Hierarchical Bayesian Optimization Algorithm: Toward a New Generation of Evolutionary Algorithms

This book provides a framework for the design of competent optimization techniques by combining advanced evolutionary algorithms with state-of-the-art machine learning techniques. The primary focus of the book is on two algorithms that replace traditional variation operators of evolutionary algorithms, by learning and sampling Bayesian networks: the Bayesian optimization algorithm (BOA) and the hierarchical BOA (hBOA). They provide a scalable solution to a broad class of problems. The book provides an overview of evolutionary algorithms that use probabilistic models to guide their search, motivates and describes BOA and hBOA in a way accessible to a wide audience, and presents numerous results confirming that they are revolutionary approaches to black-box optimization. We could start writing this book by saying, with several other authors, that the brain is the most powerful and complex information processing device known, whether naturally developed or created artificially. Although we fully agree with this statement, in doing so we would be misleading the reader, in the sense that the present book basically aims to formalize the knowledge concerning brain physiology accumulated over the past few decades. Instead of merely describing the complexity of the cerebral str- ture or presenting a collection of commentaries and reviews of interesting experimental results, we take into account novel achievements in quantum information and quantum computation, and avail ourselves of recently - veloped mathematical tools. Neuroscience was bom in the 19'~ century with the works of Paul Brocca. However, this fledgling field experienced a boom only in recent times, following the development of powerful non-invasive techniques for probing the neural circuitry supporting the complex cognitive functions of the human brain. Although sophisticated mathematical models and phy- cal theories are the basic tools behind the conceptual foundations and a- lytical implementation of these modem techniques, to the best of our knowledge no effort was made to formalize the actual knowledge about brain function into a coherent theoretical framework incorporating the - cent developments in mathematical and physical science. Addressing this lack was our first motivation in writing this book. "The Brain- From Fuzzy Arithmetic to Quantum Computing presents a new understanding of the brain by taking into account novel achievements in Fuzziness and Quantum Information Theory. Bringing together Neuroscience, Soft Computing, Quantum Theory, and recent developments in mathematics the actual knowledge about the brain functioning is formalized into a coherent theoretical framework. This monograph develops new and powerful neural models providing formal descriptions of biochemical transactions in the brain to guide neuroscience experiments and to better interpret their results. This book demonstrates how the physiology of the neuron can be understood based on the fundamentals of fuzzy formal languages and introduces the basics of quantum computation and quantum information to the brain. It discusses how molecular transactions at the cellular level implement such concepts, shows how certain neural structures, like the dendritic spine, are specialized to function as quantum computing devices and demonstrates how the brain can be viewed as a quantum processing intelligent system."--BOOK JACKET

"The Brain- From Fuzzy Arithmetic to Quantum Computing" presents an original and astounding new understanding of the brain by taking into account novel achievements in Fuzziness and Quantum Information Theory. Bringing together Neuroscience, Soft Computing, Quantum Theory, and recent developments in mathematics the actual knowledge about the brain functioning is formalized into a coherent theoretical framework. This monograph develops new and powerful neural models providing formal descriptions of biochemical transactions in the brain to guide neuroscience experiments and to better interpret their results. This book demonstrates how the physiology of the neuron can be understood based on the fundamentals of fuzzy formal languages and introduces the basics of quantum computation and quantum information to the brain.

Quantifying and Calculating in Nature.- The brain and its components.- Brain - a Distributed Intelligent Processing System.- How Fuzzy Quantification and Fuzzy Numbers appeared in Nature.- KFN evolution and the creation of Crisp Numbers.- Neural quantum computation.- Gene, Meme and Mathematics.- Mapping arithmetic brain functioning; Education in Mathematics.- Future Perspectives