Discrete Optimization Algorithms
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| Author | : Maciej M. Sys?o |
| Publisher | : Courier Corporation |
| Total Pages | : 564 |
| Release | : 2006-01-01 |
| Genre | : Computers |
| ISBN | : 0486453537 |
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.
| Author | : Gautam M. Appa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 443 |
| Release | : 2006-08-18 |
| Genre | : Mathematics |
| ISBN | : 0387329420 |
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.
| Author | : R. Gary Parker |
| Publisher | : Elsevier |
| Total Pages | : 485 |
| Release | : 2014-06-28 |
| Genre | : Mathematics |
| ISBN | : 1483294803 |
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.
| Author | : Panos Kouvelis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475726201 |
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.
| Author | : William Kocay |
| Publisher | : CRC Press |
| Total Pages | : 504 |
| Release | : 2017-09-20 |
| Genre | : Mathematics |
| ISBN | : 135198912X |
Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms. Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.
| Author | : Nisheeth K. Vishnoi |
| Publisher | : Cambridge University Press |
| Total Pages | : 314 |
| Release | : 2021-10-07 |
| Genre | : Computers |
| ISBN | : 1108633994 |
In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.
| Author | : E. Boros |
| Publisher | : Elsevier |
| Total Pages | : 587 |
| Release | : 2003-03-19 |
| Genre | : Mathematics |
| ISBN | : 008093028X |
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
| Author | : Rajesh Kumar Arora |
| Publisher | : CRC Press |
| Total Pages | : 454 |
| Release | : 2015-05-06 |
| Genre | : Business & Economics |
| ISBN | : 149872115X |
Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and co
| 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 | : Giuseppe C. Calafiore |
| Publisher | : Cambridge University Press |
| Total Pages | : 651 |
| Release | : 2014-10-31 |
| Genre | : Business & Economics |
| ISBN | : 1107050871 |
This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.
