Adaptive Differential Evolution: A Robust Approach to Multimodal Problem Optimization (Adaptation, Learning, and Optimization (1))

I ?rst met Jingqiao when he had just commenced his PhD research in evolutionary algorithms with Arthur Sanderson at Rensselaer. Jingqiao’s goals then were the investigation and development of a novel class of se- adaptivedi?erentialevolutionalgorithms,later calledJADE. I had remarked to Jingqiao then that Arthur always appreciated strong theoretical foun- tions in his research, so Jingqiao’s prior mathematically rigorous work in communications systems would be very useful experience. Later in 2007, whenJingqiaohadcompletedmostofthetheoreticalandinitialexperimental work on JADE, I invited him to spend a year at GE Global Research where he applied his developments to several interesting and important real-world problems. Most evolutionary algorithm conferences usually have their share of in- vative algorithm oriented papers which seek to best the state of the art - gorithms. The best algorithms of a time-frame create a foundation for a new generationof innovativealgorithms, and so on, fostering a meta-evolutionary search for superior evolutionary algorithms. In the past two decades, during whichinterest andresearchin evolutionaryalgorithmshavegrownworldwide by leaps and bounds, engaging the curiosity of researchers and practitioners frommanydiversescienceandtechnologycommunities,developingstand-out algorithms is getting progressively harder. Title Contents Introduction The Need for Unified Computational Intelligence Contributions of This Work The Three Types of Machine Learning Unsupervised Learning Supervised Learning Reinforcement Learning Approximate Dynamic Programming Markov Decision Processes The Bellman Equation Heuristic Dynamic Programming A Unified Approach Future Work The Unified Art Architecture Introduction Motivation Block Diagram Operation Step 1: Calculate State Trace Step 2: Calculate Control Step 3: Process Control Step 4: Interpret Reward via Critic Supervisory Signal Positive Reinforcement Negative Reinforcement Unsupervised Mode An Extended Architecture The Vigilance Test The Weight Update Algorithm An Application of Unified Computational Intelligence Overview Introduction Machine Learning Information Fusion Approach System Architecture Information Fusion Engine Application Vehicle Tracking Analysis Force Protection Experiments Results of Training the Fusion Model Future Work Conclusion The Time Scales Calculus Introduction Fundamentals Single-Variable Calculus Calculus of Multiple Variables Extension of the Chain Rule Induction on Time Scales Quantum Calculus Approximate Dynamic Programming on Time Scales Overview Introduction Dynamic Programming Overview Dynamic Programming Algorithm on Time Scales Delta Derivative Version Quantum Calculus Version HJB Equation on Time Scales Delta Derivative Version Nabla Derivative Version Alpha Derivative Version Conclusions Backpropagation on Time Scales Overview Introduction Ordered Derivatives Network Definitions Structure of Ordered Derivatives The Chain Rule The Backpropagation Algorithm on Time Scales Quantum Calculus Conclusions Unified Computational Intelligence in Social Science Introduction Game Theory and Computational Social Science Computational Intelligence Agent-Based Computational Social Science Game Theory Economics and Finance Introduction Background Agent-Based Computational Economics Application to Economic Systems Future Research Directions Intelligence in Markets Introduction Approximate Dynamic Programming and Stochastic Control Evolving Asset Pricing Strategies The Design of Market Mechanisms Computational Markets References Optimization problems are ubiquitous in academic research and real-world applications wherever such resources as space, time and cost are limited. Researchers and practitioners need to solve problems fundamental to their daily work which, however, may show a variety of challenging characteristics such as discontinuity, nonlinearity, nonconvexity, and multimodality. It is expected that solving a complex optimization problem itself should easy to use, reliable and efficient to achieve satisfactory solutions. Differential evolution is a recent branch of evolutionary algorithms that is capable of addressing a wide set of complex optimization problems in a relatively uniform and conceptually simple manner. For better performance, the control parameters of differential evolution need to be set appropriately as they have different effects on evolutionary search behaviours for various problems or at different optimization stages of a single problem. The fundamental theme of the book is theoretical study of differential evolution and algorithmic analysis of parameter adaptive schemes. Topics covered in this book include: Theoretical analysis of differential evolution and its control parameters Algorithmic design and comparative analysis of parameter adaptive schemes Scalability analysis of adaptive differential evolution Adaptive differential evolution for multi-objective optimization Incorporation of surrogate model for computationally expensive optimization Application to winner determination in combinatorial auctions of E-Commerce Application to flight route planning in Air Traffic Management Application to transition probability matrix optimization in credit-decision making