Evolutionary Algorithms and Chaotic Systems

This book discusses the mutual intersection of two fields of research: evolutionary computation, which can handle tasks such as control of various chaotic systems, and deterministic chaos, which is investigated as a behavioral part of evolutionary algorithms. 3642107060 Studies in Computational Intelligence,Volume 267 Evolutionary Algorithms and Chaotic Systems Foreword Preface Acknowledgements Contents Part I: Theory Chapter 1 Motivation for Application of Evolutionary Computation to Chaotic Systems Introduction Evolutionary Computation and Selected Examples Evolutionary Design Application of Evolvable Hardware Automatic Design of Low-Cost Hardware Poorly Specified Problems Adaptive Systems Fault Tolerant Systems Design Innovation in Poorly Understood Design Spaces Hummies Competition Problems Solvable by Evolutionary Computation Example: Real-Time Compensation of Plasma Reactor Chaotic Systems Conclusions References Chapter 2 Evolutionary Algorithms for Chaos Researchers Historical Facts from a Slightly Different Point of View Evolutionary Algorithms – Outline Central Dogma of Evolutionary Computational Techniques Evolutionary Algorithms and Importance of Their Use Selected Evolutionary Techniques Overview Current State Selected Basic Terms from the Evolutionary Algorithms The Usability Areas of Evolutionary Algorithms Common Features Population Individuals and Their Representation Evolutionary Operators: Selection, Recombination, Mutation Limits to Computation Searched Space and Its Complexity Physical Limits of Computation Conclusion References Chapter 3 Chaos Theory for Evolutionary Algorithms Researchers Introduction Characterization of Deterministic Chaos Roots of Deterministic Chaos Universal Features of Chaos Determinism and Unpredictability of the Behavior of Deterministic Chaos – Sensitivity to Initial Conditions Lyapunov Exponents The U-Sequence Intermittence, Period Doubling, Metastable Chaos and Crises Feigenbaum Constants Self-similarity From Order to Chaos Period Doubling Intermittence Chaotic Transients Crises Selected Examples Mechanical System – Billiard Mechanical System – Duffing's Equation Electronic System – Chua's Circuit, Circuit with a Diode Biological System – Logistic Equation Meteorological System – Lorenz Weather Model Spatiotemporal Chaos Cellular Automata – Game of Life Artificial Intelligence – Neuron Networks Artificial Intelligence – Evolutionary Algorithms Astronomy – The Three-Body Problem Conclusion References Chapter 4 Evolutionary Algorithms and the Edge of Chaos Introduction Edge of Chaos Antichaos and Self-organization A Butterfly Sleeps Chaos and Antichaos Edge of Chaos in Evolutionary Algorithms Stagnation Anti-stagnation Analytical Observation Diversity Measure Population Representation Conclusion References Part II: Applications Chapter 5 Evolutionary Design of Chaos Control in 1D Introduction Evolutionary Techniques in Chaos Control Chaotic Systems Logistic Equation Henon Map Selected Method for the Controlling of Chaos Delayed Feedback Control (Pyragas Method) Evolutionary Algorithms Optimization of Chaos Control Problem Design The Cost Function Experimental Results Analysis of All Results Comparison with OGY Method Logistic Equation Henon Map Conclusion and Discussion References Chapter 6 Evolutionary Control of CML Systems Introduction Motivation Selected Evolutionary Algorithm - A Brief Introduction Differential Evolution SOMA Simulated Annealing Genetic Algorithms Evolutionary Strategies CML Control Used Hardware Problem Selection and Case Studies Cost Function Parameter Setting Experimental Results CML Real Time Control Conclusion References Chapter 7 Chaotic Systems Reconstruction Introduction Unknown Inputs Multiple Observer Design Unknown Inputs Observer Design LMI Design Conditions Pole Placement Unknown Inputs Estimation Simulation Examples Academic Example Application to Chaotic System Reconstruction Extension to Discret-Time Multiple Model Pole Assignment Application to Chaotic System Reconstruction Conclusion References Chapter 8 Evolutionary Reconstruction of Chaotic Systems Introduction Motivation Chaos System Reconstruction – Classical Methods Reconstruction Based on Time Series Analysis Evolutionary Reconstruction of Chaotic Systems Problem Selection, Used Algorithms and Computer Technology The Cost Function Experiment Setup Experimental Results Reconstruction of Similar Systems Unfinished Evolution Exotic Solutions Continuous Systems: Preliminary Study Conclusion References Chapter 9 Cryptography Based on Spatiotemporal Chaotic Systems Introduction CML-Based Pseudo-Random-Bit Generators Coupled Map Lattice Digitization Method Statistical Properties PRBGs Based on Various CMLs CML-Based Stream Cipher Algorithm of the Cipher Keyspace Cryptographic Properties of the Keystream High Efficiency CML-Based Multimedia Cryptosystem Design of CML-Based Multimedia Cryptosystem Performance Analysis Conclusion References Chapter 10 Evolutionary Decryption of Chaotically Encrypted Information Introduction Motivation Selected Evolutionary Algorithm – A Brief Introduction Evolutionary Decryption Used Hardware, Problem Selection and Case Studies Cost Function Parameter Setting Experimental Results Conclusion References Chapter 11 Chaos Synthesis by Evolutionary Algorithms Introduction Motivation Brief Review of the Selected Evolutionary Algorithm Symbolic Regression – An Introduction Genetic Programming Grammatical Evolution Analytic Programming Experiment Design Parameter Setting Cost Function Case Studies Conclusion References Chapter 12 Evolutionary Synchronization of Chaotic Systems Introduction Motivation Selected Evolutionary Algorithm – A Brief Introduction Evolutionary Synchronization Used Hardware, Problem Selection and Case Studies Cost Function Parameter Setting Experimental Results Conclusion References Chapter 13 Evolutionary Optimization and Dynamic Fitness Landscapes Introduction Constructing Dynamic Fitness Landscapes from Reaction–Diffusion Systems and CML Static and Dynamic Fitness Landscapes Hierarchy of Fitness Landscapes Relationships between Coupled Map Lattices and Reaction–Diffusion Systems Properties of Dynamic Fitness Landscapes Topological Properties and Topological Problem Difficulty Dynamical Properties and Dynamical Problem Difficulty Topological and Dynamical Landscape Measures for the CML–Based Landscape Evolutionary Optimization Numerical Experiments Concluding Remarks References Chapter 14 Controller Parameters Optimization on a Representative Set of Systems Using Deterministic-Chaotic-Mutation Evolutionary Algorithms Introduction PID Controller Proportional Algorithm Proportional Integral Algorithm Proportional Integral Derivative Algorithm Controller Tuning Ziegler Nichols Closed Loop Method System Specifications Sensitivity Specifications Optimization Specifications Differential Evolution Algorithm Tuning Parameters Chaotic Systems Lozi Map Delayed Logistic Map Problem Description Fourth Order System Third Order System Electric DC Motor Conclusion References Chapter 15 Chaotic Attributes and Permutative Optimization Introduction Chaotic Signature in Population Dynamics Population Dynamics Initial Population Solution Dynamics Chaotic Features Selection and Deletion Dynamic Clustering Metaheuristics Genetic Algorithms Differential Evolution Algorithm Self Organizing Migrating Algorithm General Template Quadratic Assignment Problem Results Genetic Algorithm Results Differential Evolution Results Self Organizing Migration Algorithm Results Analysis Conclusion References Chapter 16 Frontiers References This book discusses the mutual intersection of two interesting fields of research, i.e. deterministic chaos and evolutionary computation. Evolutionary computation which are able to handle tasks such as control of various chaotic systems and synthesis of their structure are explored, while deterministic chaos is investigated as a behavioral part of evolutionary algorithms.This book is targeted for a number of audiences. Firstly, it will be an instructional material for senior undergraduate and entry-point graduate students in computer science, physics, applied mathematics, and engineering, who are working in the area of deterministic chaos and evolutionary algorithms. Secondly, researchers who desire to know how to apply evolutionary techniques on chaos control as well as researchers interested in the emergence of chaos in evolutionary algorithms will find this book a very useful tool and starting point. And finally, this book can be viewed as a resource handbook and material for practitioners who want to apply these methods that solve practical problems to their challenging applications.