Download Modified and Ensemble Intelligent Water Drop

MODIFIED AND ENSEMBLE INTELLIGENT
WATER DROP ALGORITHMS AND THEIR
APPLICATIONS
BASEM O. F. ALIJLA
UNIVERSITI SAINS MALAYSIA
2015
MODIFIED AND ENSEMBLE INTELLIGENT
WATER DROP ALGORITHMS AND THEIR
APPLICATIONS
by
BASEM O. F. ALIJLA
Thesis submitted in fulfilment of the requirements
for the degree of
Doctor of Philosphy
October 2015
ACKNOWLEDGEMENTS
With the name of Allah, Most Gracious, Most Merciful.
First and foremost, my sincere glorifications and adorations go to almighty Allah for
his guidance, protection and strength over me to complete my research study. I would
like to express sincere gratitude to my supervisors, Professor Lim Chee Peng, Professor
Ahamad Tajudin Khader, and Dr. Wong Li Pei for their insightful guidance throughout
the entire period of my research. I will forever remain grateful for the continued help,
and wise counseling. Special thanks and appreciations to Professor Lim Chee Peng for
his endless help, especially in publishing my research work. I am also grateful to my
friend Dr. Mohammad Azmi Al-Betar for his help and useful discussion during the
course of this research.
Indeed, without Allah then my parents’ prayers, I could not have completed this research. My special thanks to my beloved parents for their continued supports, encouragements, and prayers. Thank you mum, dad, my brothers, and sisters, you are always
in my mind and heart. In the same context, love and support my deepest and special
thanks go to my wife for her patience, understanding, fervent prayers and for taking
care of our kids. Your great support, efforts, and endurance is highly appreciated.
My sincere appreciations are extended to the Islamic Development Bank (IDB) for its
financial support under the IDB merit scholarship program. I am also grateful to the
School of Computer Sciences, Universiti Sains Malaysia, which has provided all the
facilities and equipments needed throughout my research. Last but not least; thank
you to all my friends in Malaysia, and those who support me in any respect during my
research.
ii
TABLE OF CONTENTS
Page
Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
Abstrak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xx
CHAPTER 1 – INTRODUCTION
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Motivation and Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.3
Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.4
Research Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.5
Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.6
Research Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.7
Thesis Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
CHAPTER 2 – BACKGROUND AND LITERATURE REVIEW
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2
Background to the Intelligent Water Drops Algorithm . . . . . . . . . . . . . . . . . . . . . .
15
2.2.1
Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2.2
Initialization phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2.2(a) Static parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2.2(b) Dynamic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Solution construction phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2.3
iii
2.3
2.4
2.2.3(a) Edge selection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2.3(b) Velocity and local soil Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.2.4
Reinforcement phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.2.5
Termination phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.1
Foundation of optimization methods for COPs . . . . . . . . . . . . . . . . . . . . . .
25
2.3.2
Taxonomy of optimization methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.3.3
Trajectory-based meta-heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.3.3(a) Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.3.3(b) Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.3.3(c) Iterated Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.3.4
Population-based meta-heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.3.5
Critical analysis of existing methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.4.1
Feature subset selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.4.1(a) Rough set for subset feature selection (RSFS) . . . . . . . . . . .
45
2.4.1(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Travelling salesman problem (TSP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.4.2(a) Overview to TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
2.4.2(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
Multiple knapsack problem (MKP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.4.3(a) Overview to MKP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.4.3(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.4.2
2.4.3
2.5
CHAPTER 3 – A MODIFIED INTELLIGENT WATER DROPS
ALGORITHM
iv
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
3.2
The original selection method in IWD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.3
Ranking-based selection methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.3.1
Linear ranking selection.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.3.2
Exponential ranking selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
The modified IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.4.1
Experimental study for rough set feature subset selection. . . . . . . . . .
60
3.4.1(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . .
60
3.4.1(b) Results and discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
Experimental study for travelling salesman problem. . . . . . . . . . . . . . . .
68
3.4.2(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . .
69
3.4.2(b) Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
Experimental study for multiple knapsack problem. . . . . . . . . . . . . . . . .
74
3.4.3(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . .
75
3.4.3(b) Results and discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
3.5
Comparing modified IWD with other state-of-the-art methods . . . . . . . . . . . . .
79
3.6
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
3.4
3.4.2
3.4.3
CHAPTER 4 – AN ENSEMBLE OF INTELLIGENT WATER DROPS
ALGORITHMS
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.2
The proposed models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.2.1
The Master-River, Multiple-Creek IWD model . . . . . . . . . . . . . . . . . . . . .
82
4.2.1(a) Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
4.2.1(b) Master river construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
4.2.1(c) Creek construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
A hybrid MRMC-IWD model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
4.2.2
v
4.3
Experimental study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.3.1
Experiments and results for TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.3.2
Experiments and results for RSFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
4.4
Comparing MRMC-IWD with other state-of-the-art methods. . . . . . . . . . . . . . 100
4.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
CHAPTER 5 – APPLYING THE HYBRID MRMC-IWD TO
REAL-WORLD CLASSIFICATION APPLICATIONS
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2
The FS-MRMC-IWD for FS using benchmark data sets . . . . . . . . . . . . . . . . . . . . 102
5.2.1
Experiments setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.2
Experimental results and comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.2(a) Comparing the performance of FS-MRMC-IWD
against other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2.2(b) Comparison of classification accuracies.. . . . . . . . . . . . . . . . . . 116
5.3
Real-world applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.3.1
Detection and recognition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.3.1(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.1(b) Features extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.1(c) Features subset selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.1(d) Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.2
Human motion detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.2(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.2(b) Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3.2(c) Features selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3.2(d) Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.3.3
Fault detection and diagnosis of induction motors . . . . . . . . . . . . . . . . . . 129
5.3.3(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
vi
5.3.3(b) Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3.3(c) Features selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3.3(d) Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
CHAPTER 6 – CONCLUSION AND FUTUREWORK
6.1
Summary of the research and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.2
Achievement of research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.3
Direction of future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
APPENDIX A – FEATURE SELECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
A.1
Feature selection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
A.1.1 Filter-based selection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
A.1.2
A.2
Wrappers-based FS methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Rough set and fuzzy rough for feature selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
A.2.1 Fundamentals of Rough set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
A.2.2 Rough set feature selection (RSFS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A.2.3 Fundamentals of fuzzy rough set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A.2.4 Fuzzy rough set for feature selection (FRFS). . . . . . . . . . . . . . . . . . . . . . . . 166
vii
LIST OF TABLES
Page
Table 2.1
Applications of the IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
Table 2.2
The main properties of the data sets used for RSFS experiments .
47
Table 2.3
Characteristics of the data sets used for TSP . . . . . . . . . . . . . . . . . . . . . .
49
Table 2.4
The main Characteristics of ten mknapcb1 instances obtained
from the OR-Library.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
Table 3.1
Parameters settings of the IWD algorithm for RSFS. . . . . . . . . . . . . .
60
Table 3.2
Comparison of the results of the ERS-IWD algorithm with
various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
Comparison of the results of the LRS-IWD algorithm with
various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
Performance comparison of the proposed methods with other
algorithms on rough set feature subset selection benchmark
problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
Significance tests of the LRS-IWD and ERS-IWD algorithms
using t-test with α < 0.05. "None" denotes that both results are
the same (i.e., no valid p-values). Highlight (bold) denote that
result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
Significance tests of the FPS-IWD and ERS-IWD algorithms
using t-test with α < 0.05. Highlight (bold) denote that result is
significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
Table 3.7
Parameters setting of the IWD algorithm for TSP. . . . . . . . . . . . . . . . .
68
Table 3.8
The average tour lengths from 10 runs of the ERS-IWD
algorithm with different SP values. The highlighted (bold)
values denote the best result for each data set. . . . . . . . . . . . . . . . . . . . .
69
The average tour lengths from 10 runs of the LRS-IWD
algorithm with different SP values. The highlighted (bold)
values denote the best result for each data set. . . . . . . . . . . . . . . . . . . . . .
70
Compare the Performance of the ERS-IWD, LRS-IWD, and
FPS-IWD algorithms in solving eight TSPLIB data sets. The
highlighted (bold) values denote the best result for each data set.
72
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 3.9
Table 3.10
viii
Table 3.11
Significance tests of the ERS-IWD and LRS-IWD algorithms
using t-test with α < 0.05. Highlight (bold) denote that result is
significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Significance tests of the FPS-IWD and LRS-IWD algorithms
using t-test with α < 0.05. Highlight (bold) denote that result is
significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Significance tests of the ERS-IWD and FPS-IWD algorithms
using t-test with α < 0.05. Highlight (bold) denote that result is
significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Table 3.14
Parameters settings of the IWD algorithm for MKP. . . . . . . . . . . . . . .
74
Table 3.15
Average profits from10 runs of the ERS-IWD method with
different SP values. The highlighted (bold) values denote the
best result of each data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Average profits from10 runs of the LRS-IWD method with
different SP values. The highlighted (bold) values denote the
best result of each data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Performance comparison of ERS-IWD, LRS-IWD, and
FPS-IWD in solving 10 instances of mknapcb1 data set
obtained from the OR-Library. The highlighted (bold) values
denote the best result for each instance. . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
The results of MRMC-IWD for three TSPLIB data sets with
various C settings. Avg. indicates the average tour length of 10
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
The results of MRMC-IWD as compared with those of the
modified IWD algorithm, and GCGA without local search
(Yang et al., 2008). The Error (%) denotes the percentage
deviation of the average tour length from the best known
results. Avg. indicates the average tour length. . . . . . . . . . . . . . . . . . . . .
94
The results of hybrid MRMC-IWD as compared with those of
MRMC-IWD, GCGA with local search (Yang et al., 2008),
improved ABC with local search (Kocer and Akca, 2014)and
PSO (Kocer and Akca, 2014). The error (%) denotes the
percentage of deviation of the average from the best known
result, Avg. indicates the average tour length, "-" indicates that
result is not available in publications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
The results of MRMC-IWD for three RSFS data sets with
various C settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
Table 3.12
Table 3.13
Table 3.16
Table 3.17
Table 4.1
Table 4.2
Table 4.3
Table 4.4
ix
Table 4.5
The results of MRMC-IWD as compared with those from the
modified IWD algorithm and other models published by Jensen
and Shen (2003). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Table 4.6
Comparison between hybrid MRMC-IWD and MRMC-IWD.
Note that column "Iterations" indicates the average number of
iterations required to achieve the optimal solution. . . . . . . . . . . . . . . . . 100
Table 5.1
The main properties of the real UCI data sets. . . . . . . . . . . . . . . . . . . . . . 104
Table 5.2
Parameters setting for the hybrid MRMC-IWD for feature
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Table 5.3
Comparison between FS-MRMC-IWD and four state-of-the-art
methods (i.e., HS,GA,PSO, and HC) published in (Diao and
Shen, 2012), using the consistency-based evaluation technique
in terms of the average subset size and evaluation score.
Symbols v, -, and * respectively, denote that the result is
significantly better, no statistical difference, and worse than
those provided by HS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Table 5.4
Comparison between FS-MRMC-IWD and four state-of-the-art
methods (i.e., HS,GA,PSO, and HC published in Diao and Shen
(2012), (2012), using CFS in terms of the average subset size
and evaluation score. Symbols v, -, and *, respectively, denote
that the result is significantly better, no statistical difference,
and worse than those provided by HS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Table 5.5
Comparison between FS-MRMC-IWD and four state-of-the-art
methods (i.e., HS,GA,PSO, and HC published in Diao and Shen
(2012), using the FRFS evaluation technique in terms of the
average subset size and evaluation score. Symbols v, -, and *,
respectively denote that the result is significantly better, no
statistical difference, and worse than those provided by HS. . . . . . 115
Table 5.6
Classification accuracy rates (measured in %) of C4.5 using
features selected by the consistency-based evaluation technique
and from different optimization methods published in Diao and
Shen (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Table 5.7
C4.5 classification accuracy rates (measured in %) using the
feature subsets selected by CFS and different optimization
methods published in Diao and Shen (2012). . . . . . . . . . . . . . . . . . . . . . . 118
Table 5.8
C4.5 classification accuracy (measured in %) using feature
subsets selected by FRFS and different optimization methods
published in Diao and Shen (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
x
Table 5.9
Comparing the classification accuracies between full and
reduced features using different evaluation techniques.
Highlight (bold) denote that result is significantly better. . . . . . . . . . 120
Table 5.10
Time-domain features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Table 5.11
Frequency-domain features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Table 5.12
Number of samples collected for human motion data set. . . . . . . . . 125
Table 5.13
The results of feature selection for human motion detection
using FS-MRMC-IWD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Table 5.14
Comparing the classification performance accuracies (measured
in %) between full and selected features for human motion
detection. Highlight (bold) denote that result is significantly
better. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Table 5.15
Data samples for fault detection of induction motors. . . . . . . . . . . . . . 130
Table 5.16
The results of feature subset selected using FS-MRMC-IWD
for motor fault detection.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Table 5.17
Comparing the classification accuracies performance (measured
in %) between full and reduced feature sets for motor fault
detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Table A.1
real values Information system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Table A.2
Similarity relation for three features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Table A.3
Positive Regions and Degree of dependency. . . . . . . . . . . . . . . . . . . . . . . 169
xi
LIST OF FIGURES
Page
Figure 1.1
A 3D-fitness landscape of an optimization problem (Coppin,
2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Figure 1.2
The main stages of the research methodology.. . . . . . . . . . . . . . . . . . . . .
10
Figure 2.1
A flowchart shows the fundamental of the IWD algorithm
(Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
Figure 2.2
General taxonomy of optimization methods. . . . . . . . . . . . . . . . . . . . . . .
27
Figure 3.1
An example showing the selection probabilities of five
candidate location according to the FPS method (Alijla et al.,
2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
Sensitivity of FPS method to the scaling function with a
indistinguishable fitness value (Alijla et al., 2014) . . . . . . . . . . . . . . . .
55
Inability of the FPS method to handle the selection dominated
by an outstanding location (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . .
55
Linear probability distribution of 10 individuals with different
values of SP (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
Exponential probability distribution of 10 individuals with
different values of SP (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . .
58
Average length of reducts from 20 runs of the ERS-IWD
algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
Average length of reducts from 20 runs of the LRS-IWD
algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
Decrement of the SP value results in improvement of the
ERS-IWD performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Increment of the SP value results in improvement of the
performance of the LRS-IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . .
70
Figure 4.1
The structure of MRMC-IWD and its communication model. . . .
83
Figure 4.2
The main phases of the MRMC-IWD model. . . . . . . . . . . . . . . . . . . . . .
86
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
xii
Figure 4.3
The convergence trends of MRMC-IWD and hybrid
MRMC-IWD for the first 300 iterations of seven selected
TSPLIB data sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(a) eil51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(b) eil76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(c) eil101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(d) kroA100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(e) kroA200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(f)
lin105 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 4.3(g) lin318 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Figure 5.1
Comparing the bootstrapped means and 95% confidence
intervals of the subset size from FS-MRMC-IWD and average
subset sizes from HS (as published in Diao and Shen (2012)
using the consistency-based evaluation technique. . . . . . . . . . . . . . . . . 107
Figure 5.1(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(c) Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(d) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(e) Ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(f)
Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.1(g) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Figure 5.2
Comparing the average subset sizes of HS (published in Diao
and Shen (2012) with the bootstrap results (i.e., means and 95%
confidence intervals ) of MRMC-IWD using the CFS evaluation
technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(c) Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(d) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(e) Ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
xiii
Figure 5.2(f)
Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.2(g) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.3
Comparing the average subset size of HS published in Diao and
Shen (2012) with the bootstrap results (i.e., mean and 95%
confidence interval) of FS-MRMC-IWD using the FRFS
evaluation technique.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.3(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.3(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.3(c) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.3(d) Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.3(e) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.4
The main components of a pattern recognition system. . . . . . . . . . . 121
Figure A.1
A flowchart shows the fundamental of the IWD algorithm. . . . . . . . 156
Figure A.2
Filter-based approach for feature selection. . . . . . . . . . . . . . . . . . . . . . . . . 157
Figure A.3
Wrapper-based approach feature selection. . . . . . . . . . . . . . . . . . . . . . . . . 158
Figure A.4
Fuzzy Rough Quick Reduct Algorithm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
xiv
LIST OF ABBREVIATIONS
ABC
Artificial Bee Colony
ACO
Ant Colony Optimization
ACS
Ant Colony System
AIWD
Adaptive Intelligent Water Drops
CFS
Correlation-based Feature Selection
CLB
Creek Local Best
EC
Evolutionary Computation
EIWD
Enhanced Intelligent Water Drops
ERS-IWD
Exponential Ranking selection Intelligent Water Drops
FCV
Fold Cross Validation
FFT
Fast Fourier Transform
FPS
Fitness Proportionate Selection
FPS-IWD
Fitness Proportionate Selection Intelligent Water Drops
FRFS
Fuzzy Rough Feature subset Selection
FS
Feature Selection
FS-MRMC-IWD Feature Selection Master River Multiple Creeks Intelligent Water Drops
GA
Genetic Algorithm
GD
Great Deluge
HC
Hill Climbing
HMC
Harmony Memory Consideration
HS
Harmony Search
IILS
Iterative Improvement Local Search
xv
IWD
Intelligent Water Drops
IWD-CO
IWD-Continuous Optimization
LAHC
Late Acceptance Hill Climbing
LRS-IWD
Linear Ranking Selection Intelligent Water Drops
MACO
Mutated Ant Colony Optimization
MHC
Multiple Hill Climbing
MKP
Multiple Knapsack Problem
MLB
Master Local Best
MRMC-IWD
Master River Multiple Creeks Intelligent Water Drops
NB
Naive Bayes
NP-hard
Non-deterministic Polynomial-time hard
PA
Pitch Adjustment
PSO
Particle Swarm Optimization
QoS
Quality of Service
RC
Random Consideration
RMHC
Random Mutation Hill Climbing
RMS
Root Mean Square
RS
Rough Set
RSFS
Rough Set Feature Subset Selection
RST
Rough Set Theory
SA
Simulated Annealing
SI
Swarm Intelligence
SP
Selection Pressure
std
Standard Deviation
xvi
SVM
Support Vector Machine
TSP
Travelling Salesman Problem
UCI
University of California Irvine machine learning repository
USM
Universiti Sains Malaysia
VQNN
Vaguely Quantified Nearest Neighbor
WEKA
Waikato Environment for Knowledge Analysis
xvii
ALGORITMA TITISAN AIR CERDAS TERUBAH
SUAI DAN GABUNGAN SERTA APLIKASINYA
ABSTRAK
Algoritma Titisan Air Cerdas (TAC) ialah model berasaskan kawanan yang sememangnya berguna untuk mengatasi masalah-masalah pengoptimuman. Tujuan utama kajian
ini adalah untuk meningkatkan keupayaan algoritma TAC dan mengatasi keterbatasan algoritma tersebut, yang berkaitan dengan kepelbagaian populasi serta mengimbangangi penerokaan dan pengeksploitasian dalam menangani masalah-masalah pengoptimuman. Pertama, algoritma TAC yang diubahsuai, diperkenalkan. Dua kaedah
pemilihan berdasarkan kedudukan, iaitu kedudukan linear dan kedudukan eksponen,
dicadangkan untuk menggantikan kaedah pemilihan kelekapan yang seimbang. Kedua, algoritma Titisan Air Cerdas yang berdasarkan Sungai Induk Pelbagai Caruk Alir
Sungai (SICAS-TAC) dicadangkan untuk mengeksploitasikan keupayaan penerokaan
algoritma TAC yang diubahsuai. Di samping itu, model hibrid SICAS-TAC juga dibentangkan. Model hibrid ini menggabungkan algoritma SICAS-TAC dengan peningkatan lelaran carian setempat, untuk meningkatkan keupayaan penjelajahan kepada
algoritma SICAS-TAC. Keberkesanan model-model yang dicadangkan dinilai secara
sistematik dan menyeluruh dengan menggunakan tiga masalah pengoptimuman kombinatorik iaitu, masalah pemilihan ciri subset berdasarkan set kasar, masalah beg galas
berbilang, dan masalah jurujual kembara. Kesesuaian dan keberkesanan model hibrid
SICAS-TAC disiasat dengan menyelesaikan masalah pengoptimuman dunia sebenar
xviii
yang berkaitan dengan pemilihan ciri dan klasifikasi. Beberapa set data tanda aras
umum dan dua masalah dunia sebenar, iaitu masalah pengesanan pergerakan manusia
dan masalah pengesanan kerosakan motor, telah dikaji. Keputusan kajian telah menunjukkan keberkesanan model-model yang dicadangkan dalam meningkatkan prestasi algoritma TAC yang asal dan juga menyelesaikan masalah-masalah pengoptimuman
dunia sebenar.
xix
MODIFIED AND ENSEMBLE INTELLIGENT
WATER DROP ALGORITHMS AND THEIR
APPLICATIONS
ABSTRACT
The Intelligent Water Drop (IWD) algorithm is a swarm-based model that is useful for
undertaking optimization problems. The main aim of this research is to enhance the
IWD algorithm and overcome its limitations pertaining to population diversity, as well
as balanced exploration and exploitation in handling optimization problems. Firstly,
a modified IWD algorithm is introduced. Two ranking-based selection methods, i.e.
linear ranking and exponential ranking, are proposed to replace the fitness proportionate selection method. Secondly, the Master River Multiple Creeks Intelligent Water
Drops (MRMC-IWD) algorithm is proposed in an attempt to exploit the exploration
capability of the modified IWD algorithm. In addition, the hybrid MRMC-IWD model
is proposed. It combines MRMC-IWD with the iterated improvement local search
method, to empower MRMC-IWD with the exploitation capability. The usefulness
of the proposed models is evaluated systematically and comprehensively using three
combinatorial optimization problems, i.e., rough set feature subset selection, multiple knapsack problem, and travelling salesman problem. The applicability of the hybrid MRMC-IWD model is investigated to solving real-world optimization problems
related to feature selection and classification tasks. A number of publicly available
benchmark data sets and two real-world problems, namely human motion detection
and motor fault detection, are studied. The results ascertain the effectiveness of the
xx
proposed models in improving the performance of the original IWD algorithm as well
as undertaking real-world optimization problems.
xxi
CHAPTER 1
INTRODUCTION
1.1 Introduction
Optimization is a process that concerns with finding the best solution of a given
problem from among the possible solutions within an affordable time and cost (Weise
et al., 2009). The first step in the optimization process is formulating the optimization
problem through an objective function and a set of constrains that encompass the problem search space (i.e., regions of feasible solutions). Every alternative (i.e., solution) is
represented by a set of decision variables. Each decision variable has a domain, which
is a representation of the set of all possible values that the decision variable can take.
The second step in optimization starts by utilizing an optimization method (i.e., search
method) to find the best candidate solutions. Candidate solution has a configuration
of decision variables that satisfies the set of problem constrains, and that maximizes
or minimizes the objective function (Boussaid et al., 2013). It converges to the optimal solution (i.e., local or global optimal solution) by reaching the optimal values of
the decision variables. Figure 1.1 depicts a 3D-fitness landscape of an optimization
problem. It shows the concept of the local and global optima, where the local optimal
solution is not necessarily the same as the global one (Weise et al., 2009). Optimization can be applied to many real-world problems in various domains. As an example,
mathematicians apply optimization methods to identify the best outcome pertaining to
some mathematical functions within a range of variables (Vesterstrom and Thomsen,
2004). In the presence of conflicting criteria, engineers use optimization methods to
1
Figure 1.1: A 3D-fitness landscape of an optimization problem (Coppin, 2004).
find the best performance of a model subject to certain criteria, e.g. cost, profit, and
quality (Machado et al., 2001; Marler and Arora, 2004; Yildiz, 2009).
In general, optimization problems can be categorized into several categories, depending on whether they are discrete or continuous, single objective or multi-objectives,
and constrained or unconstrained (Boussaid et al., 2013). They can be classified into
discrete or continuous based on the domain of encoding the solution. Solutions of continuous problems are encoded with real-valued variables, while solutions of discrete
problems are encoded with discrete variables. In this light, discrete optimization problems, which are known as combinatorial optimization problems (COPs), include problems that have a finite set of solutions (Blum and Roli, 2003). Optimization problems
can be categorized into constrained and unconstrained based on whether the decision
variables are restricted to some limitations (i.e., constrains) or otherwise. The number of objective function is the distinctive property that differentiates between singleobjective and multi-objectives optimization problems (Marler and Arora, 2004).
2
Numerous optimization methods have been devised and successfully applied to
solving optimization problems. Generally, they can be classified into two main categories: deterministic (exact) and non-deterministic (stochastic) methods (Lin et al.,
2012). Deterministic methods such as linear programming and dynamic programming
exhaustively employ the analytical properties of a problem to search for the optimal
solution. However, no method can be guaranteed to find the optimal solution especially
for NP-hard problems (i.e. problems that have no known solution in polynomial time)
(Lin et al., 2012). Non-deterministic methods search with some randomness to solve
NP-hard problems to achieve good (near-optimal) solutions in polynomial time. In this
regards, meta-heuristic methods play a major role in tackling optimization problems.
They utilize heuristic information within a high-level problem-agonistic framework to
solve optimization problems. In this context, a branch of meta-heuristic optimization
methods that has attracted much attention of researchers is emulating the natural behaviors of real systems in solving optimization problems. These methods are known
as nature-inspired meta-heuristics (Yang, 2010). As an example, the genetic algorithm
(GA) (Holland, 1975; Goldberg and Holland, 1988) is inspired by biological evolution
of organisms, such as inheritance, mutation, crossover, and selection, to solve optimization problems. An innovative family of nature-inspired models known as swarm
intelligence (SI) has emerged (Blum and Li, 2008). SI methods are based on the phenomena of different natural swarms, e.g. ant colony optimization (ACO) inspired by
the foraging behavior of real ants (Dorigo and Di Caro, 1999; Dorigo and Blum, 2005),
particle swarm optimization (PSO) inspired by the social behavior of bird flocking or
fish schooling (Shi, 2001; Kennedy, 2010), artificial bee colony (ABC) inspired by
the foraging behavior of honey bees in their colony (Karaboga, 2005). A variety of SI-
3
based methods have been successfully used in solving different optimization problems.
They are characterized by collaborative learning, i.e., a population of agents collaborates and cooperates among themselves within their environment to solve a problem
(Blum and Li, 2008). Furthermore, the interactions among agents enable the model to
explore several regions of the search space simultaneously, in order to converge to the
global optimum solution in an effective manner (Blum and Li, 2008).
The Intelligent Water Drop (IWD) algorithm (Shah-Hosseini, 2007) is a relatively
recent SI model. It is inspired by the natural phenomenon of water drops flowing with
soil and velocity along a river. It imitates a number of natural phenomena pertaining to
the water drops flowing through an easier path in a river, i.e., a path with less barriers
and obstacles. Technically, the IWD algorithm is a constructive-based meta-heuristic
algorithm (Shah-Hosseini, 2007) that comprises a set of cooperative computational
agents (water drops) iteratively constructing the solution of a problem. The water drop
constructs a solution by traversing a path with a finite set of discrete movements. It
begins the process with an initial state. Thereafter, it iteratively moves step-by-step
passing through several intermediate states (partial solutions) until a final sate (complete solution) is reached. A probabilistic approach is used to control the movements of
the water drops. At every iteration of the IWD algorithm, a new complete population
(i.e., a set of solutions) is generated. The new generation of solutions benefits from the
previous generation through the environment attributes, i.e., soil and velocity. They
are used to control the probability distribution of selecting the candidate movements,
and to extend the partial solution. The soil level indicates the cumulative proficiency
of a particular movement. It represents the communication mechanism that enables the
water drops to cooperate among themselves. The velocity is an attribute that influences
4
the dynamics updating process of the soil level based on heuristic information, which
is related to the problem under scrutiny.
Although the IWD algorithm has been successfully employed to solve numerous
optimization problems (i.e., combinatorial, continuous, and multi-objectives) from different application fields (Siddique and Adeli, 2014), little efforts have been made by
researchers in investigating the fundamental algorithmic aspects of IWD. Many researchers focus on the application field of IWD as an optimization method. This research is focused on investigating the algorithmic aspects of the IWD algorithm to
tackle optimization problems, i.e., how to preserve population diversity and balance
exploration and exploitation of the search process.
The rest of this chapter is organized as follows. Section 1.2 provides the research
motivation and problem statement. Sections 1.3 and 1.4, respectively, present the research objectives and contributions. An overview of the research methodology is presented in Section 1.5. Section 1.6 introduces the research scope. Section 1.7 explains
thesis structure with indication to the contents of each chapter.
1.2 Motivation and Problem Statement
The IWD algorithm was proposed by Shah-Hosseini (2007), adding a new SI-based
nature-inspired optimization method to the literature. It has been shown to be effective
in solving COPs, such as travelling salesman problem (TSP), multiple knapsack problem (MKP), and n-queen puzzle problem (Shah-Hosseini, 2007, 2008, 2012a,b). As
a new meta-heuristic optimization method, IWD has also been successfully applied to
solving numerous optimization problems in different fields (Siddique and Adeli, 2014).
5
However, research to enhance the performance of IWD in solving COPs is still active.
In Niu et al. (2012), five modified schemes that explore three IWD operators (i.e., soil
and velocity values, transition rule, and soil update mechanism) were proposed to enhance the IWD performance. These schemes could overcome the early convergence
and population diversity problems in IWD. Therefore, the key motivation of this research is to investigate the fundamental algorithmic aspects (i.e., population diversity
as well as balance in exploration and exploitation) to enhance the performance of IWD
for undertaking optimization problems.
IWD is a constructive-based meta-heuristic algorithm that iteratively constructs
new solutions at every iteration. The process of solution construction is influenced
by a probabilistic procedure, i.e., fitness proportionate selection (FPS), which is based
on two parameters i.e., soil and velocity. They are updated throughout the solution
construction process at every iteration, in order to guide the search process toward the
optimal solution
The published results by Shah-Hosseini (2007) indicated that good results could
be achieved at the early stage of the IWD optimization process ( i.e., the first few
iterations ). However, all the water drops could stuck at a local solution, and unable
to achieve further improvements. This problem is known as search stagnation (Stützle
and Dorigo, 1999). It is a common problem in constructive, swarm-based optimization
methods, which include IWD (Niu et al., 2012).
Swarm-based optimization methods depend on global optimal solutions found thus
far to generate new solutions. While this technique could lead to good solutions, other
6
sub-optimal solutions could also contribute towards generating better solutions. As
the swarm-based methods inject a strong selection pressure to the global-optimal solutions found thus far, the search process could converge prematurely at a rapid pace.
Conversely, a weak selection pressure could diverse the search to unfavorable regions,
resulting in a slow convergence. Therefore, the Darwinian’s survival of the fittest principle should be observed to control the balance between diversification and intensification during the search process.
The soil update mechanism and FPS are the main factors affecting the selection
pressure in IWD (Niu et al., 2012). After certain number of IWD iterations, it is
possible for lower soil levels to be assigned to the components of the local optimal
solutions. As such, in successive iterations, the water drops are likely to combine
these components in the solution, causing the water drops to be stuck in local optima,
therefore unable to escape and explore another region of the search space.
Furthermore, IWD works with single large population of water drops. Many findings in the literature indicate that re-running IWD with different random initialization
and using the best solution found among all runs could allow IWD to escape from
stagnation (Ahmed and Glasgow, 2012). Splitting the large population into several
small sub-populations and running IWD in an asynchronous way could also maintain
diversity in a good way (Reimann et al., 2004). In addition, the divide-and-conquer
technique can be considered to maintain interaction among the sub-populations.
7
1.3 Research Objectives
The aim of this research is to develop enhanced IWD algorithms, which can be
used to tackle combinatorial optimization problems effectively. The ultimate goal is to
show that enhanced IWD algorithms perform better than the original IWD algorithm
and other state-of-the-art methods in solving COPs.
The primary objectives of this research are as follows:
• to utilize a suitable selection mechanism in the solution construction phase of
the IWD algorithm to enhance its population diversity;
• to modify the IWD algorithm by utilizing the divide-and-conquer and multipopulation strategies to empowering its exploration capability;
• to hybridize the modified IWD algorithm with a local based search method to
enhance its exploitation capability;
• to assess the usefulness of the enhanced IWD algorithms using benchmark COPs
and demonstrating its applicability to real-world problems.
1.4 Research Contributions
In this research, the objectives mentioned in Section 1.3 lead to the following tangible contributions.
• The original IWD algorithm is modified by replacing the fitness proportionate selection method (FPS) in the solution construction phase with two ranking-based
selection methods i.e. the exponential and linear ranking selection methods. This
8
proposed modification results in a model called Modified IWD. It is proposed to
avoid the search stagnation problem by enhancing population diversity.
• An ensemble model of the Modified IWD algorithm is proposed to improve the
exploration capability of the Modified IWD algorithm. The resulting model
is known as the Master River Multiple Creeks IWD model, and is denoted as
MRMC-IWD.
• The MRMC-IWD model is hybridized with a local search algorithm, which enhances local exploitation of the search space; therefore achieving a balance between exploration and exploitation in the resulting model, which known as hybrid MRMC-IWD.
• The applicability of the hybrid MRMC-IWD model is comprehensively assessed
using benchmark and real-world optimization problems. The problems include
UCI (University of California Irvine machine learning repository) benchmark
data sets (Bache and Lichman, 2013) and two real-world problems, namely human motion detection and motor fault detection.
1.5 Research Methodology
Figure 1.2 depicts a three-stage methodology, which has been employed to achieve
the research objectives mentioned in Section 1.3. The first stage modifies the original IWD algorithm to improve its performance for solving COPs. It includes two
subsequent steps: (i) modifies the original IWD algorithm by replacing the original
selection (i.e., FPS) method in the solution construction phase by two ranking-based
selection methods ( i.e., linear and exponential ranking); (ii) modifies the fundamental
9
algorithmic aspect (i.e., exploration) of the IWD by proposing an ensemble model of
the modified IWD algorithms called MRMC-IWD. In each step, benchmark data sets
are used in the experimental study to evaluate the usefulness of the proposed modification. The second stage combines the MRMC-IWD model with a local based method.
Again, evaluation is conducted to assess the effectiveness of the proposed models. The
last stage assess the applicability of the proposed model (i.e., Hybrid MRMC-IWD) to
real-world problems.
Figure 1.2: The main stages of the research methodology.
10
To evaluate the proposed models (i.e. MRMC-IWD and hybrid MRMC-IWD) and
to facilitate performance comparison with other state-of-the-art methods, three case
studies are carried out, namely TSP, MKP, and rough set features subset selection
(RSFS) that are widely used in the literature (Chu and Beasley, 1998; Yu and Liu,
2004; Matthias et al., 2007; Shah-Hosseini, 2008; Xie and Liu, 2009; Smith-Miles and
Lopes, 2012; Azad et al., 2014). These problems are selected because they are NPhard, and have different level of difficulties. The problem complexity (i.e., the number
of alternatives) grows exponentially with respect to the size of the problem (Helsgaun,
2000). Since TSP and MKP have known bounds, they are useful to ascertain the effectiveness of the solutions produced by the proposed models. On the other hand, RSFS
is crucial in pattern recognition applications. Contrary to TSP, RSFS presents strong
inter-dependency among the decision variables (i.e., features). The feature sequences
within the subset are not important, and the optimal solutions are normally unknown
(Yu and Liu, 2004). Contrarily to both TSP and RSFS, the MKP is a constrain based
optimization problem (Shah-Hosseini, 2008; Azad et al., 2014). Therefore, TSP, MKP,
and RSFS problems are selected as case studies to evaluate the usefulness of the proposed models and to benchmark the results against those published in the literature. As
a result, the effectiveness of the proposed models for undertaking general optimization
problems can be validated.
11
1.6 Research Scope
This research focuses on enhancing the performance of the IWD algorithm to tackle
COPs. Three main approaches, namely the selection mechanism in the solution construction phase of the IWD algorithm, the ensemble model of the IWD algorithm with
a novel problem decomposition technique, and the hybrid IWD model have been investigated to overcome the search stagnation problem; therefore improving original IWD
performance. In this context, this research is limited to the use ranking-based selection
methods (i.e., linear and exponential), as well as it is limited to k-means clustering algorithm to decompose the entire problem into few simple sub-problems. To assess the
effectiveness of the proposed models, a series of experiments pertaining to three COPs
(i.e., TSP, RSFS, and MKP) with performance comparison against other state-of-theart methods is conducted. In this regards, this research is limited to the combinatorial
single-objective optimization problems. The applicability of the proposed models to
two real-world problems related to feature selection and classification task, namely
human motion detection and motor fault detection, is investigated.
12
1.7 Thesis Structure
The rest of this thesis is organized as follows:
Chapter 2 (Background and Literature Review): In this chapter, a detailed descriptions of the IWD algorithm, including learning mechanisms, fundamental steps
and mathematical formulation. A review pertaining to optimization and the associated
approaches (i.e., selection methods, multi-populations, and hybridization), which are
used to enhance the performance of the IWD algorithm in solving COPs is presented.
An overview of the evaluation problems (i.e., RSFS, TSP, and MKP) and the associated
data sets used in the experiments are also presented.
Chapter 3 (Modified Intelligent Water Drops Algorithm): This chapter introduces
the first contribution, i.e., the modified IWD algorithm. The effectiveness of the selection mechanism in the solution construction phase of the IWD algorithm is investigated. Two ranking-based methods are proposed to replace the FPS method in the
solutions construction phase of the original IWD algorithm. The experimental results
pertaining to benchmark COPs and evaluation of the proposed ranking-based selection
methods are presented.
Chapter 4 (An Ensemble of Intelligent Water Drops Algorithms): In this chapter
two new contributions are presented. Firstly, the Master-River Multiple-Creek IWD
(MRMC-IWD) model is introduced. The proposed model is motivated by a multipopulation scheme with the divide-and-conquer strategy to simplify the search process, and to exploit the exploration capability of the modified IWD algorithm. Secondly, the hybrid MRMC-IWD model is proposed by hybridizing MRMC-IWD with
13
a local search method, i.e., Iterative Improvement Local search (IILS). The aim is to
empower MRMC-IWD with local exploitation capabilities, therefore achieving a balance between exploration and exploitation. The effectiveness of the proposed models
is investigated using a series of experiments pertaining to the benchmark COPs.
Chapter 5 (Applications of the hybrid MRMC-IWD model): The hybrid MRMCIWD model devised in Chapter 5 is applied to UCI benchmark feature selection and
classification problems. Comparative studies against other state-of-the-art methods are
presented. In addition, two real-world problems, namely human motion detection as
well as motor fault detection are examined, to assess and demonstrate the applicability
of the hybrid MRMC-IWD model.
Chapter 6 (Conclusion): Concluding remarks and a summary of the key findings
are presented in this chapter. A discussion of future researches that can be carried
out to further investigate the enhanced IWD models to handle different optimization
problems is presented.
Appendices (Appendix A): A detail description to feature selection methods is presented. It is mainly organized into two part, First part provides a succinct review of
categories of feature selection methods. In the second part, a detailed description of
rough set and fuzzy rough set for subset feature selection and illustrative example are
provided.
14
CHAPTER 2
BACKGROUND AND LITERATURE REVIEW
2.1 Introduction
The main focus of this research is to enhance the performance of the IWD algorithm to tackle COPs. This chapter is mainly organized into three sections. In section
2.2 a detailed description on the IWD algorithm is presented. Section 2.3 reviews optimization methods and literatures related to the IWD method to solve COPs. Section
2.4 presents an overview of the three COPs (i.e., RSFS, TSP, MKP) as well as the characteristics of the data sets, which are employed in the experimental studies to evaluate
and validate the usefulness of the proposed model and to benchmark the results against
those published in the literature.
2.2 Background to the Intelligent Water Drops Algorithm
In nature, water in a river follows an easier path with fewer barriers and obstacles.
Water flows with a particular speed. Water stream changes the environmental properties of the river, and subsequently changes the direction of water flow to create an
optimal path between the upstream and downstream of a river. The IWD algorithm is
a constructive-based SI optimization method introduced by Shah-Hosseini (2007). It
is inspired by the natural phenomena of water drops moving along the river bed. The
IWD algorithm computationally realizes some of the natural phenomena and uses them
as a computational mechanism to solve COPs. It comprises a number of computational
15
agents (i.e., water drops). At each iteration, water drops construct a solution based on
a finite set of discrete movements. Two key properties of natural water drops are imitated by the IWD algorithm, i.e. velocity and soil, which are changed during a series
of transitions pertaining to the movement of water drops. Each water drop iteratively
moves step-by-step from one location to the next until a complete solution is produced.
It begins with an initial state, i.e. an initial velocity, and carries zero amount of soil.
Water drops cooperate with each other to update the environmental properties, i.e.
soil and velocity. Changes in the soil and velocity parameters have an influential role
on the selection probability of the flow direction. When a water drop moves from one
location to the next, its velocity and soil level are updated. The velocity is changed nonlinearly, and is proportional to the inverse of the amount of soil between two locations.
Therefore, water drops in a path with less soil move faster. The water drop carries an
amount of soil in each movement, which is non-linearly proportional to the inverse of
the time needed by the water drop to move from the current location to the next. On
the other hand, the time taken by a water drop to move from one location to another
is proportional to its velocity and inversely proportional to the distance between two
locations.
Figure 2.1 depicts a flowchart of the fundamental of the IWD algorithm, as presented in Algorithm 2.1. In the following sub-sections, a detailed description of the
problem formulation as well as the main phases of the IWD algorithm i.e. initialization, solution construction, reinforcement, and termination are presented.
16
Figure 2.1: A flowchart shows the fundamental of the IWD algorithm (Alijla et al.,
2014).
17
Algorithm 2.1 : The main steps of the IWD algorithm (Alijla et al., 2014).
1: Input: Data instances.
2: Output: Subset of features.
3: Formulate the optimization problem as fully connected graph.
4: Initialize the static parameters i.e. parameters are not changed during the search
process.
5: while algorithm termination condition is not met do
6:
Initialize the dynamic parameters i.e. parameters changed during the search
process.
7:
Spread iwd number of water drops randomly on a construction graph.
8:
Update the list of visited vertex (Vvisited ), to include the source vertex.
9:
while construction termination condition is not met do
10:
for k = 1 to iwd do
11:
i = the current vertex for drop k.
12:
j = selected next vertex, which does not violate problem constrains.
13:
move drop k from vertex i to vertex j.
14:
update the following parameters.
(a). Velocity of the drop k.
(b). Soil value within the drop k.
(c). Soil value within the edge e(i,j).
15:
end for
16:
end while
17:
Select the best solution in the iteration population (T IB )
18:
Update the soil value of all edges included in the (T IB )
19:
Update the global best solution (T T B )
20:
if quality of T T B < quality of T IB then
21:
T T B = T IB
22:
end if
23: end while
24: return T T B
18
2.2.1 Problem formulation
As shown in Algorithm 2.1 (line 3), formulating an appropriate problem is a preliminary step for solving any optimization problem using the IWD algorithm. The
IWD algorithm uses a fully connected weighted graph called the construction graph
i.e. G(V, E), to represent an optimization problem, where V = {vi |i = 1...N} denotes
the set of vertices in the graph, E = {(i, j)|(i, j) ∈ V × V, i 6= j, i, j = 1...N}. denotes
a set of edges, and N is the total number of decision variables. Consider a solution,
πk = {ak j |k = 1...iwd, j = 1...|Dk |}, where k denotes the index of a solution within
the population, iwd is the total number of solutions in the population (i.e., the number
of water drops), and ak j ∈ A is a set of all possible components of the solution. As
an example, solution πk = {ak1 , ak2 , ..., ak|Dk | }, where |Dk | ≤ N is the dimension of the
solution k, which is one of the possible permutations constructed from the possible
components of A.
2.2.2 Initialization phase
As show in Algorithm 2.1 (line 4), the initialization phase is used to initialize a set
of static and dynamic parameters of the IWD algorithm. Thereafter, the water drops
are spread randomly.
2.2.2(a) Static parameters
The static parameters are initialized with static values, and they remain unchanged
during the search process. They are:
19
• iwd: is the number of water drops, which denotes a set of agents that forms the
solution population.
• Velocity updating parameters (av , bv , cv ): a set of parameters used to control
the velocity update function, as defined in Eq. (2.4)
• Soil updating parameters (as , bs , cs ): a set of parameters used to control the
soil update function, as defined in Eq. (2.7)
• Max_iter: the maximum number of iterations before terminating the IWD algorithm.
• initSoil: the initial value of the local soil.
2.2.2(b) Dynamic parameters
The dynamic parameters are initialized before search begins, and are updated during the search process. They are reverted to their initial values at the beginning of each
iteration. The dynamic parameters are:
• Vkvisited : a list of vertices visited by water drop k.
• intiVelk : the initial velocity of water drop k.
• Soilk : the initial soil loaded on water drop k.
At the beginning, water drops are spread randomly at the vertices of the construction
graph, and Vkvisited is updated to include the initial state (i.e., vertex).
20
2.2.3 Solution construction phase
The main aim of this phase is to construct a population of iwd solutions. A solution comprises a finite set of components, πk = {ak j |k = 1...iwd, j = 1...|Dk |}, Dk is
the dimension of solution k. Water drop k starts with an empty set of solution components, πk = {}. The first vertex of the tour is added to πk whenever the water drop is
spread. Then, at each step of the construction phase, the water drop extends the partial
solution by traversing a new vertex, i.e., a feasible component that does not violate any
constraints of the problem. The construction phase is completed by the transition of all
water drops through the graph until the stopping criteria for constructing a complete
population is met (see Algorithm 2.1, lines 9-16). The construction phase is composed
of the following steps:
2.2.3(a) Edge selection mechanism
Consider water drop k residing at the current vertex i intends to move to the next
vertex j through an edge, e(i, j), where e ∈ E. The probability of selecting e(i, j) is
determined by pki (j), as defined in Eqs. (2.1) and (2.2). Then, the water drop visits
k
vertex j by adding it to Vvisited
.
f (soil(i, j))
pki (j) =
∑
f (soil(i, l))
(2.1)
k
∀l ∈V
/ visited
f (soil(i, j)) =
1
ε + g(soil(i, j))
(2.2)
where ε is a small positive number used to prevent division by zero in function f (.)
21
g(soil(i, j)) =




 soil(i, j)
if



soil(i, l)
 soil(i, j) − min
k
min soil(i, l) > 0,
k
∀l ∈V
/ visited
(2.3)
Otherwise.
∀l ∈V
/ visited
where soil(i, l) refers to the amount of soil within the local path between vertices i,
and j.
2.2.3(b) Velocity and local soil Update
The velocity of water drop k at time t + 1 is denoted by vel k (t + 1). It is updated
every time it moves from vertex i to vertex j using Eq. (2.4).
vel k (t + 1) = vel k (t) +
av
bv + cv ∗ soil2 (i, j)
(2.4)
where av , bv , and cv are the static parameters used to represent the non-linear relationship between the velocity of water drop k (i.e., vel k ) and the inverse of the amount
of soil in the local path (i.e., soil(i, j)). When water drop k moves from vertex i to
vertex j, both soil k (i.e., the soil within water drop k)and soil(i, j) are updated using
Eqs. (2.6) and (2.5) respectively.
soilk = soilk + ∆soil(i, j)
(2.5)
soil(i, j) = (1 − ρn ) ∗ soil(i,j) − ρn ∗ ∆soil(i, j)
(2.6)
22
where ρn is a small positive constant between zero and one, (i.e., 0 < ρn < 1 );
∆soil(i, j) is the amount of soil removed from the local path and carried by the water
drop. Note that ∆soil(i, j) is non-linearly proportional to the inverse of the time needed
for a water drop to travel from the current vertex to the next, as defined in Eq. (2.7).
∆soil(i, j) =
bs + cs
as
2
∗ time (i, j : velk (t + 1))
(2.7)
where as , bs , and cs are the static parameters used to represent the non-linear relationship between ∆soil(i, j) and the inverse of the time. Note that time(i, j : vel k (t +1))
refers to the time needed for water drop k to transit from vertex i to vertex j at time
t + 1. It is proportional to the distance between the two vertices as well as is proportional to the inverse of the vel k (t + 1) as is defined as shown in Eq. (2.8).
time(i, j : velk (t + 1)) =
HUD(i, j)
vel k (t + 1)
(2.8)
where HUD(i, j) refers to a heuristic desirability degree between vertices i and j.
The processes of selecting a vertex to visit as well as updating the velocity and
local soil are iterated subject to the stopping criteria for obtaining a complete solution.
23
2.2.4 Reinforcement phase
As shown in Algorithm 2.1 (lines 17-21), the fittest solution of each population is
known as the iteration-best solution, and is denoted as T IB . It is determined using Eq.
(2.9).
TTB = arg min q(x)
(2.9)
∀l∈T IWB
where q(.) is the fitness function which is used to evaluate the quality of the solutions, and T IW B is the population of the solutions. To reinforce the water drops in the
subsequent iterations to follow T IB and achieve the fittest solution over the iterations,
the soil of all edges in T IB is updated using Eq. (2.10). This update process is known
as global soil update.
soil(i, j) = (1 + ρiwd ) ∗ soil(i,j) − ρiwd ∗
1
q(TIB )
(2.10)
where ρiwd is a small positive constant between zero and one, (i.e., 0 < ρiwd < 1 ).
In each iteration, the best solution (global best), (i.e.,T T B ), is either replaced by
T IB or maintained, as defined in Eq. (2.11).
T
TB
=



 T IB
i f q(T IB ) < q(T TB )


 T TB
Otherwise.
(2.11)
24