Algorithms for Variable-Size Optimization: Applications in Space Systems and Renewable Energy

Cover
Title Page
Copyright Page
Dedication Page
Preface
Contents
Symbol Description
Section I: Background and Motivation
	1. Introduction and Background
		1.1 Mathematical Background
			1.1.1 Definitions
			1.1.2 Differentiability and Taylor’s Theorem
			1.1.3 Orthogonal Vectors
				1.1.3.1 Gram-Schmidt Orthogonalization
				1.1.3.2 Q-Orthogonal (Q-Conjugate) Directions
			1.1.4 Convergence Rates
		1.2 Systems Architecture Optimization
			1.2.1 Interplanetary Trajectory Optimization
			1.2.2 Microgrid Optimization
			1.2.3 Traffic Network Signal Coordination Planning
			1.2.4 Optimal Grouping Problems
			1.2.5 Systems Design Optimization
			1.2.6 Structural Topology Optimization
			1.2.7 Pixel Classification Problems
	2. Modeling Examples of Variable-Size Design Space Problems
		2.1 Satellite Orbit Design Optimization
		2.2 Interplanetary Trajectory Optimization
		2.3 Optimization of Wave Energy Converters
Section II: Classical Optimization Algorithms
	3. Fundamentals and Core Algorithms
		3.1 Equal Interval Search Algorithm
		3.2 Golden Section Method
		3.3 Linear versus Nonlinear Optimization
			3.3.1 Linear Programming
			3.3.2 Nonlinear Programming
	4. Unconstrained Optimization
		4.1 Non-Gradient Algorithms
			4.1.1 Cyclic Coordinated Descent Method
			4.1.2 Pattern Search Method
			4.1.3 Powell’s Method
		4.2 Gradient-Based Optimization
			4.2.1 Steepest Descent Method
			4.2.2 Conjugate Gradient Method
			4.2.3 Variable Metric Methods
		4.3 Second Order Methods
	5. Numerical Algorithms for Constrained Optimization
		5.1 Indirect Methods
			5.1.1 Barrier Methods
			5.1.2 Exterior Penalty Function Methods
			5.1.3 Augmented Lagrange Multiplier Method
			5.1.4 Algorithm for Indirect Methods
		5.2 Direct Methods
			5.2.1 Sequential Linear Programming
			5.2.2 Quadratic Programming
			5.2.3 Sequential Quadratic Programming
Section III: Variable-Size Design Space Optimization
	6. Hidden Genes Genetic Algorithms
		6.1 Introduction to Global Optimization
		6.2 Genetic Algorithms
			6.2.1 Similarity Templates (schemata)
			6.2.2 Markov Chain Model
		6.3 Fundamental Concepts of Hidden Genes Genetic Algorithms
			6.3.1 The Hidden Genes Concept in Biology
			6.3.2 Concept of Optimization using Hidden Genes Genetic Algorithms
			6.3.3 Outline of a Simple HGGA
		6.4 The Schema Theorem and the Simple HGGA
			6.4.1 Reproduction
			6.4.2 Crossover
			6.4.3 Mutation
		6.5 Hidden Genes Assignment Methods
			6.5.1 Logical Evolution of Tags
			6.5.2 Stochastic Evolution of Tags
		6.6 Examples: VSDS Mathematical Functions
			6.6.1 Examples using Stochastically Evolving Tags
			6.6.2 Examples using Logically Evolving Tags
		6.7 Statistical Analysis
		6.8 Markov Chain Model of HGGA
		6.9 Final Remarks
	7. Structured Chromosome Genetic Algorithms
		7.1 Structured-Chromosome Evolutionary Algorithms (SCEAs)
			7.1.1 Crossover in SCGA
			7.1.2 Mutation in SCGA
			7.1.3 Transformation in SCDE
			7.1.4 Niching in SCGA and SCDE
		7.2 Trajectory Optimization using SCEA
			7.2.1 Earth-Mars Mission
			7.2.2 Earth-Saturn Mission (Cassini 2-like Mission)
			7.2.3 Jupiter Europa Orbiter Mission
		7.3 Comparisons and Discussion
	8. Dynamic-Size Multiple Population Genetic Algorithms
		8.1 The Concept of DSMPGA
		8.2 Application: Space Trajectory Optimization
		8.3 Numerical Examples
		8.4 Discussion
Section IV: Applications
	9. Space Trajectory Optimization
		9.1 Background
		9.2 A Simple Implementation of HGGA
			9.2.1 Optimization
			9.2.2 Numerical Results
			9.2.3 Discussion
		9.3 Trajectory Optimization using HGGA with Binary Tags
			9.3.1 Earth–Jupiter Mission using HGGA
			9.3.2 Earth–Jupiter Mission: Numerical Results and Comparisons
	10. Control and Shape Optimization of Wave Energy Converters
		10.1 A Conical Buoy in Regular Wave
		10.2 General Shape Buoys in Regular Waves
		10.3 WECs in Irregular Waves
			10.3.1 Simultaneous Optimization of Shape and Control
		10.4 Discussion
Bibliography
Index