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Advanced Optimization by Nature-Inspired Algorithms
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This book, compiles, presents, and explains the most important meta-heuristic and evolutionary optimization algorithms whose successful performance has been proven in different fields of engineering, and it includes application of these algorithms to important engineering optimization problems. In addition, this book guides readers to studies that have implemented these algorithms by providing a literature review on developments and applications of each algorithm. This book is intended for students, but can be used by researchers and professionals in the area of engineering optimization.
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Table of Contents

Chapter 1: Overview of Optimization Summary This chapter briefly explains optimization and its basic concepts. Also, examples of the different types of engineering optimization problems are presented in this chapter. 1.1 Optimization 1.2 Examples of engineering optimization problems 1.3 Conclusion Chapter 2: Introduction to Meta-heuristic and Evolutionary Algorithms Summary This chapter begins with a brief review of different independent-problem methods for searching the decision space, describes the components of meta-heuristic and evolutionary algorithms by relating them to engineering optimization problems. Other related topics such as coding meta-heuristic and evolutionary algorithms, dealing with constraints, objective functions, solution strategies, are reviewed. A general algorithm is presented that encompasses most of the steps of all known meta-heuristic and evolutionary algorithms. This generic presentation provides a standard reference with which to compare all the known meta-heuristic and evolutionary algorithms. The chapter closes with the performance evaluation of the meta-heuristic and evolutionary algorithms covered by the book. 2.1 Searching decision space for optima 2.2 Definition of terms related meta-heuristic and evolutionary algorithms 2.3 Foundation of meta-heuristic and evolutionary algorithms 2.4 Classification of meta-heuristic and evolutionary algorithms 2.5 Coding meta-heuristic and evolutionary algorithms in both discrete and continuous domains 2.6 Generating random values 2.7 Dealing with constraints 2.8 Fitness functions 2.9 Selection of decision variables, parameters 2.10 Generating new solutions 2.11 The best solution 2.12 Termination criteria 2.13 General algorithm 2.14 Performance evaluation of meta-heuristic and evolutionary algorithms 2.15 Conclusion Chapter 3: Pattern Search (PS) Summary This chapter explains the pattern search (PS) algorithm, which is classified as a direct search method. The chapter starts with a brief literature review of the development of PS, important modification of the algorithm, and its applications to engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the different steps of the algorithm are described in detail. A pseudo code of the algorithm is presented that serves as an easy and sufficient guideline for coding the algorithm. 3.1 Introduction 3.2 Pattern search (PS) foundation 3.3 Generating initial solution 3.4 Generate trial solutions 3.5 Update mesh size 3.6 Termination criteria 3.7 User-defined parameters of the PS 3.8 Pseudo code of the PS 3.9 Conclusion 3.10 References Chapter 4: The Genetic Algorithm (GA) Summary This chapter describes the genetic algorithm (GA), which is a well-known evolutionary algorithm. The chapter starts with a brief literature review of the GA's development, followed by presentation of the modification that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the different steps of the algorithm are described in detail. A pseudo code of the algorithm is presented that serves as an easy and sufficient guideline for coding the algorithm. 4.1 Introduction 4.2 Mapping natural evolution into genetic algorithm (GA) 4.3 Creating the initial population 4.4 Selection of decision variables, parameters 4.4.1. Proportionate selection 4.4.2. Ranking selection 4.4.3. Tournament selection 4.5 Reproduction 4.6 Population diversity and selective pressure4.7 Termination criteria 4.8 User-defined parameters of the GA 4.9 Pseudo code of the GA 4.10 Conclusion 4.11 References Chapter 5: Simulated Annealing (SA) Summary This explains the simulated annealing (SA) algorithm, which is inspired by the process of annealing in metal work. The chapter starts with a brief literature review of the SA development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 5.1 Introduction 5.2 Mapping physical annealing process into simulated annealing (SA) algorithm 5.3 Generating initial state 5.4 Generating a new state 5.5 Acceptance function 5.6 Temperature equilibrium 5.7 Temperature reduction 5.8 Termination criteria 5.9 User-defined parameters of the SA 5.10 Pseudo code of the SA 5.11 Conclusion 5.12 References Chapter 6: The Tabu Search Algorithm (TSA) Summary This chapter explains the Tabu search algorithm (TSA) which is combinatorial in nature. The chapter starts with a brief literature review of the TSA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding.6.1 Introduction 6.2 Tabu search foundation 6.3 Generating initial searching point 6.4 Neighbor points 6.5 Tabu list 6.6 Updating Tabu list 6.7 Attributive Memory 6.8 Aspiration criteria 6.9 Intensification and diversification strategies 6.10 Termination criteria6.11 User-defined parameters of the TS 6.12 Pseudo code of the TS 6.13 Conclusion 6.14 References Chapter 7: Ant Colony Optimization (ACO) Summary This chapter explains ant colony optimization (ACO). The basic concepts of the ACO are derived from nature and are based on the forging behavior of ants. The chapter starts with a brief literature review of ACO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding.7.1 Introduction 7.2 Mapping ants' behavior into ant colony optimization (ACO) 7.3 Creating the initial population 7.4 Allocating pheromone to decision space 7.5 Generation new solutions 7.6 Termination criteria 7.7 User-defined parameters of the ACO 7.8 Pseudo code of the ACO 7.9 Conclusion 7.10 References Chapter 8: Particle Swarm Optimization (PSO) Summary This describes the particle swarm optimization (PSO) technique which is based on the swarm intelligence mechanism and behavior of swarms. The chapter starts with a brief literature review of the PSO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 8.1 Introduction 8.2 Mapping social behavior into particle swarm optimization 8.3 Creating the initial population of particles 8.4 Personal and global best position 8.5 Velocities of particles 8.6 Update the particle's position 8.7 Termination criteria 8.8 User-defined parameters of the PSO 8.9 Pseudo code of the PSO 8.10 Conclusion 8.11 References Chapter 9: Differential Evolution (DE) Summary This chapter describes differential evolution (DE). The DE, which is basically a parallel direct search method that takes advantage of some features of evolutionary algorithms (EAs), is a simple yet powerful meta-heuristic method. The chapter starts with a brief literature review of DE's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 9.1 Introduction 9.2 Differential evolution (DE) foundation 9.3 Creating the initial population 9.4 Generating trial solutions 9.5 Greedy criteria 9.6 Termination criteria 9.7 User-defined parameters of the DE 9.8 Pseudo code of the DE 9.9 Conclusion 9.10 References Chapter 10: Harmony Search (HS) Summary This chapter describes the harmony search (HS) which is a meta-heuristic algorithm for discrete optimization. The chapter starts with a brief literature review of HS's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 10.1 Introduction 10.2 Inspiration of harmony search (HS) 10.3 Initializing harmony memory 10.4 Improvising new harmony 10.5 Updating the harmony memory 10.6 Termination criteria 10.7 User-defined parameters of the HS 10.8 Pseudo code of the HS 10.9 Conclusion<10.10 References Chapter 11: The Shuffled Frog-Leaping Algorithm (SFLA) Summary This chapter explains the shuffled frog-leaping algorithm (SFLA). The SFLA is a swarm intelligence algorithm based on the memetic evolution of the social behavior of frogs. The chapter starts with a brief literature review of SFLA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 11.1 Introduction 11.2 Mapping memtic evolution of frogs into the SFLA 11.3 Creating the initial population 11.4 Classification of frogs into memeplexes 11.5 Frog leaping 11.6 Shuffling process 11.7 Termination criteria 11.8 User-defined parameters of the SFLA 11.9 Pseudo code of the SFLA 11.10 Conclusion 11.11 References Chapter 12: Honey-Bee Mating Optimization (HBMO) Summary This chapter describes the honey-bee mating optimization (HBMO) algorithm which is based on the honey-bees' social structure and mating in the bee hive. The chapter starts with a brief literature review of HBMO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 12.1 Introduction 12.2 Mapping honey-bee colony structure into the HBMO algorithm 12.3 Creating the initial population 12.4 Queen 12.5 Drone selection 12.6 Brood production 12.7 Improving broods by workers 12.8 Termination criteria12.9 User-defined parameters of the HBMO 12.10 Pseudo code of the HBMO 12.11 Conclusion 12.12 References Chapter 13: Invasive Weed Optimization (IWO) Summary This chapter describes the invasive weed optimization (IWO) algorithm which mimics the adaptive and evolutionary characteristics of weeds. The chapter starts with a brief literature review of IWO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 13.1 Introduction 13.2 Mapping weeds' biology into invasive weed optimization (IWO) 13.3 Creating the initial population 13.4 Reproduction 13.5 Spread of seeds 13.6 Eliminate weeds with low fitness 13.7 Termination criteria 13.8 User-defined parameters of the IWO 13.9 Pseudo code of the IWO 13.10 Conclusion 13.11 References Chapter 14: Central Force Optimization (CFO) Summary This chapter describes the central force optimization (CFO) algorithm. The basic concepts of the CFO come from kinesiology in physics. The chapter starts with a brief literature review of CFO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 14.1 Introduction 14.2 Mapping Newton's gravitational low into the central force optimization (CFO) 14.3 Initializing the position of probes 14.4 Calculation of accelerations 14.5 Movement of Probes 14.6 Modification of deviated probes 14.7 Termination criteria 14.8 User-defined Parameters of the CFO 14.9 Pseudo code of the CFO 14.10 Conclusion 14.11 References Chapter 15: Biogeography-Based Optimization (BBO) Summary This chapter describes the biogeography-based optimization (BBO) which is inspired by the science of biogeography. The chapter starts with a brief literature review of BBO's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 15.1 Introduction 15.2 Mapping biogeography concepts into biogeography-based optimization (BBO) 15.3 Creating the initial population 15.4 Migration process 15.5 Mutation 15.6 Termination criteria 15.7 User-define parameters of the BBO 15.8 Pseudo code of the BBO 15.9 Conclusion 15.10 References Chapter 16: The Firefly Algorithm (FA) Summary This chapter describes the firefly algorithm (FA) which is inspired by the flashing light emitted by fireflies. The chapter starts with a brief literature review of the FA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 16.1 Introduction 16.2 Mapping behavior of fireflies into firefly algorithm (FA) 16.3 Creating the initial population 16.4 Attractiveness 16.5 Distance and Movement 16.6 Termination criteria 16.7 User defined parameters of the FA16.8 Pseudo code of the FA 16.9 Conclusion 16.10 References Chapter 17: The Gravity Search Algorithm (GSA) Summary This chapter explains the gravity search algorithm (GSA). The GSA is an evolutionary optimization algorithm based on the law of gravity and mass interactions. The chapter starts with a brief literature review of the GSA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 17.1 Introduction 17.2 Mapping the law of gravity into gravity search algorithm (GSA) 17.3 Creating the initial population 17.4 Evaluation of particle's mass 17.5 Update velocities and positions 17.6 Update Newton gravitational factor 17.7 Termination criteria 17.8 User-defined parameters of the GSA 17.9 Pseudo code of the GSA 17.10 Conclusion 17.11 References Chapter 18: The Bat Algorithm (BA) Summary This chapter describes the bat algorithm (BA) that is a relatively recent meta-heuristic optimization algorithms. The chapter starts with a brief literature review of the BA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 18.1 Introduction 18.2 Mapping behavior of microbats into bat algorithm (BA) 18.3 Creating the initial population 18.4 Movement of virtual bats 18.5 Local search and random fly 18.6 Loudness and pulse emission 18.7 Termination criteria^8.8 User-defined parameters of the BA 18.9 Pseudo code of the BA 18.10 Conclusion 18.11 References Chapter 19: The Plant Propagation Algorithm (PPA) Summary This chapter describes the plant propagation algorithm (PPA) which simulates the multiplication of some plants such as the strawberry plant. The chapter starts with a brief literature review of the PPA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 19.1 Introduction 19.2 Mapping the natural process into planet propagation algorithm (PPA) 19.3 Creating the initial population of plants 19.4 Normalizing the fitness function 19.5 Propagation 19.6 Elimination of extra solutions 19.7 Termination Criteria 19.8 User-defined parameters of the PPA 19.9 Pseudo code of the PPA 19.10 Conclusion 19.11 References Chapter 20: The Water Cycle Algorithm (WCA) Summary This chapter describes the water cycle algorithm (WCA) that is a relatively recent meta-heuristic optimization algorithm. The chapter starts with a brief literature review of the WCA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 20.1 Introduction 20.2 Mapping the water cycle into the water cycle algorithm (WCA) 20.3 Creating the initial population 20.4 Classified raindrops 20.5 Flowing streams to the rivers or sea 20.6 Evaporation condition20.7 Raining process 20.8 Termination criteria 20.9 User-defined parameters of the WCA 20.10 Pseudo Code of the WCA 20.11 Conclusion 20.12 References Chapter 21: Symbiotic Organisms Search (SOS) algorithm Summary This chapter explains the symbiotic organisms search (SOS) algorithm, a recently-developed meta-heuristic algorithm which is inspired by symbiotic relationships among species. The chapter starts with a brief literature review of the SOS algorithm's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 21.1 Introduction 21.2 Mapping symbiotic relationships into symbiotic organisms search (SOS) 21.3 Creating the initial ecosystem 21.4 Mutualism 21.5 Commensalism 21.6 Parasitism 21.7 Termination criteria 21.8 Pseudo code of the SOS 21.9 Conclusion 21.10 References Chapter 22: The Comprehensive evolutionary algorithm (CEA) Summary This chapter explains a new meta-heuristic optimization algorithm called comprehensive evolutionary algorithm (CEA). This algorithm combines and takes advantages of some aspects of different algorithms, especially the genetic algorithm (GA) and the honey bee mating optimization (HBMO) algorithm. The chapter starts with a brief literature review of the CEA's development, important modifications that it has experienced, and its applications in engineering domains. The basic idea underlying the algorithm is presented and mapped to its mathematical statement. Afterwards, the steps of the algorithm are described in detail. A pseudo code of the algorithm is presented to serve as an easy and sufficient guideline for its coding. 22.1 Introduction22.2 Foundation of the CEA 22.3 Generating the initial population 22.4 Selection 22.5 Reproduction 22.7 Input information of the CEA 22.8 Termination criteria 22.9 Pseudo code of the CEA 22.10 Conclusion 22.11 References

About the Author

Dr. Omid Bozorg-Haddad is a Professor at the department of irrigation and reclamation engineering, University of Tehran, Iran. His teaching and research interests include water resources and environmental systems analysis, planning, and management as well as application of optimization algorithms in water related systems. He has published more than 100 articles in peer reviewed journals and 100 papers in conference proceedings. He has also supervised more than 50 M.Sc. and Ph.D. students. Prof. Hugo Loaiciga served as the Water Commissioner for the City of Santa Barbara for six years before joining the Department in 1988. He received the 2002 Service to the Profession Award from the American Society of Civil Engineers and the Environmental and Water Resources Institute for his "longstanding contributions to research and technical activities" of the two groups, and he was elected a Fellow of the American Society of Civil Engineers for his "outstanding contributions to the planning, analysis, and operation of water resources engineering" in 2007.

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