Metaheuristic algorithms are significant techniques that have seen a lot of application in recent years in a variety of industries. They are higher-level heuristics that guide the entire search process, allowing for the systematic and efficient discovery of global optimal solutions. There are numerous challenges in engineering that can be solved using optimization techniques. Practically everything in engineering can be optimised. Optimization can be found in a variety of domains, such as quality control, design, and surveillance. Although metaheuristics cannot always guarantee the genuine global optimal solution, they can produce excellent outcomes in a wide range of situations. Under varied difficult constraints, the majority of real-world optimizations are highly nonlinear and multimodal. Different goals are frequently at odds. Even for a single goal, there are situations when optimal solutions do not exist. Finding an ideal or even sub-optimal solution is not an easy undertaking in general. Because money, resources, and time are all finite, making the best use of what is available is critical.
The book aims to shed light on some of the unexplored aspects of metaheuristics and optimization in engineering. In a multidisciplinary perspective, this book elucidates novel approaches and their applications. It goes over the many techniques and methodologies in great detail. It deals with engineering optimization, metaheuristics with machine learning for optimization, mathematical foundations and classic optimization methods. It also focuses on multiobjective algorithms, calculus of variations, random numbers generators, monte carlo methods and genetic algorithms. The goal of this book is to present this difficult subject in an approachable and student-friendly manner. The topics included in this book are of utmost significance and bound to provide incredible insights to readers. Those in search of information to further their knowledge will be greatly assisted by the book.
Preface
1. Introduction to Metaheuristics and its Foundations 1
1. Introduction 1
2. Foundations of optimization and algorithms 3
3. Concepts of metaheuristics optimization 3
4. Ingredients of optimization problems and their classification 4
5. Metaheuristic algorithms for optimization 10
6. Heuristics and metaheuristics 19
7. Advantages and disadvantages of using heuristics 19
Epilogue 21
References 21
2. Engineering Optimization 25
1. Introduction 25
2. Types of optimization 28
3. Optimization algorithms 34
4. Analysis of algorithms 39
5. Time & space complexity 44
6. Algorithm complexity 46
7. No free lunch theorem 48
Epilogue 51
References 51
3. Metaheuristics With Machine Learning for Optimization 54
1. Introduction to metaheuristics 54
2. Using machine learning for enhancing metaheuristics 58
Epilogue 62
References 63
4. Mathematical Foundations 66
1. Introduction 66
2. Upper and lower bounds 67
3. Basic calculus 67
4. Vector and matrix norms 69
5. Eigenvalues and definiteness 78
6. Linear and affine functions 80
Epilogue 84
References 84
5. Classic Optimization Methods 88
1. Introduction 88
2. Unconstrained optimization 88
3. Gradient-based methods 91
4. Constrained optimization 93
5. Linear programming 97
6. Non-linear optimization 101
7. Penalty method 103
8. Lagrange multipliers 103
9. Bfgs method 107
10. Sequential quadratic programming 110
Epilogue 113
References 114
6. Multiobjective Algorithms 117
1. Introduction 117
2. Overview of metaheuristic algorithms in moop 119
3. Archive multi-objective simulated annealing algorithm 119
4. Multi-objective artificial bee colony algorithm 120
5. Multi-objective standard particle swarm optimization
algorithm 120
6. Non-dominated sorting genetic algorithm-ii 121
Epilogue 138
References: 139
7. Calculus of Variations 142
1. Introduction 142
2. Historical background 142
3. General form 143
4. Ordinary differential equation 152
Epilogue 161
References 162
8. Random Numbers generators 165
1. Introduction 165
2. Practical applications and uses 166
3. Generation methods 167
4. Hardware random number generators 169
5. Physical phenomena with random properties 170
6. Pseudorandom number generator 173
7. Uniform distributions 180
8. Metropolis algorithms 182
Epilogue 183
References 183
9. Monte Carlo Methods, Random Walk and Markov Chain 186
1. Introduction to monte carlo methods 186
2. Estimating pi 190
3. Monte carlo algorithm 190
4. Monte carlo integration 191
5. Importance sampling 192
6. Monte carlo simulation 193
7. Introduction to random walk 194
8. Levy flights 198
Epilogue 206
References: 207
10 Genetic Algorithms 210
1. Introduction 210
2. Foundation of genetic algorithms 210
3. Search space 211
4. Genetic algorithms and optimization 212
5. Solving difficulties in ga 215
6. Fundamentals of genetic algorithm 216
7. Implementations 227
8. Limitations 228
9. Application areas in genetic algorithms 230
Epilogue 230
References 231
Stanton Purnell obtained his Ph.D. in Computer and Information Science from Public State University, Plymouth. He is an Assistant Professor at Community College, Nova Scotia. He has over fifteen years of research experience in the field of experimental and computational modeling, simulation, design and optimization of multiphase reactors and separation processes with several industrial realizations.He has written numerous articles in the field of computational mathematics, metaheuristic and engineering optimization.
