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

Section I: Background and Motivation Introduction and Background Mathematical Background Definitions Differentiability and Taylor’s Theorem Orthogonal Vectors Gram-Schmidt Orthogonalization Q-Orthogonal (Q-Conjugate) Directions Convergence Rates Systems Architecture Optimization Interplanetary Trajectory Optimization Microgrid Optimization Traffic Network Signal Coordination Planning Optimal Grouping Problems Systems Design Optimization Structural Topology Optimization Pixel Classification Problems Modeling Examples of Variable-Size Design Space Problems Satellite Orbit Design Optimization Interplanetary Trajectory Optimization Optimization of Wave Energy Converters Section II: Classical Optimization Algorithms Fundamentals and Core Algorithms Equal Interval Search Algorithm Golden Section Method Linear versus Nonlinear Optimization Linear Programming Nonlinear Programming Unconstrained Optimization Non-Gradient Algorithms Cyclic Coordinated Descent Method Pattern Search Method Powell’s Method Gradient-Based Optimization Steepest Descent Method Conjugate Gradient Method Variable Metric Methods Second Order Methods Numerical Algorithms for Constrained Optimization Indirect Methods Barrier Methods Exterior Penalty Function Methods Augmented Lagrange Multiplier Method Algorithm for Indirect Methods Direct Methods Sequential Linear Programming Quadratic Programming Sequential Quadratic Programming Section III: Variable-Size Design Space Optimization Hidden Genes Genetic Algorithms Introduction to Global Optimization Genetic Algorithms Similarity Templates (schemata)Markov Chain Model Fundamental Concepts of Hidden Genes Genetic Algorithms The Hidden Genes Concept in Biology Concept of Optimization using Hidden Genes Genetic Algorithms Outline of a Simple HGGA The Schema Theorem and the Simple HGGA Reproduction Crossover Mutation Hidden Genes Assignment Methods Logical Evolution of Tags Stochastic Evolution of Tags Examples: VSDS Mathematical Functions Examples using Stochastically Evolving Tags Examples using Logically Evolving Tags Statistical Analysis Markov Chain Model of HGGA Final Remarks Structured Chromosome Genetic Algorithms Structured-Chromosome Evolutionary Algorithms (SCEAs)Crossover in SCGA Mutation in SCGA Transformation in SCDE Niching in SCGA and SCDE Trajectory Optimization using SCEA Earth-Mars Mission Earth-Saturn Mission (Cassini 2-like Mission)Jupiter Europa Orbiter Mission Comparisons and Discussion Dynamic-Size Multiple Population Genetic Algorithms The Concept of DSMPGA Application: Space Trajectory Optimization Numerical Examples Discussion Space Trajectory Optimization Background A Simple Implementation of HGGA Optimization Numerical Results Discussion Trajectory Optimization using HGGA with Binary Tags Earth–Jupiter Mission using HGGA Earth–Jupiter Mission: Numerical Results and Comparisons Control and Shape Optimization of Wave Energy Converters A Conical Buoy in Regular Wave General Shape Buoys in Regular Waves WECs in Irregular Waves Simultaneous Optimization of Shape and Control Discussion Bibliography

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