Table Of ContentDiscrete Problems in Nature
Inspired Algorithms
Discrete Problems in Nature
Inspired Algorithms
Anupam Shukla
Ritu Tiwari
CRC Press
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Contents
Foreword I ......................................................................................................................................xv
Foreword II ..................................................................................................................................xvii
Foreword III ..................................................................................................................................xix
Preface ............................................................................................................................................xxi
Acknowledgments ....................................................................................................................xxiii
Authors .........................................................................................................................................xxv
1. Introduction to Optimization Problems .............................................................................1
1.1 Introduction ...................................................................................................................1
1.1.1 Artificial Intelligence ....................................................................................2
1.1.2 Soft Computing .............................................................................................3
1.1.3 Intelligent Systems ........................................................................................3
1.1.4 Expert Systems...............................................................................................4
1.1.5 Inference Systems ..........................................................................................4
1.1.6 Machine Learning .........................................................................................5
1.1.7 Adaptive Learning ........................................................................................5
1.1.8 Related Work Done .......................................................................................6
1.1.8.1 Heuristics ........................................................................................6
1.1.8.2 Meta-Heuristics ..............................................................................6
1.1.8.3 Hyper-Heuristics ............................................................................7
1.1.8.4 Nature-Inspired Computation .....................................................7
1.1.8.5 Multiagent System .........................................................................9
1.1.8.6 Multiagent Coordination ..............................................................9
1.1.8.7 Multiagent Learning ....................................................................10
1.1.8.8 Learning in Uncertainty ..............................................................10
1.1.8.9 Knowledge Acquisition in Graph-Based Problems
Knowledge ....................................................................................10
1.2 Combinatorial Optimization Problems ....................................................................11
1.2.1 Traveling Salesman Problem .....................................................................12
1.2.2 Assignment Problem ..................................................................................12
1.2.3 Quadratic Assignment Problem ................................................................13
1.2.4 Quadratic Bottleneck Assignment Problem ............................................14
1.2.5 0/1 Knapsack Problem ...............................................................................14
1.2.6 Bounded Knapsack Problem .....................................................................15
1.2.7 Unbounded Knapsack Problem ................................................................15
1.2.8 Multichoice Multidimensional Knapsack Problem ................................16
1.2.9 Multidemand Multidimensional Knapsack Problem ............................16
1.2.10 Quadratic Knapsack Problem ....................................................................16
1.2.11 Sharing Knapsack Problem ........................................................................17
1.2.12 Corporate Structuring .................................................................................17
1.2.13 Sequential Ordering Problem ....................................................................18
1.2.14 Vehicle Routing Problem ............................................................................18
1.2.15 Constrained Vehicle Routing Problem .....................................................18
1.2.16 Fixed Charge Transportation Problem .....................................................19
v
vi Contents
1.2.17 Job Scheduling .............................................................................................19
1.2.18 One-Dimensional Bin Packing Problem ..................................................20
1.2.19 Two-Dimensional Bin Packing Problem ..................................................20
1.3 Graph-Based Problems ...............................................................................................21
1.3.1 Graph Coloring Problem ..............................................................................21
1.3.2 Path Planning Problem .................................................................................21
1.3.3 Resource Constraint Shortest Path Problem ..............................................22
1.4 Aim of This Book .........................................................................................................22
1.5 Summary ......................................................................................................................22
Solved Examples ....................................................................................................................23
Exercises ..................................................................................................................................25
References ...............................................................................................................................26
2. Particle Swarm Optimization .............................................................................................29
2.1 Introduction .................................................................................................................29
2.2 Traditional Particle Swarm Optimization Algorithm ............................................30
2.3 Variants of Particle Swarm Optimization Algorithm ............................................31
2.3.1 Sequential Particle Swarm Optimization Algorithm ................................32
2.3.1.1 Random Propagation ...................................................................32
2.3.1.2 Adaptive Schema for Sequential Particle Swarm
Optimization Algorithm .............................................................33
2.3.1.3 Convergence Criterion ................................................................33
2.3.2 Inertia Weight Strategies in Particle Swarm Optimization Algorithm ......34
2.3.2.1 Constant Inertia Weight ..............................................................34
2.3.2.2 Random Inertia Weight ...............................................................34
2.3.2.3 Adaptive Inertia Weight ..............................................................34
2.3.2.4 Sigmoid Increasing Inertia Weight ............................................35
2.3.2.5 Sigmoid Decreasing Inertia Weight ...........................................35
2.3.2.6 Linear Decreasing Inertia Weight ..............................................35
2.3.2.7 The Chaotic Inertia Weight .........................................................35
2.3.2.8 Chaotic Random Inertia Weight .................................................36
2.3.2.9 Oscillating Inertia Weight ...........................................................36
2.3.2.10 Global–Local Best Inertia Weight ...............................................36
2.3.2.11 Simulated Annealing Inertia Weight .........................................36
2.3.2.12 Logarithm Decreasing Inertia Weight .......................................37
2.3.2.13 Exponent Decreasing Inertia Weight .........................................37
2.3.3 Fine Grained Inertia Weight Particle Swarm Optimization
Algorithm ...................................................................................................37
2.3.4 Double Exponential Self-Adaptive Inertia Weight Particle
Swarm Optimization Algorithm ..................................................................38
2.3.5 Double Exponential Dynamic Inertia Weight Particle Swarm
Optimization Algorithm ...............................................................................39
2.3.6 Adaptive Inertia Weight Particle Swarm Optimization Algorithm........40
2.3.7 Chaotic Inertial Weight Approach in Particle Swarm
Optimization Algorithm ...............................................................................41
2.3.7.1 Application of Chaotic Sequences in Particle Swarm
Optimization Algorithm .............................................................41
2.3.7.2 Crossover Operation ....................................................................42
Contents vii
2.3.8 Distance-Based Locally Informed Particle Swarm
Optimization Algorithm ............................................................................42
2.3.8.1 Fitness Euclidean-Distance Ratio Particle Swarm
Optimization ................................................................................42
2.3.9 Speciation-Based Particle Swarm Optimization .....................................43
2.3.10 Ring Topology Particle Swarm Optimization .........................................43
2.3.11 Distance-Based Locally Informed Particle Swarm .................................43
2.3.12 Inertia-Adaptive Particle Swarm Optimization Algorithm with
Particle Mobility Factor ..............................................................................45
2.3.13 Discrete Particle Swarm Optimization Algorithm .................................46
2.3.14 Particle Swarm Optimization Algorithm for Continuous
Applications .................................................................................................47
2.4 Convergence Analysis of Particle Swarm Optimization Algorithm ....................48
2.5 Search Capability of Particle Swarm Optimization Algorithm ............................49
2.6 Summary ......................................................................................................................49
Solved Examples ....................................................................................................................50
Exercises ..................................................................................................................................55
References ...............................................................................................................................56
3. Genetic Algorithms ..............................................................................................................57
3.1 Introduction .................................................................................................................57
3.2 Encoding Schemes ......................................................................................................59
3.2.1 Continuous Value Encoding ......................................................................59
3.2.2 Binary Encoding ..........................................................................................60
3.2.3 Integer Encoding .........................................................................................60
3.2.4 Value Encoding or Real Encoding ............................................................61
3.2.5 Tree Encoding ..............................................................................................61
3.2.6 Permutation Encoding ................................................................................61
3.3 Selection ........................................................................................................................62
3.3.1 Roulette Wheel Selection ............................................................................63
3.3.2 Rank Selection ..............................................................................................63
3.3.3 Tournament Selection .................................................................................64
3.3.4 Steady-State Selection .................................................................................64
3.3.5 Random Selection ........................................................................................64
3.4 Crossover ......................................................................................................................64
3.4.1 Single Point Crossover................................................................................64
3.4.2 N Point Crossover .......................................................................................65
3.4.3 Uniform Crossover ......................................................................................65
3.4.4 Arithmetic Crossover ..................................................................................65
3.4.5 Tree Crossover .............................................................................................66
3.4.6 Order Changing Crossover ........................................................................66
3.4.7 Shuffle Crossover ........................................................................................66
3.5 Mutation .......................................................................................................................66
3.5.1 Inversion Mutation .....................................................................................67
3.5.2 Insertion Mutation ......................................................................................67
3.5.3 Displacement Mutation ..............................................................................67
viii Contents
3.5.4 Reciprocal Exchange Mutation (Swap Mutation) ...................................68
3.5.5 Shift Mutation ..............................................................................................68
3.6 Similarity Template ...................................................................................................68
3.7 Building Blocks .........................................................................................................69
3.8 Control Parameters ...................................................................................................70
3.9 Nontraditional Techniques in GAs .........................................................................70
3.9.1 Genetic Programming .................................................................................71
3.9.2 Discrete Genetic Algorithms ......................................................................71
3.9.3 Genetic Algorithms for Continuous Applications ..................................72
3.10 Convergence Analysis of Genetic Algorithms ......................................................72
3.11 Limitations and Drawbacks of Genetic Algorithms ............................................72
3.12 Summary ....................................................................................................................73
Solved Examples ....................................................................................................................73
Exercises ..................................................................................................................................78
References ...............................................................................................................................78
4. Ant Colony Optimization ...................................................................................................81
4.1 Introduction ...............................................................................................................81
4.2 Biological Inspiration ...............................................................................................81
4.2.1 Competition ..................................................................................................82
4.2.2 High Availability .........................................................................................82
4.2.3 Brownian Motion .........................................................................................82
4.2.4 Pheromones and Foraging .........................................................................83
4.3 Basic Process and Flowchart ...................................................................................84
4.4 Variants of Ant Colony Optimization ....................................................................85
4.4.1 Ant System ...................................................................................................85
4.4.2 Ant Colony Optimization...........................................................................85
4.4.3 Best–Worst Ant System ...............................................................................86
4.4.4 MAX–MIN Ant System ..............................................................................87
4.4.5 Rank-Based Ant System .............................................................................87
4.4.6 Ant-Q .............................................................................................................87
4.4.7 Hyper Cube Ant System .............................................................................88
4.4.8 Mean-Minded Ant Colony Optimization Algorithm .............................88
4.4.8.1 Mathematical Formulations for Mean-Minded
Ant Colony Optimization Algorithm ........................................89
4.5 Applications ...............................................................................................................90
4.6 Summary ....................................................................................................................91
Solved Examples ....................................................................................................................91
Exercises ..................................................................................................................................93
References ...............................................................................................................................93
5. Bat Algorithm ........................................................................................................................95
5.1 Biological Inspiration ...............................................................................................95
5.2 Algorithm ...................................................................................................................95
5.3 Related Work .............................................................................................................96
Solved Examples ..................................................................................................................105
Exercises ................................................................................................................................106
References .............................................................................................................................107
Contents ix
6. Cuckoo Search Algorithm .................................................................................................109
6.1 Introduction ...............................................................................................................109
6.2 Traditional Cuckoo Search Optimization Algorithm ...........................................110
6.3 Variants of Cuckoo Search Algorithm ....................................................................112
6.3.1 Modified Cuckoo Search .............................................................................113
6.3.2 Improved Cuckoo Search Algorithm with Adaptive Method...............113
6.3.3 Multiobjective Cuckoo Search Algorithm for Design
Optimization .......................................................................................115
6.3.3.1 Pareto Front ...................................................................................116
6.3.4 Gradient-Based Cuckoo Search for Global Optimization ......................117
6.4 Applications ...............................................................................................................118
6.4.1 Recognition of Parkinson Disease .............................................................118
6.4.2 Practical Design of Steel Structures ...........................................................118
6.4.3 Manufacturing Optimization Problems ...................................................119
6.4.4 Business Optimization ................................................................................119
6.4.5 Optimized Design for Reliable Embedded System ................................119
6.4.6 Face Recognition ..........................................................................................120
6.5 Summary and Concluding Remarks ......................................................................121
Solved Examples ..................................................................................................................122
Exercises ................................................................................................................................123
References .............................................................................................................................124
7. Artificial Bee Colony ..........................................................................................................127
7.1 Introduction ...............................................................................................................127
7.2 Biological Inspiration ................................................................................................127
7.3 Swarm Behavior ........................................................................................................128
7.3.1 ABC Algorithm.............................................................................................130
7.4 Various Stages of Artificial Bee Colony Algorithm ..............................................131
7.5 Related Work..............................................................................................................132
Solved Examples ..................................................................................................................141
Exercises ................................................................................................................................142
References .............................................................................................................................143
8. Shuffled Frog Leap Algorithm .........................................................................................145
8.1 Introduction ...............................................................................................................145
8.2 Related Work Done ...................................................................................................146
8.2.1 Discrete Shuffled Flog Leaping Algorithm ..............................................150
8.2.2 Quantum Shuffled Frog Leaping Algorithm ...........................................151
Solved Questions .................................................................................................................157
Unsolved Questions ............................................................................................................158
References .............................................................................................................................159
9. Brain Storm Swarm Optimization Algorithm ...............................................................161
9.1 Introduction ...............................................................................................................161
9.2 Brain Storm Optimization ........................................................................................161
9.2.1 Brain Storm Optimization Algorithm .......................................................162
9.3 Related Work in Brain Storm Optimization and Other Contemporary
Algorithms .................................................................................................................164
