Foreword |
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xvii | |
Preface |
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xix | |
Acknowledgments |
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xxiii | |
Authors |
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xxv | |
Chapter 1 Dialectics of Nature: Inspiration for Computing |
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1 | (50) |
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1.1 Inspiration from Nature |
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1 | (1) |
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1.2 Brief History of Natural Sciences |
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2 | (12) |
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3 | (1) |
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3 | (1) |
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1.2.3 Transformation between Heat and Mechanical Energy |
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4 | (3) |
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1.2.4 Transformation between Mass and Energy |
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7 | (2) |
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9 | (1) |
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1.2.6 Sound and Acoustics |
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9 | (1) |
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1.2.7 Hydrology and Dynamics |
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10 | (1) |
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1.2.8 Development in Chemistry |
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11 | (1) |
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1.2.9 Development in Biological Sciences |
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12 | (2) |
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1.3 Traditional Approaches to Search and Optimization |
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14 | (13) |
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16 | (1) |
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1.3.2 Golden Section Search |
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16 | (1) |
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17 | (1) |
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17 | (1) |
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17 | (1) |
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1.3.6 Gradient-Based Methods |
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18 | (1) |
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18 | (1) |
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19 | (1) |
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1.3.6.3 Steepest Descent Method (or Gradient Descent) |
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19 | (1) |
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1.3.7 Classical Newton's Method |
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19 | (1) |
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1.3.8 Modified Newton's Method |
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20 | (1) |
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1.3.9 Levenberg-Marquardt Modification |
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20 | (1) |
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1.3.10 Quasi-Newton Method |
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21 | (1) |
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1.3.11 Conjugate Direction Methods |
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21 | (1) |
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1.3.12 Conjugate Gradient Methods |
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22 | (1) |
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23 | (1) |
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1.3.14 Deterministic vs Stochastic Algorithms |
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23 | (2) |
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1.3.15 Local Search Methods |
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25 | (27) |
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26 | (1) |
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1.3.15.2 Tabu Search (TS) |
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26 | (1) |
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1.3.15.3 Random Search (RS) |
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26 | (1) |
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1.3.15.4 Downhill Simplex (Nelder-Mead) Method |
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26 | (1) |
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27 | (1) |
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1.5 Physics-Based Algorithms |
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28 | (3) |
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1.6 Chemistry-Based Algorithms |
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31 | (1) |
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1.7 Biology-Based Algorithms |
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32 | (4) |
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1.8 Culture-, Society-, and Civilization-Based Algorithms |
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36 | (1) |
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37 | (3) |
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40 | (1) |
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40 | (11) |
Chapter 2 Gravitational Search Algorithm |
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51 | (68) |
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51 | (1) |
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52 | (2) |
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2.2.1 Acceleration of Objects |
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53 | (1) |
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2.2.2 Mass of Moving Objects |
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53 | (1) |
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2.3 Gravitational Search Algorithm |
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54 | (7) |
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61 | (1) |
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62 | (1) |
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62 | (1) |
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63 | (18) |
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63 | (2) |
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65 | (1) |
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2.6.3 Piece-Wise Linear Chaotic Map and Sequential Quadratic Programming with GSA |
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66 | (1) |
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2.6.4 GSA with Chaotic Local Search |
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67 | (1) |
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68 | (1) |
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69 | (1) |
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2.6.7 Opposition-Based GSA |
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70 | (1) |
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2.6.8 GSA with Wavelet Mutation |
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71 | (1) |
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2.6.9 Quantum-Inspired GSA |
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72 | (1) |
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2.6.10 Quantum-Inspired BGSA |
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73 | (1) |
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2.6.11 Piece-Wise Function-Based GSA |
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74 | (1) |
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75 | (1) |
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2.6.13 Mutation-Based GSA |
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76 | (2) |
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76 | (1) |
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2.6.13.2 Reordering Mutation |
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77 | (1) |
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2.6.14 Disruption-Based GSA |
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78 | (1) |
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2.6.15 Random Local Extrema-Based GSA |
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79 | (1) |
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80 | (1) |
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81 | (6) |
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81 | (3) |
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84 | (1) |
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85 | (1) |
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86 | (1) |
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2.7.5 Hybrid K-Harmonic Means and GSA |
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86 | (1) |
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2.8 Application to Engineering Problems |
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87 | (23) |
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2.8.1 Benchmark Function Optimization |
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87 | (1) |
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2.8.2 Combinatorial Optimization Problems |
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88 | (1) |
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2.8.3 Economic Load Dispatch (ELD) Problem |
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88 | (1) |
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2.8.4 Economic and Emission Dispatch (EED) Problem |
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89 | (2) |
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2.8.5 Optimal Power Flow (OPF) Problem |
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91 | (1) |
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2.8.6 Reactive Power Dispatch (RPD) Problem |
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92 | (3) |
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2.8.7 Energy Management System (EMS) |
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95 | (1) |
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96 | (2) |
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2.8.9 Classification Problem |
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98 | (1) |
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2.8.10 Feature Subset Selection (FSS) |
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99 | (2) |
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2.8.11 Parameter Identification |
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101 | (3) |
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104 | (1) |
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2.8.13 Traveling Salesman Problem (TSP) |
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105 | (1) |
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2.8.14 Filter Design and Communication Systems |
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106 | (1) |
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2.8.15 Unit Commitment Problem (UCP) |
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107 | (2) |
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2.8.16 Multiobjective Optimization Problem (MOOP) |
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109 | (1) |
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2.8.17 Fuzzy Controller Design |
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109 | (1) |
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110 | (1) |
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110 | (9) |
Chapter 3 Central Force Optimization |
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119 | (40) |
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119 | (1) |
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3.2 Central Force Optimization Metaphor |
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119 | (5) |
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124 | (4) |
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3.4 Parameters of the CFO Algorithm |
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128 | (1) |
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3.5 Decision Space and Probe Distribution |
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129 | (3) |
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3.5.1 Standard or Fully Connected |
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129 | (1) |
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130 | (1) |
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130 | (1) |
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130 | (1) |
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130 | (1) |
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131 | (1) |
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131 | (1) |
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132 | (8) |
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132 | (1) |
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133 | (1) |
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134 | (1) |
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135 | (1) |
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136 | (2) |
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3.6.6 CFO with Acceleration Clipping |
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138 | (1) |
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138 | (2) |
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140 | (1) |
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140 | (3) |
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3.7.1 Hybrid CFO-Nelder-Mead (CFO-NM) |
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140 | (1) |
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3.7.2 Hybrid CFO and Intelligent State Space Pruning |
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141 | (1) |
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3.7.3 Multistart or Modified CFO (MCFO) |
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142 | (1) |
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3.7.4 Hybrid CFO and Hill-Climbing |
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143 | (1) |
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3.8 Applications to Engineering Problems |
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143 | (11) |
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3.8.1 Electronic Circuit Design |
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143 | (1) |
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144 | (3) |
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3.8.3 Benchmark Function Optimization |
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147 | (3) |
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3.8.4 Training Neural Network |
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150 | (1) |
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3.8.5 Water Pipe Networks |
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151 | (2) |
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3.8.6 Multiobjective CFO Algorithm |
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153 | (1) |
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154 | (1) |
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155 | (1) |
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155 | (4) |
Chapter 4 Electromagnetism-Like Optimization |
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159 | (36) |
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159 | (1) |
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160 | (2) |
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162 | (21) |
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4.3.1 EMO Variants Based on Parameters |
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163 | (6) |
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163 | (1) |
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4.3.1.2 Discrete EMO (DEMO) |
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164 | (2) |
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4.3.1.3 Opposition-Based EMO |
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166 | (1) |
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167 | (1) |
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4.3.1.5 Multipopulation EMO |
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167 | (2) |
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169 | (1) |
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4.3.2 Hybrid EMO with Other Meta-Heuristics |
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169 | (14) |
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4.3.2.1 Hybrid Modified EMO and Scatter Search |
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169 | (1) |
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4.3.2.2 Hybrid EMO and Restarted Arnoldi Algorithm |
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170 | (1) |
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4.3.2.3 Hybrid EMO and Iterated Swap Procedure |
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171 | (1) |
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4.3.2.4 Hybrid EMO and SA |
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172 | (1) |
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4.3.2.5 Hybrid EMO and Solis-Wets Search |
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173 | (1) |
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4.3.2.6 Hybrid EMO and Great Deluge (GD) |
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174 | (2) |
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4.3.2.7 Hybrid EMO and GA |
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176 | (1) |
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4.3.2.8 Species-Based Improved EMO |
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177 | (1) |
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4.3.2.9 Hybrid EMO and Davidon-Fletcher-Powell Search |
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178 | (1) |
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4.3.2.10 Hybrid EMO and PSO |
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179 | (1) |
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4.3.2.11 Hybrid EMO and TS |
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180 | (1) |
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4.3.2.12 Hybrid EMO and DE |
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181 | (2) |
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4.3.2.13 Opposite Sign Test-Based EMO (EMO-OST) |
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183 | (1) |
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4.4 Applications to Engineering Problems |
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183 | (7) |
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4.4.1 Constrained Optimization Problem |
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183 | (1) |
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4.4.2 Traveling Salesman Problem |
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184 | (1) |
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4.4.3 Timetabling Problem |
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184 | (1) |
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4.4.4 Job Shop Scheduling Problem |
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184 | (1) |
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4.4.5 Knapsack Problem (KP) |
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185 | (1) |
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4.4.6 Set Covering Problem |
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185 | (1) |
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4.4.7 Feature Subset Selection |
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185 | (1) |
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4.4.8 Inverse Kinematics Problem in Robotics |
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186 | (1) |
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4.4.9 Vehicle Routing Problem |
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186 | (1) |
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4.4.10 Maximum Betweenness Problem |
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186 | (1) |
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4.4.11 Redundancy Allocation Problem (RAP) |
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186 | (1) |
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4.4.12 Uncapacitated Multiple Allocation p-hub Median Problem |
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187 | (1) |
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4.4.13 Resource-Constrained Project Scheduling (RCPS) Problem |
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188 | (1) |
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4.4.14 Multiobjective Optimization Problem |
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189 | (1) |
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4.4.15 Other Applications |
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189 | (1) |
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190 | (1) |
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190 | (5) |
Chapter 5 Harmony Search |
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195 | (96) |
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195 | (1) |
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196 | (1) |
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5.3 Musical Improvisation |
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197 | (3) |
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200 | (2) |
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5.5 Harmony Search Algorithm |
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202 | (4) |
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5.5.1 Initializing the Optimization Problem and Algorithm Parameters |
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203 | (1) |
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203 | (1) |
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5.5.3 Improvising Harmony from HM |
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203 | (3) |
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5.5.3.1 Harmony Memory Consideration |
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204 | (1) |
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5.5.3.2 Random Consideration |
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205 | (1) |
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205 | (1) |
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206 | (1) |
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206 | (1) |
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5.6 Characteristic Features of Parameters in the HSA |
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206 | (2) |
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208 | (47) |
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5.7.1 HSA Variants Based on Parameters |
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208 | (28) |
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5.7.1.1 Binary Harmony Search (HS) |
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209 | (1) |
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5.7.1.2 Improved HS (IHS) |
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210 | (3) |
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5.7.1.3 Global Best HS (GHS) |
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213 | (2) |
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215 | (2) |
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5.7.1.5 Self-Adaptive GHS |
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217 | (1) |
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218 | (1) |
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219 | (1) |
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220 | (2) |
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222 | (1) |
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5.7.1.10 Dynamic/Parameter Adaptive HS |
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223 | (1) |
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5.7.1.11 Explorative HS (EHS) |
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224 | (1) |
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5.7.1.12 Quantum-Inspired HS |
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225 | (3) |
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5.7.1.13 Opposition-Based HS |
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228 | (1) |
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229 | (2) |
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5.7.1.15 Design-Driven HS (DDHS) |
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231 | (1) |
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232 | (1) |
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5.7.1.17 Harmony Memory (HM) Initialization |
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233 | (1) |
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234 | (1) |
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5.7.1.19 Multiple Pitch Adjustment Rate HS (PAR HS) |
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235 | (1) |
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5.7.1.20 Geometric Selective HS |
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235 | (1) |
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5.7.1.21 Adaptive Binary HS |
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235 | (1) |
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5.7.2 HSA Variants Based on Hybridization with Other Methods |
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236 | (19) |
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5.7.2.1 Hybridizing HS with Other Meta-Heuristic Algorithms |
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236 | (18) |
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5.7.2.2 Hybridizing HS Components into Other Meta-Heuristic Algorithms |
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254 | (1) |
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5.8 Application of HSA to Engineering Problems |
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255 | (21) |
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5.8.1 Function and Constrained Optimization Problems |
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255 | (1) |
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5.8.2 Structural Design Optimization |
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256 | (2) |
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5.8.3 Hydrologic Model Optimization |
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258 | (1) |
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5.8.4 Water Distribution Network (WDN) |
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259 | (1) |
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5.8.5 Water Pump Switching Problem |
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260 | (2) |
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5.8.6 Transmission Network Expansion Planning Problem |
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262 | (2) |
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5.8.7 Job Shop Scheduling |
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264 | (1) |
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5.8.8 Timetabling and Rostering Problem |
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265 | (1) |
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266 | (2) |
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5.8.10 Clustering Problem |
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268 | (3) |
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5.8.11 Combined Heat and Power Economic Dispatch Problem |
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271 | (2) |
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273 | (1) |
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5.8.13 Economic and Emission Dispatch Problem |
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274 | (1) |
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275 | (1) |
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276 | (1) |
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277 | (14) |
Chapter 6 Water Drop Algorithm |
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291 | (38) |
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291 | (1) |
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291 | (4) |
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6.2.1 Sediment Production, Transport, and Storage in the Working River |
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292 | (3) |
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295 | (4) |
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299 | (3) |
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302 | (2) |
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304 | (2) |
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306 | (3) |
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306 | (1) |
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307 | (1) |
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308 | (1) |
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6.7.4 WDA Continuous Optimization Algorithm |
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308 | (1) |
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6.8 Applications to Engineering Problems |
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309 | (17) |
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6.8.1 Traveling Salesman Problem |
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310 | (1) |
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6.8.2 The n-Queen Problem |
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311 | (2) |
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6.8.3 Multidimensional Knapsack Problem |
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313 | (1) |
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6.8.4 Vehicle Routing Problem (VRP) |
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313 | (1) |
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6.8.5 Economic Load Dispatch Problem |
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314 | (1) |
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6.8.6 Combined Economic and Emission Dispatch Problem |
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315 | (1) |
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6.8.7 Reactive Power Dispatch Problem |
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316 | (1) |
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6.8.8 Vehicle Guidance in Road Graph Networks |
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317 | (1) |
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317 | (1) |
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6.8.10 Trajectory Planning |
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318 | (1) |
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319 | (1) |
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6.8.12 Automatic Multilevel Thresholding |
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319 | (1) |
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6.8.13 Data Aggregation and Routing in Wireless Networks |
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320 | (2) |
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6.8.14 Mobile ad hoc Networks (MANET) |
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322 | (1) |
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322 | (1) |
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6.8.16 Web Service Selection |
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322 | (1) |
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6.8.17 Max-Clique Problem |
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323 | (1) |
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6.8.18 Reservoir Operation Problem |
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323 | (1) |
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324 | (1) |
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6.8.20 Steiner Tree Problem |
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325 | (1) |
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6.8.21 Other Applications |
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325 | (1) |
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326 | (1) |
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326 | (3) |
Chapter 7 Spiral Dynamics Algorithms |
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329 | (34) |
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329 | (1) |
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7.2 Spiral Phenomena in Nature |
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329 | (1) |
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7.3 Parametric Representation of Curves |
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329 | (8) |
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7.3.1 Parametric Representation of Spirals |
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330 | (9) |
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7.3.1.1 Archimedes or Arithmetic Spiral |
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332 | (1) |
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7.3.1.2 Hyperbolic Spirals |
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333 | (1) |
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7.3.1.3 Farmat's or Parabolic Spiral |
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334 | (1) |
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335 | (1) |
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336 | (1) |
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337 | (2) |
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339 | (5) |
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339 | (2) |
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7.5.2 n-Dimensional Spiral Models |
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341 | (3) |
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7.6 SpD-Based Optimization Algorithm |
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344 | (2) |
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7.6.1 2-D Spiral Dynamics Optimization Algorithm |
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344 | (1) |
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7.6.2 n-Dimensional SpDO Algorithm |
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345 | (1) |
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7.6.3 Parameters of SpDO Algorithm |
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345 | (1) |
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7.7 Variants of SpDO Algorithm |
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346 | (8) |
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7.7.1 Adaptive SpDO Algorithm |
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346 | (3) |
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7.7.1.1 Linear Adaptive SpDO |
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347 | (1) |
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7.7.1.2 Quadratic Adaptive SpDO |
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348 | (1) |
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7.7.1.3 Exponential Adaptive SpDO |
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348 | (1) |
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7.7.1.4 Fuzzy Adaptive SpDO |
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348 | (1) |
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7.7.2 Hybrid SpDO Algorithms |
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349 | (6) |
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7.7.2.1 Hybrid Spiral-Dynamics Bacterial-Chemotaxis Algorithm |
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349 | (1) |
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7.7.2.2 Hybrid Spiral-Dynamics Random-Chemotaxis Algorithm |
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350 | (1) |
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7.7.2.3 Hybrid Spiral-Dynamics Bacterial-Foraging Algorithm |
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351 | (3) |
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7.8 Stability of Spiral Models |
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354 | (1) |
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7.9 Applications to Engineering Problems |
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355 | (5) |
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7.9.1 Modeling and Control Design |
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357 | (1) |
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7.9.2 Training of Neural Network |
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358 | (1) |
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7.9.3 Combined Economic and Emission Dispatch |
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359 | (1) |
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7.9.4 Clustering Applications |
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359 | (1) |
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360 | (1) |
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360 | (1) |
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360 | (3) |
Chapter 8 Simulated Annealing |
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363 | (52) |
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363 | (1) |
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8.2 Principles of Statistical Thermodynamics |
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363 | (1) |
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364 | (1) |
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365 | (2) |
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8.5 Cooling (Annealing) Schedule |
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367 | (9) |
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8.5.1 Monotonic Schedules (or Simple Time Schedule) |
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369 | (3) |
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8.5.2 Geometric (or Exponential) Cooling Schedule |
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372 | (1) |
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372 | (2) |
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8.5.4 Initial Temperature |
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374 | (1) |
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375 | (1) |
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375 | (1) |
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376 | (1) |
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377 | (7) |
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8.7.1 Boltzmann Annealing |
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377 | (1) |
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377 | (1) |
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8.7.3 Very Fast Simulated Reannealing |
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378 | (1) |
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378 | (1) |
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379 | (1) |
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379 | (2) |
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381 | (1) |
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381 | (1) |
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382 | (1) |
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383 | (1) |
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384 | (1) |
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384 | (9) |
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384 | (1) |
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8.8.2 Hybrid Harmony Search-Based SA |
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385 | (2) |
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387 | (2) |
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8.8.4 Hybrid Ant Colony Optimization and SA |
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389 | (1) |
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8.8.5 Hybrid ACO, GA, and SA |
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390 | (1) |
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390 | (1) |
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8.8.7 Hybrid Artificial Immune System and SA |
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391 | (1) |
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8.8.8 Noising Method with SA |
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392 | (1) |
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393 | (1) |
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8.10 Application to Engineering Problems |
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394 | (12) |
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8.10.1 Travelling Salesman Problem |
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395 | (1) |
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8.10.2 Job-Shop Scheduling Problem |
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396 | (3) |
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399 | (1) |
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8.10.4 Clustering Problem |
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400 | (3) |
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8.10.5 Vertex Covering Problem |
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403 | (2) |
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8.10.6 Flow Shop Sequencing Problem |
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405 | (1) |
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8.10.7 Multiobjective Optimization |
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406 | (1) |
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406 | (1) |
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407 | (8) |
Chapter 9 Chemical Reaction Optimization |
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415 | (32) |
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415 | (5) |
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9.2 Mechanisms of Chemical Reaction |
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420 | (1) |
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9.3 Chemical Reaction Optimization |
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420 | (5) |
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425 | (2) |
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427 | (1) |
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427 | (1) |
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428 | (5) |
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9.6.1 Real-Coded CRO (RCCRO) |
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428 | (2) |
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9.6.2 Opposition-Based CRO |
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430 | (1) |
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431 | (1) |
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9.6.4 Adaptive Collision CRO |
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431 | (1) |
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432 | (1) |
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9.6.6 Artificial Chemical Reaction Optimization (ACRD) Algorithm |
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432 | (1) |
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433 | (2) |
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433 | (1) |
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433 | (1) |
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9.7.3 Hybrid CRO and Lin-Kernighan Local Search |
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434 | (1) |
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435 | (8) |
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9.8.1 Quadratic Assignment Problem |
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435 | (2) |
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9.8.2 Traveling Salesman Problem |
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437 | (1) |
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9.8.3 Resource-Constrained Project Scheduling Problem |
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437 | (1) |
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9.8.4 Economic Load Dispatch Problem |
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438 | (1) |
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9.8.5 Optimal Power Flow Problem |
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439 | (1) |
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9.8.6 Training Neural Networks |
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439 | (1) |
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9.8.7 Fuzzy Rules Learning |
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439 | (1) |
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9.8.8 Communications and Networking Problems |
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|
440 | (2) |
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9.8.8.1 Peer-to-Peer Streaming |
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|
440 | (1) |
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9.8.8.2 Cognitive Radio Spectrum Allocation Problem |
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|
440 | (1) |
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9.8.8.3 Channel Assignment Problem |
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|
440 | (1) |
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9.8.8.4 Network Coding Optimization Problem |
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|
441 | (1) |
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9.8.8.5 Bus Sensor Deployment Problems |
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|
441 | (1) |
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9.8.9 Multiobjective Optimization Problems |
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|
442 | (1) |
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9.8.10 Other Applications |
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442 | (1) |
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|
443 | (1) |
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|
443 | (4) |
Chapter 10 Miscellaneous Algorithms |
|
447 | (106) |
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|
447 | (1) |
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10.2 Big Bang-Big Crunch (BB-BC) Algorithm |
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|
447 | (4) |
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10.2.1 Inspiration and Algorithm |
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|
447 | (3) |
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|
450 | (1) |
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10.3 Black Hole Algorithm |
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|
451 | (4) |
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10.3.1 Inspiration and Algorithm |
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|
451 | (4) |
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|
455 | (1) |
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|
455 | (4) |
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10.4.1 Inspiration and Algorithm |
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|
455 | (4) |
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10.4.1.1 Spiral Chaotic Move |
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|
456 | (1) |
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|
457 | (2) |
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|
459 | (1) |
|
10.5 Artificial Physics Optimization |
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|
459 | (10) |
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10.5.1 Inspiration and Algorithm |
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|
459 | (4) |
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|
463 | (1) |
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|
464 | (1) |
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10.5.4 Extended APO Algorithm |
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|
465 | (1) |
|
10.5.5 Local APO Algorithm |
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|
466 | (1) |
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10.5.6 APO with Feasibility-Based Rule |
|
|
467 | (1) |
|
|
468 | (1) |
|
10.6 Space Gravitational Optimization |
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|
469 | (6) |
|
10.6.1 Inspiration and Algorithm |
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|
469 | (3) |
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|
472 | (1) |
|
10.6.3 Consideration of Shape of Universe in SGO |
|
|
473 | (1) |
|
|
474 | (1) |
|
10.7 Integrated Radiation Optimization |
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|
475 | (4) |
|
10.7.1 Inspiration and Algorithm |
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|
475 | (3) |
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|
478 | (1) |
|
10.8 Gravitational Interactions Optimization |
|
|
479 | (2) |
|
10.8.1 Inspiration and Algorithm |
|
|
479 | (2) |
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|
481 | (1) |
|
10.9 Charged System Search |
|
|
481 | (14) |
|
10.9.1 Inspiration and Algorithm |
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|
481 | (5) |
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|
486 | (1) |
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|
486 | (2) |
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|
488 | (1) |
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|
489 | (3) |
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|
492 | (1) |
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|
493 | (2) |
|
10.10 Hysteretic Optimization |
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|
495 | (2) |
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10.10.1 Inspiration and Algorithm |
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|
495 | (2) |
|
|
497 | (1) |
|
10.11 Colliding Bodies Optimization |
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|
497 | (6) |
|
10.11.1 Inspiration and Algorithm |
|
|
497 | (5) |
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|
502 | (1) |
|
10.12 Ray Optimization (RO) Algorithm |
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|
503 | (4) |
|
10.12.1 Inspiration and Algorithm |
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|
503 | (4) |
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|
507 | (1) |
|
10.13 Extremal Optimization (EO) Algorithm |
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|
507 | (4) |
|
10.13.1 Inspiration and Algorithm |
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|
507 | (2) |
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|
509 | (1) |
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|
510 | (1) |
|
10.14 Particle Collision Algorithm |
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|
511 | (2) |
|
10.14.1 Inspiration and Algorithm |
|
|
511 | (2) |
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|
513 | (1) |
|
10.15 River Formation Dynamics |
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|
513 | (4) |
|
10.15.1 Inspiration and Algorithm |
|
|
513 | (3) |
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|
516 | (1) |
|
10.16 Water Cycle Algorithm |
|
|
517 | (7) |
|
10.16.1 Inspiration and Algorithm |
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|
517 | (6) |
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|
523 | (1) |
|
|
523 | (1) |
|
10.17 Artificial Chemical Process Algorithm |
|
|
524 | (6) |
|
10.17.1 Inspiration and Algorithm |
|
|
524 | (4) |
|
|
528 | (2) |
|
10.18 Artificial Chemical Reaction Optimization Algorithm |
|
|
530 | (3) |
|
10.18.1 Inspiration and Algorithm |
|
|
530 | (1) |
|
|
531 | (2) |
|
10.19 Chemical Reaction Algorithm |
|
|
533 | (4) |
|
10.19.1 Inspiration and Algorithm |
|
|
533 | (3) |
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|
536 | (1) |
|
10.20 Gases Brownian Motion Optimization (GBMO) Algorithm |
|
|
537 | (4) |
|
10.20.1 Inspiration and Algorithm |
|
|
537 | (3) |
|
|
540 | (1) |
|
|
541 | (1) |
|
|
541 | (12) |
Appendix A: Vector and Matrix |
|
553 | (8) |
Appendix B: Random Numbers |
|
561 | (2) |
Appendix C: Chaotic Maps |
|
563 | (4) |
Appendix D: Optimization |
|
567 | (4) |
Appendix E: Probability Distribution Function |
|
571 | (4) |
Index |
|
575 | |