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Table of Contents
Intro; Preface; Contents; About the Authors; 1 Introduction to Optimization; 1.1 Introduction; 1.2 Essence of an Algorithm; 1.3 Unconstrained Optimization; 1.3.1 Univariate Functions; 1.3.2 Multivariate Functions; 1.4 Optimization; 1.5 Gradient-Based Methods; 1.5.1 Newton's Method; 1.5.2 Steepest Descent Method; 1.5.3 Line Search; 1.5.4 Conjugate Gradient Method; 1.5.5 Stochastic Gradient Descent; 1.5.6 Subgradient Method; 2 Nature-Inspired Algorithms; 2.1 A Brief History of Nature-Inspired Algorithms; 2.2 Genetic Algorithms; 2.3 Simulated Annealing; 2.4 Ant Colony Optimization
2.5 Differential Evolution2.6 Particle Swarm Optimization; 2.7 Bees-Inspired Algorithms; 2.8 Bat Algorithm; 2.9 Firefly Algorithm; 2.10 Cuckoo Search; 2.11 Flower Pollination Algorithm; 2.12 Other Algorithms; 3 Mathematical Foundations; 3.1 Convergence Analysis; 3.1.1 Rate of Convergence; 3.1.2 Convergence Analysis of Newton's Method; 3.2 Stability of an Algorithm; 3.3 Robustness Analysis; 3.4 Probability Theory; 3.4.1 Random Variables; 3.4.2 Poisson Distribution and Gaussian Distribution; 3.4.3 Common Probability Distributions; 3.5 Random Walks and Lévy Flights; 3.6 Performance Measures
3.7 Monte Carlo and Markov Chains4 Mathematical Analysis of Algorithms: Part I; 4.1 Algorithm Analysis and Insight; 4.1.1 Characteristics of Nature-Inspired Algorithms; 4.1.2 What's Wrong with Traditional Algorithms?; 4.2 Advantages of Heuristics and Metaheuristics; 4.3 Key Components of Algorithms; 4.3.1 Deterministic or Stochastic; 4.3.2 Exploration and Exploitation; 4.3.3 Role of Components; 4.4 Complexity; 4.4.1 Time and Space Complexity; 4.4.2 Complexity of Algorithms; 4.5 Fixed Point Theory; 4.6 Dynamical System; 4.7 Self-organized Systems; 4.8 Markov Chain Monte Carlo
4.8.1 Biased Monte Carlo4.8.2 Random Walks; 4.9 No-Free-Lunch Theorems; 5 Mathematical Analysis of Algorithms: Part II; 5.1 Swarm Intelligence; 5.2 Filter Theory; 5.3 Bayesian Framework and Statistical Analysis; 5.4 Stochastic Learning; 5.5 Parameter Tuning and Control; 5.5.1 Parameter Tuning; 5.5.2 Parameter Control; 5.6 Hyper-Optimization; 5.6.1 A Multiobjective View; 5.6.2 Self-tuning Framework; 5.6.3 Self-tuning Firefly Algorithm; 5.7 Multidisciplinary Perspectives; 5.8 Future Directions; 6 Applications of Nature-Inspired Algorithms; 6.1 Design Optimization in Engineering
6.1.1 Design of a Spring6.1.2 Pressure Vessel Design; 6.1.3 Speed Reducer Design; 6.1.4 Other Design Problems; 6.2 Inverse Problems and Parameter Identification; 6.3 Image Processing; 6.4 Classification, Clustering and Feature Selection; 6.5 Travelling Salesman Problem; 6.6 Vehicle Routing; 6.7 Scheduling; 6.8 Software Testing; 6.9 Deep Belief Networks; 6.10 Swarm Robots; References; Index
2.5 Differential Evolution2.6 Particle Swarm Optimization; 2.7 Bees-Inspired Algorithms; 2.8 Bat Algorithm; 2.9 Firefly Algorithm; 2.10 Cuckoo Search; 2.11 Flower Pollination Algorithm; 2.12 Other Algorithms; 3 Mathematical Foundations; 3.1 Convergence Analysis; 3.1.1 Rate of Convergence; 3.1.2 Convergence Analysis of Newton's Method; 3.2 Stability of an Algorithm; 3.3 Robustness Analysis; 3.4 Probability Theory; 3.4.1 Random Variables; 3.4.2 Poisson Distribution and Gaussian Distribution; 3.4.3 Common Probability Distributions; 3.5 Random Walks and Lévy Flights; 3.6 Performance Measures
3.7 Monte Carlo and Markov Chains4 Mathematical Analysis of Algorithms: Part I; 4.1 Algorithm Analysis and Insight; 4.1.1 Characteristics of Nature-Inspired Algorithms; 4.1.2 What's Wrong with Traditional Algorithms?; 4.2 Advantages of Heuristics and Metaheuristics; 4.3 Key Components of Algorithms; 4.3.1 Deterministic or Stochastic; 4.3.2 Exploration and Exploitation; 4.3.3 Role of Components; 4.4 Complexity; 4.4.1 Time and Space Complexity; 4.4.2 Complexity of Algorithms; 4.5 Fixed Point Theory; 4.6 Dynamical System; 4.7 Self-organized Systems; 4.8 Markov Chain Monte Carlo
4.8.1 Biased Monte Carlo4.8.2 Random Walks; 4.9 No-Free-Lunch Theorems; 5 Mathematical Analysis of Algorithms: Part II; 5.1 Swarm Intelligence; 5.2 Filter Theory; 5.3 Bayesian Framework and Statistical Analysis; 5.4 Stochastic Learning; 5.5 Parameter Tuning and Control; 5.5.1 Parameter Tuning; 5.5.2 Parameter Control; 5.6 Hyper-Optimization; 5.6.1 A Multiobjective View; 5.6.2 Self-tuning Framework; 5.6.3 Self-tuning Firefly Algorithm; 5.7 Multidisciplinary Perspectives; 5.8 Future Directions; 6 Applications of Nature-Inspired Algorithms; 6.1 Design Optimization in Engineering
6.1.1 Design of a Spring6.1.2 Pressure Vessel Design; 6.1.3 Speed Reducer Design; 6.1.4 Other Design Problems; 6.2 Inverse Problems and Parameter Identification; 6.3 Image Processing; 6.4 Classification, Clustering and Feature Selection; 6.5 Travelling Salesman Problem; 6.6 Vehicle Routing; 6.7 Scheduling; 6.8 Software Testing; 6.9 Deep Belief Networks; 6.10 Swarm Robots; References; Index