pipes
,
nodes

(
junctions

and
demand points
),
hydraulic devices

(such as
pumps
) and
sources

(
tanks

and
reservoirs
) and constitutes the infrastructure that delivers water from the
source

(
often a
reservoir
)

to
various locations where it is drawn from the network f
or consumption (e.g., residentia
l housing or
industrial sites).

Real world water distribution networks are, more often than not, large and complicated structures
which are commonly interlinked with other neighbouring networks. The set of national water dis
tribution
networks in the UK alone represents a significant infrastructure that requires constant operational
management, maintenance and
rehabilitation
. In order to satisfy consumer demand, the networks must be
constructed with a good layout that connects

all points of demand to a source and are designed to provide
the best possible hydraulic conditions to meet operational requirements. The creation of a
water
distribution network

can be broken down into three constituent parts:
layout
,
design

and
operatio
n
. The
layout problem is concerned with deciding the geographic structure of the network, which nodes are
connected to other nodes and so on as well as where to place infrastructure like tanks. The design problem
is concerned with sizing the pipes, tanks a
nd pumps. The operation problem is concerned with controlling
the
pumping schedules
,
valve operations

and so on.

Each of these parts represent complex individual problems that require significant expertise and
resources to solve. Although, it should be no
ted that decisions made for one problem has an effect on the
next; i.e., selecting a network layout will affect the possible design choices and thus overall cost of the
network. However, attempting to optimise all three parts simultaneously would represent

a significantly
Background


24

more complex task and would need to take into account a much larger range of decision maker
considerations which are not normally modelled in the individual problems. For example, the design
problem is primarily concerned with the sizing (
diameters) of pipes in the network. Changing pipes sizes
effects the hydraulic conditions in the network and hence the quality of the network based on its ability to
serve the various demand points.

The design problem is complicated as the overall hydraulic conditions are affected by each pipe
and so changes to one pipe will have a different effect on the overall conditions depending on the sizes of
all the other pipes in the network. As such, each pi
pe cannot be designed in isolation, but rather as a
combination of sizes for all pipes in the network. Therefore, even for relatively small networks, the
number of possible combinations of pipes is very large
and so

makes enumeration of all the feasible
de
signs impossible within reasonable time. If, for example, there were six potential sizes for each pipe in
a network of just thirty pipes, there would be 2.21
×
10
23

possible combinations
-

far more than is possible
to compute within reasonable time

(i.e., wi
thin “polynomial time”)
.

Traditionally the design problem was solved entirely by human experts who applied their
knowledge, experience and rules of best practice to
create a single design (solution). However, with the
advent of automated design methods it

is now more common for part or all of a network to be designed
with modern optimisation algorithms. Optimisation algorithms are able to design and compare many
thousands of different designs in order to systematically search through a wide set of differen
t design
solutions (known as the search space) and potentially produce better, more optimal designs. However,
given the very large number of combinations available it is not often possible to enumerate all possible
designs and so the optimisation algorithm
s use heuristic methods to more efficiently search the set of
possible solutions. Importantly, this

relationship between the number of pipes and the increase in search
space means that WDN optimisation is known to be a
NP
-
hard problem

(Yates

et al.,

1984)

and so
requires powerful optimisation methods to solve it.

The non
-
linearity of the hydraulic equations also has an effect on the complexity of the search
space, creating a
multi
-
modal landscape
. Multi
-
modal problems are particularly difficult as good netw
ork
designs are separated by regions of less
-
good or infeasible network designs. As a result, early methods
like
Linear Programming

(Schaake & Lai, 1969)

and
Hill
-
climbing

algorithms are not as effective
as
stochastic population

based methods like Genetic Algorithms (GAs)
at solving these problems and often
get stuck in local optima: i.e., the best network design in the local area of the search space but not optimal
in the context of the total (global)
search space
.

2.2

Discolouratio
n

The UK water industry is a tightly regulated public services sector where

water company
performance is closely monitored through a range of
indicators
; from water quality, customer service
(e.g., sufficient pressure) to customer satisfaction. Recently, a
n emphasis has been placed on customer
satisfaction in particular which is partly measured by monitoring customer complaints and contacts.
Motivated by these regulatory demands, water companies are now focusing efforts on reducing the
frequency of water di
scolouration events
(Cook, 2007)

prior to customer contacts occurring as

Background


25

discolouration events

(the visible discolouration of water at the tap) have been attributed to approximately
30% of all complaints received by water companies in the UK
(Cook, 2007)
. In addition, water authorities
are applying pressure on companies

to

implement planned activities to control discolouration prior to
contacts occurring


(Vreeburg & Boxall, 2007)
. Given that many water authorities use customer contacts
as a key performance indicator
(Cook

et al.,

2005)

and

coupled with the fact that over a third of contacts
to water companies now occur as a result of customers experiencing discoloured water
(
Cook

et al.,

2005
;
Vreeburg & Boxall, 2007)

it can assumed that industry expectations of the modelling available
tech
nologies will only increase.

Furthermore, it is important to note that the drive to reduce the number of
discolouration events

is
not isolated to the UK, bu
t experienced in many countries

worldwide. In addition, the phenomenon does
not appear to display re
gional variances, outside of temperature and material differences, with

Boxall &
Prince

(2006)

demonstrating the validity of UK models abroad. As such, it can be supposed that any
advancement relating to discolouration m
odelling may have world wide application.

2.2.1

Causes of Discolouration

Discolouration is the visible change in water colour resulting from the suspension of sediment and
particles (called suspended solids) that are not individually visible to the naked eye but collectively
change the
colour,
diffraction and absorption of ligh
t passing through the liquid, which is measured as
turbidity (expressed in Nephelometric Turbidity Units, NTU)

(Gaultier

et al.,

1996)
. Generally, the

darker


the water colour is the greater the density of suspended solids in the water which is represente
d
by higher values of NTU. The NTU scale measures the amount of light
which is diffracted by the water
which correlates to the number of total suspended solids in the water, usually measured by projecting a
light beam through the water and recording light
levels to the side of the beam

(Twort

et al.,

2000)
.

The events where the suspended solids become visible to customers is the result of a three stage
process: delivery of solids into the system from a source; accumulation of the solids in a system; and re
-
suspension or mobilisation into water that is provided to a demand point (e.g., customer’s property)
(Boxall & Saul, 2005)
.

Sedimentary and other particles in water distribution systems can come from a number of different
sourc
es

(Blokker

et al.,

2008)
. One of the largest contributors is

the

outputs from the water treatment
facilities which supply the network or reservoirs in which potable water is stored prior to distribution.
Other sources include sedimentary build
-
up at dead
ends (i.e., district metered area (DMA) boundaries)

(Barbeau

et al.,

2005)
, sedimentary deposits in pipes

(Vreeburg

et al.,

2005)
, accumulation of biomass
and particle on pipe walls

(Boxall & Saul, 2005)
, pipe degradation

(Husband & Boxall, 2011)
, as well as
ingress from cracks and holes in broken pipes and/or poor fitting assets. The combined effect of all these