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Advanced Optimization by Nature-Inspired Algorithms
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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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