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Introduction to Algorithms for Data Mining and Machine Learning

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Introduction to Algorithms for Data Mining and Machine Learning

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Book * 2019

Book * 2019

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Introduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along ... read full description

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Description

Introduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along with optimization techniques. Its strong formal mathematical approach, well selected examples, and practical software recommendations help readers develop confidence in their data modeling skills so they can process and interpret data for classification, clustering, curve-fitting and predictions. Masterfully balancing theory and practice, it is especially useful for those who need relevant, well explained, but not rigorous (proofs based) background theory and clear guidelines for working with big data.

Show more

Introduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along with optimization techniques. Its strong formal mathematical approach, well selected examples, and practical software recommendations help readers develop confidence in their data modeling skills so they can process and interpret data for classification, clustering, curve-fitting and predictions. Masterfully balancing theory and practice, it is especially useful for those who need relevant, well explained, but not rigorous (proofs based) background theory and clear guidelines for working with big data.

Key Features

Presents an informal, theorem-free approach with concise, compact coverage of all fundamental topics

Includes worked examples that help users increase confidence in their understanding of key algorithms, thus encouraging self-study

Provides algorithms and techniques that can be implemented in any programming language, with each chapter including notes about relevant software packages

Show more

Presents an informal, theorem-free approach with concise, compact coverage of all fundamental topics

Includes worked examples that help users increase confidence in their understanding of key algorithms, thus encouraging self-study

Provides algorithms and techniques that can be implemented in any programming language, with each chapter including notes about relevant software packages

Details

Copyright

Copyright © 2019 Elsevier Inc. All rights reserved.

You currently don't have access to this book, however you can purchase separate chapters directly from the table of contents or buy the full version.
Purchase the book

Authors

Xin-She Yang

Middlesex University, School of Science and Technology, London, United Kingdom

# data[].attributes.attachment_link.title
Introduction to Algorithms for Data Mining and Machine Learning

# data[].attributes.attachment_link.description
Book * 2019 Book * 2019 Introduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along ... read full description Introduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along with optimization techniques.

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Paperback ISBN: 9780128219867

eBook ISBN: 9780128219898

Published Date: 14th September 2020

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Nature-Inspired Optimization Algorithms, Second Edition provides an introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, and multi-objective optimization. This book can serve as an introductory book for graduates, for lecturers in computer science, engineering and natural sciences, and as a source of inspiration for new applications.

Key Features

Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature

Provides a theoretical understanding and practical implementation hints

Presents a step-by-step introduction to each algorithm

Includes four new chapters covering mathematical foundations, techniques for solving discrete and combination optimization problems, data mining techniques and their links to optimization algorithms, and the latest deep learning techniques, background and various applications

Readership

Graduates, PhD students and lecturers in computer science, engineering and natural sciences and also researchers and biomedical engineers

Table of Contents

1. Introduction to Algorithms
2. Mathematical Foundations
3. Analysis of Algorithms
4. Random Walks and Optimization
5. Simulated Annealing
6. Genetic Algorithms
7. Differential Evolution
8. Particle Swarm Optimization
9. Firefly Algorithms
10. Cuckoo Search
11. Bat Algorithms
12. Flower Pollination Algorithms
13. A Framework for Self-Tuning Algorithms
14. How to Deal With Constraints
15. Multi-Objective Optimization
16. Data Mining and Deep Learning
Appendix A Test Function Benchmarks for Global Optimization
Appendix B Matlab® Programs

Details

No. of pages:

310

Language:

English

Copyright:

© Academic Press

Published:

Imprint:

Academic Press

Paperback ISBN:

9780128219867

eBook ISBN:

9780128219898

Xin-She Yang

Xin-She Yang obtained his DPhil in Applied Mathematics from the University of Oxford. He then worked at Cambridge University and National Physical Laboratory (UK) as a Senior Research Scientist. He is currently a Reader at Middlesex University London, Adjunct Professor at Reykjavik University (Iceland) and Guest Professor at Xi'an Polytechnic University (China). He is an elected Bye-Fellow at Downing College, Cambridge University. He is also the IEEE CIS Chair for the Task Force on Business Intelligence and Knowledge Management, and the Editor-in-Chief of International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO).

Affiliations and Expertise

School of Science and Technology, Middlesex University, UK

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COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.

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Engineering Mathematics with Examples and Applications

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Engineering Mathematics with Examples and Applications

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Book * 2017

Book * 2017

Book description

Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advan ... read full description

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Table of contents

Description

Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics.

The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs.

Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner.

Show more

Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics.

The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs.

Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner.

Key Features

Covers fundamental engineering topics that are presented at the right level, without worry of rigorous proofs

Includes step-by-step worked examples (of which 100+ feature in the work)

Provides an emphasis on numerical methods, such as root-finding algorithms, numerical integration, and numerical methods of differential equations

Balances theory and practice to aid in practical problem-solving in various contexts and applications

Show more

Covers fundamental engineering topics that are presented at the right level, without worry of rigorous proofs

Includes step-by-step worked examples (of which 100+ feature in the work)

Provides an emphasis on numerical methods, such as root-finding algorithms, numerical integration, and numerical methods of differential equations

Balances theory and practice to aid in practical problem-solving in various contexts and applications

Details

Copyright

Copyright © 2017 Elsevier Inc. All rights reserved.

You currently don't have access to this book, however you can purchase separate chapters directly from the table of contents or buy the full version.
Purchase the book

Authors

Xin-She Yang

Middlesex University, School of Science and Technology, London, United Kingdom

# data[].attributes.attachment_link.title
Engineering Mathematics with Examples and Applications

# data[].attributes.attachment_link.description
Book * 2017 Book * 2017 Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advan ...

# data[].attributes.attachment_link.readable_text
Book * 2014

Book * 2014

Book description

Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorith ... read full description

Browse content

Table of contents

Description

Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization.

This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference.

Show more

Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization.

This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference.

Key Features

Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature

Provides a theoretical understanding as well as practical implementation hints

Provides a step-by-step introduction to each algorithm

Show more

Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature

Provides a theoretical understanding as well as practical implementation hints

Provides a step-by-step introduction to each algorithm

Details

Copyright

Copyright © 2014 Elsevier Inc. All rights reserved.

You currently don't have access to this book, however you can purchase separate chapters directly from the table of contents or buy the full version.
Purchase the book

# data[].attributes.attachment_link.description
Book * 2014 Book * 2014 Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorith ... read full description Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization.

# data[].attributes.headline
Optimization Techniques and Applications with Examples

# data[].attributes.subject
Optimization Techniques and Applications with Examples

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List of Figures xiii

List of Tables xvii

Preface xix

Acknowledgements xxi

Acronyms xxiii

Introduction xxv
Part I Fundamentals 1 1 Mathematical Foundations 3
1.1 Functions and Continuity 3

1.1.1 Functions 3

1.1.2 Continuity 4

1.1.3 Upper and Lower Bounds 4

1.2 Review of Calculus 6

1.2.1 Differentiation 6

1.2.2 Taylor Expansions 9

1.2.3 Partial Derivatives 12

1.2.4 Lipschitz Continuity 13

1.2.5 Integration 14

1.3 Vectors 16

1.3.1 Vector Algebra 17

1.3.2 Norms 17

1.3.3 2D Norms 19

1.4 Matrix Algebra 19

1.4.1 Matrices 19

1.4.2 Determinant 23

1.4.3 Rank of a Matrix 24

1.4.4 Frobenius Norm 25

1.5 Eigenvalues and Eigenvectors 25

1.5.1 Definiteness 28

1.5.2 Quadratic Form 29

1.6 Optimization and Optimality 31

1.6.1 Minimum and Maximum 31

1.6.2 Feasible Solution 32

1.6.3 Gradient and Hessian Matrix 32

1.6.4 Optimality Conditions 34

1.7 General Formulation of Optimization Problems 35

Exercises 36

Further Reading 36
2 Algorithms, Complexity, and Convexity 37
2.1 What Is an Algorithm? 37

2.2 Order Notations 39

2.3 Convergence Rate 40

2.4 Computational Complexity 42

2.4.1 Time and Space Complexity 42

2.4.2 Class P 43

2.4.3 Class NP 44

2.4.4 NP-Completeness 44

2.4.5 Complexity of Algorithms 45

2.5 Convexity 46

2.5.1 Linear and Affine Functions 46

2.5.2 Convex Functions 48

2.5.3 Subgradients 50

2.6 Stochastic Nature in Algorithms 51

2.6.1 Algorithms with Randomization 51

2.6.2 Random Variables 51

2.6.3 Poisson Distribution and Gaussian Distribution 54

2.6.4 Monte Carlo 56

2.6.5 Common Probability Distributions 58

Exercises 61

Bibliography 62
Part II Optimization Techniques and Algorithms 63 3 Optimization 65
3.1 Unconstrained Optimization 65

3.1.1 Univariate Functions 65

3.1.2 Multivariate Functions 68

3.2 Gradient-Based Methods 70

3.2.1 Newton's Method 71

3.2.2 Convergence Analysis 72

3.2.3 Steepest Descent Method 73

3.2.4 Line Search 77

3.2.5 Conjugate Gradient Method 78

3.2.6 Stochastic Gradient Descent 79

3.2.7 Subgradient Method 81

3.3 Gradient-Free Nelder-Mead Method 81

3.3.1 A Simplex 81

3.3.2 Nelder-Mead Downhill Simplex Method 82

Exercises 84

Bibliography 84
4 Constrained Optimization 87
4.1 Mathematical Formulation 87

4.2 Lagrange Multipliers 87

4.3 Slack Variables 91

4.4 Generalized Reduced Gradient Method 94

4.5 KKT Conditions 97

4.6 PenaltyMethod 99

Exercises 101

Bibliography 101
5 Optimization Techniques: Approximation Methods 103
5.1 BFGS Method 103

5.2 Trust-Region Method 105

5.3 Sequential Quadratic Programming 107

5.3.1 Quadratic Programming 107

5.3.2 SQP Procedure 107

5.4 Convex Optimization 109

5.5 Equality Constrained Optimization 113

5.6 Barrier Functions 115

5.7 Interior-PointMethods 119

5.8 Stochastic and Robust Optimization 121

Exercises 123

Bibliography 123
Part III Applied Optimization 125 6 Linear Programming 127
6.1 Introduction 127

6.2 Simplex Method 129

6.2.1 Slack Variables 129

6.2.2 Standard Formulation 130

6.2.3 Duality 131

6.2.4 Augmented Form 132

6.3 Worked Example by Simplex Method 133

6.4 Interior-PointMethod for LP 136

Exercises 139

Bibliography 139
7 Integer Programming 141
7.1 Integer Linear Programming 141

7.1.1 Review of LP 141

7.1.2 Integer LP 142

7.2 LP Relaxation 143

7.3 Branch and Bound 146

7.3.1 How to Branch 153

7.4 Mixed Integer Programming 155

7.5 Applications of LP, IP, and MIP 156

7.5.1 Transport Problem 156

7.5.2 Product Portfolio 158

7.5.3 Scheduling 160

7.5.4 Knapsack Problem 161

7.5.5 Traveling Salesman Problem 161

Exercises 163

Bibliography 163
8 Regression and Regularization 165
8.1 Sample Mean and Variance 165

8.2 Regression Analysis 168

8.2.1 Maximum Likelihood 168

8.2.2 Regression 168

8.2.3 Linearization 173

8.2.4 Generalized Linear Regression 175

8.2.5 Goodness of Fit 178

8.3 Nonlinear Least Squares 179

8.3.1 Gauss-Newton Algorithm 180

8.3.2 Levenberg-Marquardt Algorithm 182

8.3.3 Weighted Least Squares 183

8.4 Over-fitting and Information Criteria 184

8.5 Regularization and Lasso Method 186

8.6 Logistic Regression 187

8.7 Principal Component Analysis 191

Exercises 195

Bibliography 196
9 Machine Learning Algorithms 199
9.1 Data Mining 199

9.1.1 Hierarchy Clustering 200

9.1.2 k-Means Clustering 201

9.1.3 Distance Metric 202

9.2 Data Mining for Big Data 202

9.2.1 Characteristics of Big Data 203

9.2.2 Statistical Nature of Big Data 203

9.2.3 Mining Big Data 204

9.3 Artificial Neural Networks 206

9.3.1 Neuron Model 207

9.3.2 Neural Networks 208

9.3.3 Back Propagation Algorithm 210

9.3.4 Loss Functions in ANN 212

9.3.5 Stochastic Gradient Descent 213

9.3.6 Restricted Boltzmann Machine 214

9.4 Support Vector Machines 216

9.4.1 Statistical Learning Theory 216

9.4.2 Linear Support Vector Machine 217

9.4.3 Kernel Functions and Nonlinear SVM 220

9.5 Deep Learning 221

9.5.1 Learning 221

9.5.2 Deep Neural Nets 222

9.5.3 Tuning of Hyper-Parameters 223

Exercises 223

Bibliography 224
10 Queueing Theory and Simulation 227
10.1 Introduction 227

10.1.1 Components of Queueing 227

10.1.2 Notations 228

10.2 Arrival Model 230

10.2.1 Poisson Distribution 230

10.2.2 Inter-arrival Time 233

10.3 Service Model 233

10.3.1 Exponential Distribution 233

10.3.2 Service Time Model 235

10.3.3 Erlang Distribution 235

10.4 Basic QueueingModel 236

10.4.1 M/M/1 Queue 236

10.4.2 M/M/s Queue 240

10.5 Little's Law 242

10.6 Queue Management and Optimization 243

Exercises 245

Bibliography 246
Part IV Advanced Topics 249 11 Multiobjective Optimization 251
11.1 Introduction 251

11.2 Pareto Front and Pareto Optimality 253

11.3 Choice and Challenges 255

11.4 Transformation to Single Objective Optimization 256

11.4.1 Weighted Sum Method 256

11.4.2 Utility Function 259

11.5 The 𝜖-Constraint Method 261

11.6 Evolutionary Approaches 264

11.6.1 Metaheuristics 264

11.6.2 Non-Dominated Sorting Genetic Algorithm 265

Exercises 266

Bibliography 266
12 Constraint-Handling Techniques 269
12.1 Introduction and Overview 269

12.2 Method of Lagrange Multipliers 270

12.3 Barrier Function Method 272

12.4 PenaltyMethod 272

12.5 Equality Constraints via Tolerance 273

12.6 Feasibility Criteria 274

12.7 Stochastic Ranking 275

12.8 Multiobjective Constraint-Handling and Ranking 276

Exercises 276

Bibliography 277
Part V Evolutionary Computation and Nature-Inspired
Algorithms 279
13 Evolutionary Algorithms 281
13.1 Evolutionary Computation 281

13.3.1 Basic Procedure 284

13.3.2 Choice of Parameters 285

13.4 Simulated Annealing 287

13.5 Differential Evolution 290

Exercises 293

Bibliography 293
14 Nature-Inspired Algorithms 297
14.1 Introduction to SI 297

14.2 Ant and Bee Algorithms 298

14.3 Particle Swarm Optimization 299

14.3.1 Accelerated PSO 301

14.3.2 Binary PSO 302

14.4 Firefly Algorithm 303

14.5 Cuckoo Search 306

14.5.1 CS Algorithm 307

14.5.2 Lévy Flight 309

14.5.3 Advantages of CS 312

14.6 Bat Algorithm 313

14.7 Flower Pollination Algorithm 315

14.8 Other Algorithms 319

Exercises 319

Bibliography 319

Appendix A Notes on Software Packages 323

Appendix B Problem Solutions 329

Index 345

# data[].attributes.attachment_link.title
Optimization Techniques and Applications with Examples

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A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniquesin optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The authora noted expert in the fieldcovers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming.

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Engineering Optimization: An Introduction with Metaheuristic  Applications

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Engineering Optimization: An Introduction with Metaheuristic  Applications

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Description

An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences

From engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insightful examples from various fields of study, the author highlights key concepts and techniques for the successful application of commonly-used metaheuristc algorithms, including simulated annealing, particle swarm optimization, harmony search, and genetic algorithms.

The author introduces all major metaheuristic algorithms and their applications in optimization through a presentation that is organized into three succinct parts:

Foundations of Optimization and Algorithms provides a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method, and the Markov chain Monte Carlo method

Metaheuristic Algorithms presents common metaheuristic algorithms in detail, including genetic algorithms, simulated annealing, ant algorithms, bee algorithms, particle swarm optimization, firefly algorithms, and harmony search

Applications outlines a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems with detailed implementation while also introducing various modifications used for multi-objective optimization

Throughout the book, the author presents worked-out examples and real-world applications that illustrate the modern relevance of the topic. A detailed appendix features important and popular algorithms using MATLAB® and Octave software packages, and a related FTP site houses MATLAB code and programs for easy implementation of the discussed techniques. In addition, references to the current literature enable readers to investigate individual algorithms and methods in greater detail.

Engineering Optimization: An Introduction with Metaheuristic Applications is an excellent book for courses on optimization and computer simulation at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners working in the fields of mathematics, engineering, computer science, operations research, and management science who use metaheuristic algorithms to solve problems in their everyday work.

About the Author

XIN-SHE YANG, PhD, is Senior Research Fellow in the Department of Engineering at Cambridge University (United Kingdom). The Editor-in-Chief of International Journal of Mathematical Modeling and Numerical Optimization (IJMMNO), Dr. Yang has published more than sixty journal articles in his areas of research interest, which include computational mathematics, metaheuristic algorithms, numerical analysis, and engineering optimization.

Table of contents

List of Figures.

Preface.

Acknowledgments.

Introduction.

PART I Foundations of Optimization and Algorithms.

1.1 Before 1900.

1.2 Twentieth Century.

1.3 Heuristics and Metaheuristics.

Exercises.

2 Engineering Optimization.

2.1 Optimization.

2.2 Type of Optimization.

2.3 Optimization Algorithms.

2.4 Metaheuristics.

2.5 Order Notation.

2.6 Algorithm Complexity.

2.7 No Free Lunch Theorems.

Exercises.

3 Mathematical Foundations.

3.1 Upper and Lower Bounds.

3.2 Basic Calculus.

3.3 Optimality.

3.4 Vector and Matrix Norms.

3.5 Eigenvalues and Definiteness.

3.6 Linear and Affine Functions.

3.7 Gradient and Hessian Matrices.

3.8 Convexity.

Exercises.

4 Classic Optimization Methods I.

4.1 Unconstrained Optimization.

4.2 Gradient-Based Methods.

4.3 Constrained Optimization.

4.4 Linear Programming.

4.5 Simplex Method.

4.6 Nonlinear Optimization.

4.7 Penalty Method.

4.8 Lagrange Multipliers.

4.9 Karush-Kuhn-Tucker Conditions.

Exercises.

5 Classic Optimization Methods II.

5.1 BFGS Method.

5.2 Nelder-Mead Method.

5.3 Trust-Region Method.

5.4 Sequential Quadratic Programming.

Exercises.

6 Convex Optimization.

6.1 KKT Conditions.

6.2 Convex Optimization Examples.

6.3 Equality Constrained Optimization.

6.4 Barrier Functions.

6.5 Interior-Point Methods.

6.6 Stochastic and Robust Optimization.

Exercises.

7 Calculus of Variations.

7.1 Euler-Lagrange Equation.

7.2 Variations with Constraints.

7.3 Variations for Multiple Variables.

7.4 Optimal Control.

Exercises.

8 Random Number Generators.

8.1 Linear Congruential Algorithms.

8.2 Uniform Distribution.

8.3 Other Distributions.

8.4 Metropolis Algorithms.

Exercises.

9 Monte Carlo Methods.

9.1 Estimating p.

9.2 Monte Carlo Integration.

9.3 Importance of Sampling.

Exercises.

10 Random Walk and Markov Chain.

10.1 Random Process.

10.2 Random Walk.

10.3 Lévy Flights.

10.4 Markov Chain.

10.5 Markov Chain Monte Carlo.

10.6 Markov Chain and Optimisation.

Exercises.

PART II Metaheuristic Algorithms.

11 Genetic Algorithms.

11.1 Introduction.

11.2 Genetic Algorithms.

11.3 Implementation.

Exercises.

12 Simulated Annealing.

12.1 Annealing and Probability.

12.2 Choice of Parameters.

12.3 SA Algorithm.

12.4 Implementation.

Exercises.

13 Ant Algorithms.

13.1 Behaviour of Ants.

13.2 Ant Colony Optimization.

13.3 Double Bridge Problem.

13.4 Virtual Ant Algorithm.

Exercises.

14 Bee Algorithms.

14.1 Behavior of Honey Bees.

14.2 Bee Algorithms.

14.3 Applications.

Exercises.

15 Particle Swarm Optimization.

15.1 Swarm Intelligence.

15.2 PSO algorithms.

15.3 Accelerated PSO.

15.4 Implementation.

15.5 Constraints.

Exercises.

16 Harmony Search.

16.1 Music-Based Algorithms.

16.2 Harmony Search.

16.3 Implementation.

Exercises.

17 Firefly Algorithm.

17.1 Behaviour of Fireflies.

17.2 Firefly-Inspired Algorithm.

17.3 Implementation.

Exercises.

PART III Applications.

18 Multiobjective Optimization.

18.1 Pareto Optimality.

18.2 Weighted Sum Method.

18.3 Utility Method.

18.4 Metaheuristic Search.

18.5 Other Algorithms.

Exercises.

19 Engineering Applications.

19.1 Spring Design.

19.2 Pressure Vessel.

19.3 Shape Optimization.

19.4 Optimization of Eigenvalues and Frequencies.

19.5 Inverse Finite Element Analysis.

Exercises.

Appendices.

Appendix A: Test Problems in Optimization.

Appendix B: Matlab® Programs.

B.1 Genetic Algorithms.

B.2 Simulated Annealing.

B.3 Particle Swarm Optimization.

B.4 Harmony Search.

B.5 Firefly Algorithm.

B.6 Large Sparse Linear Systems.

B.7 Nonlinear Optimization.

B.7.1 Spring Design.

B.7.2 Pressure Vessel.

Appendix C: Glossary.

Appendix D: Problem Solutions.

References.

Index.

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An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences From engineering and computer science to economics and management science, optimization is a core component for problem solving.

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Springer Tracts in Nature-Inspired Computing

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The book series is aimed at providing an exchange platform for researchers to summarize the latest research and developments related to nature-inspired computing in the most general sense. It includes analysis of nature-inspired algorithms and techniques, inspiration from natural and biological systems, computational mechanisms and models that imitate them in various fields, and the applications to solve real-world problems in different disciplines. The book series addresses the most recent innovations and developments in nature-inspired computation, algorithms, models and methods, implementation, tools, architectures, frameworks, structures, applications associated with bio-inspired methodologies and other relevant areas.

The book series covers the topics and fields of Nature-Inspired Computing, Bio-inspired Methods, Swarm Intelligence, Computational Intelligence, Evolutionary Computation, Nature-Inspired Algorithms, Neural Computing, Data Mining, Artificial Intelligence, Machine Learning, Theoretical Foundations and Analysis, and Multi-Agent Systems. In addition, case studies, implementation of methods and algorithms as well as applications in a diverse range of areas such as Bioinformatics, Big Data, Computer Science, Signal and Image Processing, Computer Vision, Biomedical and Health Science, Business Planning, Vehicle Routing and others are also an important part of this book series.

The series publishes monographs, edited volumes and selected proceedings.

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springer tracts in nature-inspired computing (stnic)

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Springer Tracts in Nature-Inspired Computing (STNIC)

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The book series is aimed at providing an exchange platform for researchers to summarize the latest research and developments related to nature-inspired computing in the most general sense. It includes analysis of nature-inspired algorithms and techniques, inspiration from natural and biological systems, computational mechanisms and models that imitate them in various fields, and the applications to solve real-world problems in different disciplines.

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This book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search. Algorithms are analyzed from a wide spectrum of theories and frameworks to offer insight to the main characteristics of algorithms and understand how and why they work for solving optimization problems. In-depth mathematical analyses are carried out for different perspectives, including complexity theory, fixed point theory, dynamical systems, self-organization, Bayesian framework, Markov chain framework, filter theory, statistical learning, and statistical measures. Students and researchers in optimization, operations research, artificial intelligence, data mining, machine learning, computer science, and management sciences will see the pros and cons of a variety of algorithms through detailed examples and a comparison of algorithms.

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Mathematical Foundations of Nature-Inspired Algorithms | Xin-She Yang | Springer

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This book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search.

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https://www.researchgate.net/profile/Xin-She_Yang

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https://www.amazon.com/s?k=xin-she+yang&i=digital-text

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https://dblp.org/pid/14/6178-1.html

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https://www.scopus.com/authid/detail.uri?authorId=35754063200

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ORCID record for Xin-She Yang. ORCID provides an identifier for individuals to use with their name as they engage in research, scholarship, and innovation activities.