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Mixed Variable Bayesian Optimization
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Book Synopsis Mixed-variable Bayesian Optimization by : Julien Pelamatti
Download or read book Mixed-variable Bayesian Optimization written by Julien Pelamatti and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the framework of complex system design, such as aircraft and launch vehicles, the presence of computationallyintensive objective and/or constraint functions (e.g., finite element models and multidisciplinary analyses)coupled with the dependence on discrete and unordered technological design choices results in challenging optimizationproblems. Furthermore, part of these technological choices is associated to a number of specific continuous anddiscrete design variables which must be taken into consideration only if specific technological and/or architecturalchoices are made. As a result, the optimization problem which must be solved in order to determine the optimalsystem design presents a dynamically varying search space and feasibility domain.The few existing algorithms which allow solving this particular type of problems tend to require a large amountof function evaluations in order to converge to the feasible optimum, and result therefore inadequate when dealingwith the computationally intensive problems which can often be encountered within the design of complex systems.For this reason, this thesis explores the possibility of performing constrained mixed-variable and variable-size designspace optimization by relying on surrogate model-based design optimization performed with the help of Gaussianprocesses, also known as Bayesian optimization. More specifically, 3 main axes are discussed. First, the Gaussianprocess surrogate modeling of mixed continuous/discrete functions and the associated challenges are extensivelydiscussed. A unifying formalism is proposed in order to facilitate the description and comparison between theexisting kernels allowing to adapt Gaussian processes to the presence of discrete unordered variables. Furthermore,the actual modeling performances of these various kernels are tested and compared on a set of analytical and designrelated benchmarks with different characteristics and parameterizations.In the second part of the thesis, the possibility of extending the mixed continuous/discrete surrogate modeling toa context of Bayesian optimization is discussed. The theoretical feasibility of said extension in terms of objective/-constraint function modeling as well as acquisition function definition and optimization is shown. Different possiblealternatives are considered and described. Finally, the performance of the proposed optimization algorithm, withvarious kernels parameterizations and different initializations, is tested on a number of analytical and design relatedtest-cases and compared to reference algorithms.In the last part of this manuscript, two alternative ways of adapting the previously discussed mixed continuous/discrete Bayesian optimization algorithms in order to solve variable-size design space problems (i.e., problemscharacterized by a dynamically varying design space) are proposed. The first adaptation is based on the paralleloptimization of several sub-problems coupled with a computational budget allocation based on the informationprovided by the surrogate models. The second adaptation, instead, is based on the definition of a kernel allowingto compute the covariance between samples belonging to partially different search spaces based on the hierarchicalgrouping of design variables. Finally, the two alternatives are tested and compared on a set of analytical and designrelated benchmarks.Overall, it is shown that the proposed optimization methods allow to converge to the various constrained problemoptimum neighborhoods considerably faster when compared to the reference methods, thus representing apromising tool for the design of complex systems.
Book Synopsis Bayesian Optimization and Data Science by : Francesco Archetti
Download or read book Bayesian Optimization and Data Science written by Francesco Archetti and published by Springer Nature. This book was released on 2019-09-25 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together the main results in the field of Bayesian Optimization (BO), focusing on the last ten years and showing how, on the basic framework, new methods have been specialized to solve emerging problems from machine learning, artificial intelligence, and system optimization. It also analyzes the software resources available for BO and a few selected application areas. Some areas for which new results are shown include constrained optimization, safe optimization, and applied mathematics, specifically BO's use in solving difficult nonlinear mixed integer problems. The book will help bring readers to a full understanding of the basic Bayesian Optimization framework and gain an appreciation of its potential for emerging application areas. It will be of particular interest to the data science, computer science, optimization, and engineering communities.
Book Synopsis Bayesian Optimization Under Mixed Constraints with a Slack-variable Augmented Lagrangian by : Victor Picheny
Download or read book Bayesian Optimization Under Mixed Constraints with a Slack-variable Augmented Lagrangian written by Victor Picheny and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bayesian Optimization in Action by : Quan Nguyen
Download or read book Bayesian Optimization in Action written by Quan Nguyen and published by Simon and Schuster. This book was released on 2023-11-14 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Optimization in Action teaches you how to build Bayesian Optimisation systems from the ground up. This book transforms state-of-the-art research into usable techniques you can easily put into practice. With a range of illustrations, and concrete examples, this book proves that Bayesian Optimisation doesn't have to be difficult!
Book Synopsis Bayesian Optimization on Non-conventional Search Spaces by : Changyong Oh
Download or read book Bayesian Optimization on Non-conventional Search Spaces written by Changyong Oh and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Thanks to its high sample efficiency, BO has been successful in high-cost design problems. Nonetheless, the application of BO in the literature has been restricted to low-dimensional Euclidean spaces. Along with the ever-increasing complexity and diversity of design problems, the necessity of effective BO in various spaces is increasing. In response to such demand, in this thesis, we propose BO on spaces other than low-dimensional Euclidean ones to broaden the applicability of BO. Specifically, motivated by the successes of BO with the Gaussian process (GP) surrogate model on low-dimensional Euclidean spaces, we focus on BO with the GP surrogate model. Our contributions are as follows: We propose Bayesian optimization on high-dimensional Euclidean spaces, BOCK (Chapter 3) that achieves competitive performance on problems up to 500 dimensions without making structural assumptions on the objective; We propose Bayesian optimization on combinatorial spaces with ordinal and categorical variables, COMBO (Chapter 4) that exhibits superior sample efficiency with scalability up to a problem with 260 choices; To model dependence between different types of variables, we propose frequency modulation (Chapter 5) and a sufficient condition for the similarity measure behavior that is crucial to BO performance on mixed-variable spaces; We propose a batch acquisition method applicable to permutation spaces, LAW (Chapter 6) that adapts Determinantal point processes. By additionally taking into account quality with the acquisition weight, LAW scales to large batch sizes; We show the potential of BO for combinatorial optimization problems in chip design Ð macro placement (Chapter 7)."--
Book Synopsis Bayesian Optimization with Application to Computer Experiments by : Tony Pourmohamad
Download or read book Bayesian Optimization with Application to Computer Experiments written by Tony Pourmohamad and published by Springer Nature. This book was released on 2021-10-04 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to Bayesian optimization, highlighting advances in the field and showcasing its successful applications to computer experiments. R code is available as online supplementary material for most included examples, so that readers can better comprehend and reproduce methods. Compact and accessible, the volume is broken down into four chapters. Chapter 1 introduces the reader to the topic of computer experiments; it includes a variety of examples across many industries. Chapter 2 focuses on the task of surrogate model building and contains a mix of several different surrogate models that are used in the computer modeling and machine learning communities. Chapter 3 introduces the core concepts of Bayesian optimization and discusses unconstrained optimization. Chapter 4 moves on to constrained optimization, and showcases some of the most novel methods found in the field. This will be a useful companion to researchers and practitioners working with computer experiments and computer modeling. Additionally, readers with a background in machine learning but minimal background in computer experiments will find this book an interesting case study of the applicability of Bayesian optimization outside the realm of machine learning.
Book Synopsis Bayesian Optimization by : Roman Garnett
Download or read book Bayesian Optimization written by Roman Garnett and published by Cambridge University Press. This book was released on 2023-01-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to Bayesian optimization that starts from scratch and carefully develops all the key ideas along the way.
Book Synopsis Bayesian Approach to Global Optimization by : Jonas Mockus
Download or read book Bayesian Approach to Global Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: ·Et moi ... si j'avait su comment en revcnir. One service mathematics has rendered the je o'y semis point alle.' human race. It has put common sense back Jules Verne where it beloogs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense', able to do something with it. Eric T. BclI O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Bayesian and High-Dimensional Global Optimization by : Anatoly Zhigljavsky
Download or read book Bayesian and High-Dimensional Global Optimization written by Anatoly Zhigljavsky and published by Springer Nature. This book was released on 2021-03-02 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.
Book Synopsis Advances in Structural and Multidisciplinary Optimization by : Axel Schumacher
Download or read book Advances in Structural and Multidisciplinary Optimization written by Axel Schumacher and published by Springer. This book was released on 2017-12-04 with total page 2101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume includes papers from the WSCMO conference in Braunschweig 2017 presenting research of all aspects of the optimal design of structures as well as multidisciplinary design optimization where the involved disciplines deal with the analysis of solids, fluids or other field problems. Also presented are practical applications of optimization methods and the corresponding software development in all branches of technology.
Book Synopsis Hierarchical Bayesian Optimization Algorithm by : Martin Pelikan
Download or read book Hierarchical Bayesian Optimization Algorithm written by Martin Pelikan and published by Springer Science & Business Media. This book was released on 2005-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 book focuses 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). BOA and hBOA are theoretically and empirically shown to provide robust and scalable solution for broad classes of nearly decomposable and hierarchical problems. A theoretical model is developed that estimates the scalability and adequate parameter settings for BOA and hBOA. The performance of BOA and hBOA is analyzed on a number of artificial problems of bounded difficulty designed to test BOA and hBOA on the boundary of their design envelope. The algorithms are also extensively tested on two interesting classes of real-world problems: MAXSAT and Ising spin glasses with periodic boundary conditions in two and three dimensions. Experimental results validate the theoretical model and confirm that BOA and hBOA provide robust and scalable solution for nearly decomposable and hierarchical problems with only little problem-specific information.
Book Synopsis The Design and Analysis of Computer Experiments by : Thomas J. Santner
Download or read book The Design and Analysis of Computer Experiments written by Thomas J. Santner and published by Springer. This book was released on 2019-01-08 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners
Book Synopsis Bayesian Optimisation Over Mixed Parameter Spaces by : Marius Tudor Morar
Download or read book Bayesian Optimisation Over Mixed Parameter Spaces written by Marius Tudor Morar and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimization and Learning by : Bernabé Dorronsoro
Download or read book Optimization and Learning written by Bernabé Dorronsoro and published by Springer Nature. This book was released on 2022-12-10 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Conference on Optimization and Learning, OLA 2022, which took place in Syracuse, Sicilia, Italy, in July 2022. The 19 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The papers are organized in the following topical sections: Optimization and Learning; Novel Optimization Techniques; Logistics; and Applications.
Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Book Synopsis Information Science for Materials Discovery and Design by : Turab Lookman
Download or read book Information Science for Materials Discovery and Design written by Turab Lookman and published by Springer. This book was released on 2015-12-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with an information-driven approach to plan materials discovery and design, iterative learning. The authors present contrasting but complementary approaches, such as those based on high throughput calculations, combinatorial experiments or data driven discovery, together with machine-learning methods. Similarly, statistical methods successfully applied in other fields, such as biosciences, are presented. The content spans from materials science to information science to reflect the cross-disciplinary nature of the field. A perspective is presented that offers a paradigm (codesign loop for materials design) to involve iteratively learning from experiments and calculations to develop materials with optimum properties. Such a loop requires the elements of incorporating domain materials knowledge, a database of descriptors (the genes), a surrogate or statistical model developed to predict a given property with uncertainties, performing adaptive experimental design to guide the next experiment or calculation and aspects of high throughput calculations as well as experiments. The book is about manufacturing with the aim to halving the time to discover and design new materials. Accelerating discovery relies on using large databases, computation, and mathematics in the material sciences in a manner similar to the way used to in the Human Genome Initiative. Novel approaches are therefore called to explore the enormous phase space presented by complex materials and processes. To achieve the desired performance gains, a predictive capability is needed to guide experiments and computations in the most fruitful directions by reducing not successful trials. Despite advances in computation and experimental techniques, generating vast arrays of data; without a clear way of linkage to models, the full value of data driven discovery cannot be realized. Hence, along with experimental, theoretical and computational materials science, we need to add a “fourth leg’’ to our toolkit to make the “Materials Genome'' a reality, the science of Materials Informatics.
Book Synopsis Advances in Mechanical Design by : Jianrong Tan
Download or read book Advances in Mechanical Design written by Jianrong Tan and published by Springer Nature. This book was released on with total page 2698 pages. Available in PDF, EPUB and Kindle. Book excerpt:
