Download or read book Leveraging Space Filling Curves and the DIRECT Algorithm A Novel Approach to Derivative Free Multi Dimensional Global Optimization written by Aditi Dutta and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derivative free DIRECT type Global Optimization written by Linas Stripinis and published by Springer Nature. This book was released on 2023-12-29 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables. Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels. Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.
Download or read book Introduction to Global Optimization Exploiting Space Filling Curves written by Yaroslav D. Sergeyev and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .
Download or read book Differential Evolution written by Kenneth Price and published by Springer Science & Business Media. This book was released on 2006-03-04 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables. The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.
Download or read book Applications on Multi dimensional Sphere Packings written by Paul Belitz and published by . This book was released on 2011 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of n-dimensional sphere packings is elegant and mature in its mathematic development and characterization. However, practical application of this powerful body of work is lacking. The line of research presented in this work explores the application of sphere packings to the field of derivative-free optimization. Chapter 2 reviews the essential results available in this field, then extends these results by: (a) assembling a catalog of key properties of the principle dense and rare sphere packings and nets available, including hundreds of values not previously known; (b) introducing and characterizing several new families of regular rare sphere packings and nets; and (c) developing a new algorithm for efficient solution of discrete Thompson problems, restricted to nearest-neighbor points. These results are leveraged heavily in the applications addressed in Chapters 3 and 4. In particular, Chapter 3 builds from this presentation to develop a new algorithm for Lattice-Based Derivative-free Optimization via Global Surrogates (LABDOGS), leveraging dense sphere packings as an alternative to Cartesian grids to coordinate derivative-free searches. The LABDOGS algorithm provides a highly efficient, globally convergent optimization algorithm that requires nothing more than a definition of a feasible domain and a cost function handle. The LABDOGS algorithm demonstrates superior performance and convergence rates to its Cartesian-based competitors. Chapter 4 builds from the material of Chapter 2 and 3 to develop a highly efficient locally convergent derivative-free optimization algorithm called L-MADS, which builds from and improves upon the Mesh Adaptive Direct Search (MADS) class of optimization algorithms. The L-MADS algorithm offers an alternative to the Successive Polling substep of LABDOGS, providing a locally convergent pattern search algorithm that, unlike SP, offers good convergence behavior when challenging constraints on the feasible region are encountered. L-MADS inherits all the convergence characteristics of the best available MADS algorithms, while significantly improving convergence rates.
Download or read book High Dimensional Spatial Indexing Using Space Filling Curves written by Ankush Chauhan and published by Grin Publishing. This book was released on 2016-07-21 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Essay from the year 2015 in the subject Mathematics - Miscellaneous, language: English, abstract: Representation of two dimensional objects into one dimensional space is simple and efficient when using a two coordinate system imposed upon a grid. However, when the two dimensions are expanded far beyond visual and sometimes mental understanding, techniques are used to quantify and simplify the representation of such objects. These techniques center around spatial interpretations by means of a space-filling curve. Since the late 1800's, mathematicians and computer scientists have succeeded with algorithms that express high dimensional geometries. However, very few implementations of the algorithms beyond three dimensions for computing these geometries exist. We propose using the basic spatial computations developed by pioneers in the field like G. Peano, D. Hilbert, E. H. Moore, and others in a working model. The algorithms in this paper are fully implemented in high-level programming languages utilizing a relation database management system. We show the execution speeds of the algorithms using a space-filling curve index for searching compared to brute force searching. Finally, we contrast three space-filling curve algorithms: Moore, Hilbert, and Morton, in execution time of searching for high dimensional data in point queries and range queries.
Download or read book Global Optimization with the DIRECT Algorithm written by Daniel Edwin Finkel and published by . This book was released on 2005 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: sampling methods, derivative-free optimization, global optimization, DIRECT.
Download or read book Global Optimization written by Reiner Horst and published by . This book was released on 1993 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derivative free Optimization Algorithms for Computationally Expensive Functions written by Stefan Martin Wild and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis concerns the development and analysis of derivative-free optimization algorithms for simulation-based functions that are computationally expensive to evaluate. The first contribution is the introduction of data profiles as a tool for analyzing the performance of derivative-free optimization solvers when constrained by a computational budget. Using these profiles, together with a convergence test that measures the decrease in function value, we find that on three different sets of test problems, a model-based solver performs better than the two direct search solvers tested. The next contribution is a new model-based derivative-free algorithm, ORBIT, for unconstrained local optimization. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. RBF models allow ORBIT to interpolate nonlinear functions using fewer function evaluations than many of the polynomial models considered by present techniques. We provide an analysis of the approximation guarantees obtained by interpolating the function at a set of sufficiently affinely independent points. We detail necessary and sufficient conditions that an RBF model must obey to fit within our framework and prove that this framework allows for convergence to first-order critical points. We present numerical results on test problems as well as three application problems from environmental engineering to support ORBIT's effectiveness when relatively few func- tion evaluations are available. The framework used by ORBIT is also extended to include other models, in particular undetermined interpolating quadratics. These quadratics are flexible in their ability to interpolate at dynamic numbers of previously evaluated points. The third contribution is a new multistart global optimization algorithm, GORBIT, that takes advantage of the expensive function evaluations done in the course of both the global exploration and local refinement phases. We modify ORBIT to handle both bound constraints and external functional evaluations and use it as the local solver. For the global exploration phase, a new procedure for making maximum use of the information from previous evaluations, MIPE, is introduced. Numerical tests motivating our approach are presented and we illustrate using GORBIT on the problem of finding error-prone systems for Gaussian elimination.
Download or read book Algorithms for Optimization written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2019-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.
Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.
Download or read book Optimization of Complex Systems Theory Models Algorithms and Applications written by Hoai An Le Thi and published by Springer. This book was released on 2019-06-15 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
Download or read book Genetic Algorithms in Search Optimization and Machine Learning written by David Edward Goldberg and published by Addison-Wesley Professional. This book was released on 1989 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction to genetic algorithms. Genetic algorithms revisited: mathematical foundations. Computer implementation of a genetic algorithm. Some applications of genetic algorithms. Advanced operators and techniques in genetic search. Introduction to genetics-based machine learning. Applications of genetics-based machine learning. A look back, a glance ahead. A review of combinatorics and elementary probability. Pascal with random number generation for fortran, basic, and cobol programmers. A simple genetic algorithm (SGA) in pascal. A simple classifier system(SCS) in pascal. Partition coefficient transforms for problem-coding analysis.
Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Download or read book Towards Global Optimisation written by G. P. Szegö and published by . This book was released on 1975 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
