Discrete Optimization Algorithms
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Discrete Optimization Algorithms
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Author : Maciej M. Sys?o
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01
Discrete Optimization Algorithms written by Maciej M. Sys?o and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Computers categories.
Rich in publications, the well-established field of discrete optimization nevertheless features relatively few books with ready-to-use computer programs. This book, geared toward upper-level undergraduates and graduate students, addresses that need. In addition, it offers a look at the programs' derivation and performance characteristics. Subjects include linear and integer programming, packing and covering, optimization on networks, and coloring and scheduling. A familiarity with design, analysis, and use of computer algorithms is assumed, along with knowledge of programming in Pascal. The book can be used as a supporting text in discrete optimization courses or as a software handbook, with twenty-six programs that execute the most common algorithms in each topic area. Each chapter is self-contained, allowing readers to browse at will.
Discrete Optimization
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Author : E. Boros
language : en
Publisher: Elsevier
Release Date : 2003-03-19
Discrete Optimization written by E. Boros and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-19 with Mathematics categories.
One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world. This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc. Key features: • state of the art surveys • comprehensiveness • prominent authors • theoretical, computational and applied aspects. This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3
Discrete Optimization
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Author : R. Gary Parker
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Discrete Optimization written by R. Gary Parker and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms. Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.
Nonlinear Discrete Optimization
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Author : Shmuel Onn
language : en
Publisher: European Mathematical Society
Release Date : 2010
Nonlinear Discrete Optimization written by Shmuel Onn and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Combinatorial optimization categories.
This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.
Robust Discrete Optimization And Its Applications
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Author : Panos Kouvelis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Robust Discrete Optimization And Its Applications written by Panos Kouvelis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: • It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; • It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; • It accounts for the risk averse nature of decision makers; and • It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making.
Novel Approaches To Hard Discrete Optimization
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Author : Panos M. Pardalos
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Novel Approaches To Hard Discrete Optimization written by Panos M. Pardalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ``Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.
Parallel Processing Of Discrete Optimization Problems
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Author : Panos M. Pardalos
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-01-01
Parallel Processing Of Discrete Optimization Problems written by Panos M. Pardalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This book contains papers presented at the Workshop on Parallel Processing of Discrete Optimization Problems held at DIMACS in April 1994. The contents cover a wide spectrum of the most recent algorithms and applications in parallel processing of discrete optimization and related problems. Topics include parallel branch and bound algorithms, scalability, load balancing, parallelism and irregular data structures and scheduling task graphs on parallel machines. Applications include parallel algorithms for solving satisfiability problems, location problems, linear programming, quadratic and linear assignment problems. This book would be suitable as a textbook in advanced courses on parallel algorithms and combinatorial optimization.
Handbook On Modelling For Discrete Optimization
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Author : Gautam M. Appa
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-18
Handbook On Modelling For Discrete Optimization written by Gautam M. Appa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.
This book aims to demonstrate and detail the pervasive nature of Discrete Optimization. The handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It is done with an academic treatment outlining the state-of-the-art for researchers across the domains of the Computer Science, Math Programming, Applied Mathematics, Engineering, and Operations Research. The book utilizes the tools of mathematical modeling, optimization, and integer programming to solve a broad range of modern problems.
Bayesian Heuristic Approach To Discrete And Global Optimization
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Author : Jonas Mockus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Bayesian Heuristic Approach To Discrete And Global Optimization written by Jonas Mockus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Algebraic And Geometric Ideas In The Theory Of Discrete Optimization
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Author : Jesus A. De Loera
language : en
Publisher: SIAM
Release Date : 2013-01-31
Algebraic And Geometric Ideas In The Theory Of Discrete Optimization written by Jesus A. De Loera and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.