Advanced Optimization by Nature-Inspired Algorithms

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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

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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