DEVELOPMENT OF ARTIFICIAL BEE COLONY
(ABC) VARIANTS AND MEMETIC
OPTIMIZATION ALGORITHMS
NOORAZLIZA BINTI SULAIMAN
UNIVERSITI SAINS MALAYSIA
DEVELOPMENT OF ARTIFICIAL BEE COLONY (ABC)
VARIANTS AND MEMETIC OPTIMIZATION ALGORITHMS
by
NOORAZLIZA BINTI SULAIMAN
Thesis submitted in fulfillment of the requirements for the degree
of Doctor of Philosophy
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ACKNOWLEDGEMENTS
In the name of Allah, The most Gracious, The most Merciful,
First, I would like to praise Allah Almighty for giving me the opportunity and courage to complete this research work.
Secondly, my greatest gratitude goes to my supervisor, Associate Professor Dr. Junita Mohamad Saleh for her willingness to accept me as her postgraduate research student. Due to her continuous discussions, guidance and assistance, I have been able to survive in postgraduate research life and able to complete the objectives on time. Most importantly, her assurance that I am able to pursue my studies in PhD has boosted my confidence to convert from MSc. to PhD. degree. Her guidance has improved my research, writing and presentation skills and has broadened my vision to analyze research problems. Without her guidance, I would not have completed the assigned research tasks in such a short time. I am also highly thankful to her for spending time on correcting this thesis.
Thirdly, my gratitude also goes to my co-supervisor, Assistant Professor Dr. Abdul Ghani Abro who has guided and assisted me throughout this work. I am very thankful for his discussions and guidance which lead to the ideas presented in this research work. With his guidance, I comprehended the research work faster and hence, I have been able to contribute something towards the knowledge of science. Without his guidance and assistance, I am pretty sure that I would have taken more time to complete the research objectives.
Fourthly, I would like to thank my family for their continuous prayers and support during my postgraduate studies. My gratitude also goes to my friends especially those who have been willing to hear my problems and helped me with the ideas to solve them. All the support that I have received has made me able to face all the challenges.
Finally, my special thanks go to the Universiti Sains Malaysia (USM) RU-PRGS No: 1001/PELECT/8036007 and the Ministry of Higher Education (MOHE) FRGS Grants No: 203/PELECT/6071247 for the financial support on the project. Also, the same goes to MOHE’s Mybrain15 (MyPhD) for the scholarship. Without their support, I might not have pursued my studies.
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
TABLE OF CONTENTS iii LIST OF TABLES viii
LIST OF FIGURES xi
LIST OF ABBREVIATIONS xvii
LIST OF SYMBOLS xx
ABSTRAK xxv
ABSTRACT xxvii
CHAPTER ONE: INTRODUCTION 1.1 Background 1
1.2 Research Motivation on Honeybees Algorithms 3
1.3 Problems with ABC Algorithm 4
1.4 Objectives of Research 7
1.5 Thesis Outline 8
CHAPTER TWO: LITERATURE REVIEW 2.1 Introduction 10
2.2 Honeybees Phenomenon 10 2.3 Artificial Bee Colony (ABC) Optimization Algorithms 13 2.3.1 Standard ABC Algorithm 13 2.3.2 ABC Variants 17 2.3.3 Limitations of Existing ABC Variants 28
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2.4 Existing Memetic ABC Optimization Algorithms 30
2.4.1 Evolutionary Gradient Search (EGS) 34
2.5 Performance Analysis of ABC Algorithm 36
2.6 Summary 42
CHAPTER THREE: PROPOSED ABC VARIANTS
3.1 Introduction 44
3.2 Proposed ABC Variants 44
3.2.1 JA-ABC3 44 3.2.2 JA-ABC5 48 3.2.3 JA-ABC5a 50 3.2.4 JA-ABC5b 51 3.2.5 JA-ABC8 52 3.2.6 JA-ABC9 55
3.3 Simulation and Parameter Setup 56
3.4 Assessment of Proposed ABC Variants Performance 57
3.4.1 Determining Optimal Percentage of Poor-fitness Food 58
Sources
3.4.2 Determining Optimal Percentage of Selected-best Food 58
Sources
3.4.3 Performance Evaluation on Benchmark Functions 58
3.5 Results and Discussions 59
3.5.1 Determining Optimal Percentage of Poor-fitness Food 60
Sources
3.5.2 Determining Optimal Percentage of Selected-best Food 64
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3.5.3 Performance Evaluation on Benchmark Functions 67
3.5.4 Overall Comparison Among ABC Variants 108
3.6 Summary 110
CHAPTER FOUR: PROPOSED MEMETIC ABC ALGORITHMS 4.1 Introduction 112
4.2 Proposed Memetic ABC Algorithms 112
4.2.1 Enhanced Evolutionary Gradient Search (EGS) Technique 113 4.2.2 EGSJAABC3 115 4.2.3 EGSJAABC5 116 4.2.4 EGSJAABC5a 118 4.2.5 EGSJAABC5b 118 4.2.6 EGSJAABC8 119 4.2.7 EGSJAABC9 120 4.3 Simulation Setup 120
4.4 Performance Evaluation of Proposed Memetic ABC Algorithms 121
4.5 Results and Discussions 121
4.5.1 Performance results of EGSJAABC3 122
4.5.2 Performance results of EGSJAABC5 129
4.5.3 Performance results of EGSJAABC5a 137
4.5.4 Performance results of EGSJAABC5b 144
4.5.5 Performance results of EGSJAABC8 152
4.5.6 Performance results of EGSJAABC9 159
4.5.7 Overall Comparison Among Memetic ABC Algorithms 167
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CHAPTER FIVE: APPLICATIONS OF PROPOSED MODIFIED ABC ALGORITHMS
5.1 Introduction 171
5.2 Reactive Power Optimization 171
5.2.1 Problem Formulation 172
5.2.2 Parameter Setting 176
5.2.3 Results and Discussions of RPO 177
5.3 Economic Environmental Dispatch 179
5.3.1 Problem Formulation 181
5.3.2 Parameter Setting 185
5.3.3 Results and Discussions of EED 185
5.4 Optimal Digital IIR Filter Design 189
5.4.1 Problem Formulation 190
5.4.2 Parameter Setting 191
5.4.3 Results and Discussions of Digital IIR Filter Design 192
5.5 Summary 197
CHAPTER SIX: CONCLUSIONS & FUTURE WORKS 6.1 Conclusions 198
6.2 Research Contributions 199
6.3 Future Works 202
REFERENCES 204
APPENDICES
Appendix A [The benchmark functions used to select optimal percentage of poor-fitness and selected-best food sources]
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Appendix B [The benchmark functions used to evaluate the proposed ABC variants and memetic ABC]
Appendix C [Results of simulation investigation on selecting the optimal percentage of selected possible solution in enhanced EGS on 10 benchmark functions]
Appendix D [Data of IEEE 30-bus system network]
Appendix E [The transmission lines data of the IEEE 30-bus system network]
Appendix F [Unit data of 6-generator unit system]
Appendix G [Unit data of 10-generator unit system]
LIST OF PUBLICATIONS
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LIST OF TABLES
Page
Table 2.1 Limitations faced by the existing ABC variants 28
Table 3.1 Statistical results of comparing the performance of JA-ABC3 71
with other ABC variants on 27 benchmark functions
Table 3.2 Statistical results of comparing the performance of JA-ABC5 78
with other ABC variants on 27 benchmark functions
Table 3.3 Statistical results of comparing the performance of JA-ABC5a 85
with other ABC variants on 27 benchmark functions
Table 3.4 Statistical results of comparing the performance of JA-ABC5b 91
with other ABC variants on 27 benchmark functions
Table 3.5 Statistical results of comparing the performance of JA-ABC8 98
with other ABC variants on 27 benchmark functions
Table 3.6 Statistical results of comparing the performance of JA-ABC9 104
with other ABC variants on 27 benchmark functions
Table 3.7 Summary of performance comparison among proposed and 109
existing ABC variants
Table 4.1 Statistical results of EGSJAABC3 in comparison to other 125
optimization algorithms on 27 benchmark functions
Table 4.2 Statistical results of EGSJAABC5 in comparison to other 132
optimization algorithms on 27 benchmark functions
Table 4.3 Statistical results of EGSJAABC5a in comparison to other 140
optimization algorithms on 27 benchmark functions
Table 4.4 Statistical results of EGSJAABC5b in comparison to other 147
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Table 4.5 Statistical results of EGSJAABC8 in comparison to other 154
optimization algorithms on 27 benchmark functions
Table 4.6 Statistical results of EGSJAABC9 in comparison to other 162
optimization algorithms on 27 benchmark functions
Table 4.7 Summary of performance comparison among proposed memetic 168
and existing ABC algorithms
Table 5.1 Performance results of the ABC variants and memetic ABC 177
algorithm at solving IEEE 30-bus power system
Table 5.2 Performance results of the optimization algorithms at solving 179
IEEE 30-bus power system
Table 5.3 Performance results of the ABC variants and memetic ABC 186
algorithm at minimizing EED on 6-generator unit system
Table 5.4 Performance results of the optimization algorithms at 186
minimizing EED on 6-generator unit system
Table 5.5 Performance results of the ABC variants and memetic ABC 187
algorithm at minimizing EED on 10-generator unit system
Table 5.6 Performance results of the optimization algorithms at 188
minimizing EED on 10-generator unit system
Table 5.7 The settings of the designed digital IIR filters 192
Table 5.8 Performance results of the optimization algorithms at 193
optimizing LP filter
Table 5.9 Performance results of the optimization algorithms at 194
optimizing HP filter
Table 5.10 Performance results of the optimization algorithms at 195
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Table 5.11 Performance results of the optimization algorithms at 196
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LIST OF FIGURES
Page
Figure 1.1 The figure illustration of bio-inspired computational intelligence 2
Figure 1.2 Statistical graph of publications related to ABC algorithm 4
Figure 1.3 Comparison of convergence performance of ABC and GABC 5
algorithms
Figure 1.4 Comparison of global optimum achievement of ABC and 6
GABC algorithms
Figure 2.1 The illustration of foraging behavior of honeybees 12
Figure 2.2 Flowchart of the standard ABC algorithm 15
Figure 2.3 The performance of GABC and standard ABC on Schaffer 19
and Rastrigin functions
Figure 2.4 The performance of MABC in comparison with standard ABC 24
on Griewank and Weierstrass functions
Figure 2.5 The performance of EPS-ABC to other ABC variants on RS 27
Schwefel Ridges with Noise and RS Schwefel Ridges functions
Figure 2.6 Flowchart of the EGS technique 35
Figure 2.7 Sphere function 38
Figure 2.8 Rosenbrock function 39
Figure 2.9 Rastrigin function 39
Figure 2.10 Schwefel function 40
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Figure 2.12 Expanded Griewank and Rosenbrock function 42
Figure 2.13 Rotated Rastrigin function 42
Figure 3.1 Flowchart of JA-ABC3 with the modified stages highlighted 45
Figure 3.2 Illustration of the interaction among food sources 46
Figure 3.3 Flowchart of JA-ABC5 with the modified stages highlighted 48
Figure 3.4 Flowchart of JA-ABC8 with the modified stages highlighted 53
Figure 3.5 Simulation investigation of poor food source selection on f1 60
Figure 3.6 Simulation investigation of poor food source selection on f2 60
Figure 3.7 Simulation investigation of poor food source selection on f3 61
Figure 3.8 Simulation investigation of poor food source selection on f4 61
Figure 3.9 Simulation investigation of poor food source selection on f5 61
Figure 3.10 Simulation investigation of poor food source selection on f6 62
Figure 3.11 Simulation investigation of poor food source selection on f7 62
Figure 3.12 Simulation investigation of poor food source selection on f8 62
Figure 3.13 Simulation investigation of poor food source selection on f9 63
Figure 3.14 Simulation investigation of poor food source selection on f10 63
Figure 3.15 Simulation investigation of most-fit selected-food sources 64
selection on f1
Figure 3.16 Simulation investigation of most-fit selected-food sources 64
selection on f2
Figure 3.17 Simulation investigation of most-fit selected-food sources 65
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Figure 3.18 Simulation investigation of most-fit selected-food sources 65
selection on f4
Figure 3.19 Simulation investigation of most-fit selected-food sources 65
selection on f5
Figure 3.20 Simulation investigation of most-fit selected-food sources 66
selection on f6
Figure 3.21 Simulation investigation of most-fit selected-food sources 66
selection on f7
Figure 3.22 Simulation investigation of most-fit selected-food sources 66
selection on f8
Figure 3.23 Simulation investigation of most-fit selected-food sources 67
selection on f9
Figure 3.24 Simulation investigation of most-fit selected-food sources 67
selection on f10
Figure 3.25 The fastest convergence performance of JA-ABC3 algorithm 69
on f19
Figure 3.26 The best global optimum achievement result of JA-ABC3 69
algorithm on f26
Figure 3.27 The worst performance of JA-ABC3 algorithm on f21 70
Figure 3.28 The fastest convergence performance of JA-ABC5 algorithm 76
on f24
Figure 3.29 The best global optimum achievement result of JA-ABC5 76
algorithm on f26
Figure 3.30 The worst performance of JA-ABC5 algorithm on f2 77
xiv on f19
Figure 3.32 The best global optimum achievement result of JA-ABC5a 83
algorithm on f26
Figure 3.33 The worst performance of JA-ABC5a algorithm on f20 84
Figure 3.34 The fastest convergence and best global optimum achievement 89
result of JA-ABC5b algorithm on f17
Figure 3.35 The fastest convergence and best global optimum achievement 89
result of JA-ABC5b algorithm on f25
Figure 3.36 The worst performance of JA-ABC5b algorithm on f5 90
Figure 3.37 The fastest convergence performance of JA-ABC8 algorithm 95
on f21
Figure 3.38 The best global optimum achievement result of JA-ABC8 96
algorithm on f27
Figure 3.39 The worst performance of JA-ABC8 algorithm on f14 96
Figure 3.40 The fastest convergence performance of JA-ABC9 102
algorithm on f2
Figure 3.41 The best global optimum achievement result of JA-ABC9 102
algorithm on f26
Figure 3.42 The worst performance of JA-ABC9 algorithm on f17 103
Figure 4.1 Flowchart of enhanced EGS with the modified stages 113
highlighted
Figure 4.2 Flowchart of EGSJAABC3 with the modified and 115
incorporated stages highlighted
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Figure 4.3 Flowchart of EGSJAABC5 with the modified and 117
incorporated stages highlighted
Figure 4.4 Flowchart of EGSJAABC8 with the modified and 119
incorporated stages highlighted
Figure 4.5 The fastest convergence performance of EGSJAABC3 122
algorithm on f19
Figure 4.6 The best global optimum achievement result of 123
EGSJAABC3 algorithm on f27
Figure 4.7 The worst performance of EGSJAABC3 algorithm on f2 123
Figure 4.8 The fastest convergence and best global optimum 130
achievement result of EGSJAABC5 algorithm on f3
Figure 4.9 The fastest convergence and best global optimum 130
achievement result of EGSJAABC5 algorithm on f27
Figure 4.10 The worst performance of EGSJAABC5 algorithm on f18 131
Figure 4.11 The fastest convergence performance of EGSJAABC5a 138
algorithm on f24
Figure 4.12 The best global optimum achievement result of 138
EGSJAABC5a algorithm on f3
Figure 4.13 The worst performance of EGSJAABC5a algorithm on f17 139
Figure 4.14 The fastest convergence performance of EGSJAABC5b 145
algorithm on f20
Figure 4.15 The best global optimum achievement result of 146
EGSJAABC5b algorithm on f26
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Figure 4.17 The fastest convergence performance of EGSJAABC8 152
algorithm on f20
Figure 4.18 The best global optimum achievement result of 152
EGSJAABC8 algorithm on f3
Figure 4.19 The worst performance of EGSJAABC8 algorithm on f17 153
Figure 4.20 The fastest convergence performance of EGSJAABC9 159
algorithm on f5
Figure 4.21 The best global optimum achievement result of 160
EGSJAABC9 algorithm on f26
Figure 4.22 The worst performance of EGSJAABC9 algorithm on f17 160
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LIST OF ABBREVIATIONS
ABC Artificial bee colony algorithm
ACO Ant colony optimization algorithm
AI Artificial intelligence
AIA Artificial immune algorithm
ANN Artificial neural network
BABC Global best ABC algorithm
BIAs Bio-inspired algorithms
BP Band-pass
BS Band-stop
BsfABC Best-so-far ABC algorithm
BSO Bee swarm optimization algorithm
CI Computational intelligence
CLONALG Clonal selection algorithm
CLPSO Comprehensive learning PSO
CS Cuckoo search algorithm
DE Differential evolution
EA Evolutionary algorithm
EABC Enhanced ABC algorithm
EDA Estimation of distribution algorithm
EED Economic Environmental Dispatch
EGA-DQLF Enhanced GA with decoupled quadratic load flow
EGS Evolutionary gradient search
EP Evolutionary programming
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ES Evolutionary strategies
FIR Finite impulse response
GABC Gbest-guided ABC algorithm
GRABC Gbest-influenced random ABC algorithm
HABC Hooke-Jeeves pattern search ABC algorithm
HP High-pass
HRABC Hybrid robust ABC algorithm
HS Harmony search algorithm
HSABCA Hybrid simplex ABC algorithm
HTCMIABC Hybrid Taguchi-chaos of multilevel immune ABC algorithm
IABC Improved ABC algorithm
IIR Infinite impulse response
LP Low-pass
MABC Modified ABC algorithm
MAs Memetic algorithms
MBABC Multiple gbest-guided ABC algorithm
MBO Marriage in honey bees optimization algorithm
MDE Modified DE
MIA Multilevel immune algorithm
MODE Multi objective differential evolution
MSBA Mutable smart bee algorithm
mTSP Multiobjective travelling salesman problem
NM Nelder-Mead
NMSS Nelder-Mead Simplex Search
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NSGA Nondominating sorting GA
PDE Pareto differential evolution
PS-ABC Probability-selection ABC algorithm
PSO Particle swarm optimization algorithm
PSO-cf PSO with constriction factor
RABC Rosenbrock ABC algorithm
RCGA Real coded genetic algorithm
RM Rosenbrock rotational direction method
RPO Reactive power optimization
SaDE Self-adaptive DE
SARGA Self-adaptive real coded GA
SI Swarm intelligence
SPEA Strength pareto EA
TSMA Two-stage ensemble memetic algorithm
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LIST OF SYMBOLS
ai Cost coefficient of EED
ak First-order coefficients of
B00 Loss-coefficient constant of EED
bi Cost coefficient of EED
Bi0 Loss-coefficient-vector of EED
Bij(EED) Loss-coefficient-square-matrix of EED
Bij(RPO) Susceptance between bus i and j of RPO
bk First-order coefficients
C Nonnegative constant used in GABC
ci Cost coefficient of EED
ck1 Second-order coefficients
ck2 Second-order coefficients
D Dimension of search space
di Fuel coefficient of EED
di1 Second-order coefficients
di2 Second-order coefficients
ei Fuel coefficient of EED
fb Fitness values of best-so-far food source used in BsfABC
fi Values of objective function of i-th food source
fiti Fitness values of i-th food source
g Offspring used in EGS
gij Conductance between bus i and j of RPO
Hp Passband magnitude response error
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K Penalty term of EED
L Number of local neighbors used in EGS
M Random positive number used in IABC
MCN Maximum cycle number
Nbus Total number of the system’s buses of RPO
Ngen Total number of generator unit of EED
N Normal distribution used in EGS
NC Number of shunt compensator of RPO
NG Number of generators of RPO
NL Total number of transmission lines of RPO
NT Number of transformer of RPO
p Control parameter used in IABC
P Selective probability used in MABC
PD Active power demand of EED
PDi Active power demand at bus i of RPO
PGi Active power generation at bus i of RPO
PGi min Lower limit of active power generation at bus i of RPO
PGimax Upper limit of active power generation at bus i of RPO
Pi Probability of i-th food source
Pi(EED) Power generated at i-th generator of EED
PL Transmission line losses of EED
Ploss Power transmission loss of the power system of RPO
Pn Sampling frequency in the passband
Qci Shunt compensation at bus i of RPO
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Qci min Lower limit of shunt compensation at bus i of RPO
QDi Reactive power demand at bus i of RPO
QGi Reactive power generation at bus i of RPO
rand Random number in the range of [0,1]
Sn Sampling frequency in the stopband
SN Number of food sources
T User-defined number used in JA-ABC5a
Ti Transformer tap settings of transformer i of RPO
Timax Upper limit of transformer tap settings of transformer i of
RPO
Timin Lower limit of transformer tap settings of transformer i of
RPO
Vi Voltage magnitude at bus I of RPO
Vimax Upper limit of voltage magnitude at bus i of RPO
Vimin Lower limit of voltage magnitude at bus i of RPO
Vj Voltage magnitude at bus j of RPO
ybest,j Best-so-far food source with j-th dimension
ybest,m Best-so-far food source with m-th dimension in IABC
ybj Best-so-far food source with j-th dimension in Bsf ABC
yi Initial solution of EGS technique
yij Food source to be updated with j-th dimension
yim Food source to be updated with m-th dimension in IABC
yii Food source to be replaced in scout-bee phase
yjmax Upper limit of search space
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ykj Randomly chosen k-th food source with j-th dimension
ykm Randomly chosen food source with m-th dimension in IABC
ymj Randomly chosen m-th food source with j-th dimension
ynj Randomly chosen n-th food source with j-th dimension
ypm Randomly chosen food source with m-th dimension in IABC
yr1j Randomly chosen r1-st food source with j-th dimension
yr2j Randomly chosen r2-nd food source with j-th dimension
yr3j Randomly chosen r3-rd food source with j-th dimension
yr4j Randomly chosen r4-th food source with j-th dimension
ypm Selected best solution in enhanced EGS technique
zi Local neighbor to be generated in EGS technique
zij Candidate solution with j-th dimension
zim Candidate solution with m-th dimension
αi First emission coefficient of EED
βi Second emission coefficient of EED
γi Third emission coefficient of EED
δi Fourth emission coefficient of EED
ηi Fifth emission coefficient of EED
θij Angle difference of ij-th transmission line of RPO
Control parameter used in EGS
Global gradient direction used in EGS
ij
Random number in the range of [-1,1]
Random number in the range of [-1,1] used in BsfABCt
