Bayesian Heuristic Approach To Discrete And Global Optimization
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| Author | : Jonas Mockus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475726279 |
Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.
| Author | : Jonas Mockus |
| Publisher | : Springer |
| Total Pages | : 397 |
| Release | : 1996-12-31 |
| Genre | : Mathematics |
| ISBN | : 9780792343271 |
Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.
| Author | : Jonas Mockus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 1461546710 |
This book shows how the Bayesian Approach (BA) improves well known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of dis crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribu tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. Dif ferent examples illustrate different points of the general subject. How ever, one can consider each example separately, too.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 741 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 147574949X |
The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.
| Author | : Panos M. Pardalos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 571 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 1475753624 |
In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published. This second volume of the Handbook of Global Optimization is comprised of chapters dealing with modern approaches to global optimization, including different types of heuristics. Topics covered in the handbook include various metaheuristics, such as simulated annealing, genetic algorithms, neural networks, taboo search, shake-and-bake methods, and deformation methods. In addition, the book contains chapters on new exact stochastic and deterministic approaches to continuous and mixed-integer global optimization, such as stochastic adaptive search, two-phase methods, branch-and-bound methods with new relaxation and branching strategies, algorithms based on local optimization, and dynamical search. Finally, the book contains chapters on experimental analysis of algorithms and software, test problems, and applications.
| Author | : Panos M. Pardalos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 597 |
| Release | : 2013-06-29 |
| Genre | : Technology & Engineering |
| ISBN | : 1475731450 |
There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2013-06-29 |
| Genre | : Computers |
| ISBN | : 147573218X |
Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches covers recent developments in optimization techniques for addressing several computational chemistry and biology problems. A tantalizing problem that cuts across the fields of computational chemistry, biology, medicine, engineering and applied mathematics is how proteins fold. Global and local optimization provide a systematic framework of conformational searches for the prediction of three-dimensional protein structures that represent the global minimum free energy, as well as low-energy biomolecular conformations. Each contribution in the book is essentially expository in nature, but of scholarly treatment. The topics covered include advances in local and global optimization approaches for molecular dynamics and modeling, distance geometry, protein folding, molecular structure refinement, protein and drug design, and molecular and peptide docking. Audience: The book is addressed not only to researchers in mathematical programming, but to all scientists in various disciplines who use optimization methods in solving problems in computational chemistry and biology.
| Author | : Marco Locatelli |
| Publisher | : SIAM |
| Total Pages | : 439 |
| Release | : 2013-10-16 |
| Genre | : Mathematics |
| ISBN | : 1611972671 |
This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 4646 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 0387747583 |
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
| Author | : Thomas J. Santner |
| Publisher | : Springer |
| Total Pages | : 446 |
| Release | : 2019-01-08 |
| Genre | : Mathematics |
| ISBN | : 1493988476 |
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
