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Integer Programming

Author: Michele Conforti

Publisher: Springer

Published: 2014-11-15

Total Pages: 466

ISBN-13: 331911008X

This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.

Integer Programming

Author: Laurence A. Wolsey

Publisher: John Wiley & Sons

Published: 2020-10-20

Total Pages: 336

ISBN-13: 1119606535

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A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition. The revised second edition: Contains new developments on column generation Offers a new chapter on Benders’ algorithm Includes expanded information on preprocessing, heuristics, and branch-and-cut Presents several basic and extended formulations, for example for fixed cost network flows Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.

Theory of Linear and Integer Programming

Author: Alexander Schrijver

Publisher: John Wiley & Sons

Published: 1998-06-11

Total Pages: 488

ISBN-13: 9780471982326

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Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.

Applied Integer Programming

Author: Der-San Chen

Publisher: John Wiley & Sons

Published: 2011-09-20

Total Pages: 489

ISBN-13: 1118210026

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An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

50 Years of Integer Programming 1958-2008

Author: Michael Jünger

Publisher: Springer Science & Business Media

Published: 2009-11-06

Total Pages: 804

ISBN-13: 3540682791

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In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.

Integer Programming

Author: John K. Karlof

Publisher: CRC Press

Published: 2005-09-22

Total Pages: 333

ISBN-13: 1420039598

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Integer Programming: Theory and Practice contains refereed articles that explore both theoretical aspects of integer programming as well as major applications. This volume begins with a description of new constructive and iterative search methods for solving the Boolean optimization problem (BOOP). Following a review of recent developments

Integer Linear Programming in Computational and Systems Biology

Author: Dan Gusfield

Publisher: Cambridge University Press

Published: 2019-06-13

Total Pages: 431

ISBN-13: 1108421768

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This hands-on tutorial text for non-experts demonstrates biological applications of a versatile modeling and optimization technique.

Nonlinear Integer Programming

Author: Duan Li

Publisher: Springer Science & Business Media

Published: 2006-08-13

Total Pages: 452

ISBN-13: 0387329951

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A combination of both Integer Programming and Nonlinear Optimization, this is a powerful book that surveys the field and provides a state-of-the-art treatment of Nonlinear Integer Programming. It is the first book available on the subject. The book aims to bring the theoretical foundation and solution methods for nonlinear integer programming to students and researchers in optimization, operations research, and computer science.

Production Planning by Mixed Integer Programming

Author: Yves Pochet

Publisher: Springer Science & Business Media

Published: 2006-04-19

Total Pages: 506

ISBN-13: 0387299599

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This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations. Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised... There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)

Integer Programming and Network Models

Author: H.A. Eiselt

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 501

ISBN-13: 3662041979

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The purpose of this book is to provide readers with an introduction to the very active field of integer programming and network models. The idea is to cover the main parts of the field without being too detailed or too technical. As a matter of fact, we found it somewhat surprising that most--especially newer---books are strongly algorithmically oriented. In contrast, the main emphasis of this book is on models rather than methods. This focus expresses our view that methods are tools to solve actual problems and not ends in themselves. As such, graduate (and with some omissions, undergraduate) students may find this book helpful in their studies as will practitioners who would like to get acquainted with a field or use this text as a refresher. This premise has resulted in a coverage that omits material that is standard fare in other books, whereas it covers topics that are only infrequently found elsewhere. There are some, yet relatively few, prerequisites for the reader. Most material that is required for the understanding of more than one chapter is presented in one of the four chapters of the introductory part, which reviews the main results in linear programming, the analysis of algorithms, graphs and networks, and dynamic programming, respectively. Readers who are familiar with the issues involved can safely skip that part. The three main parts of the book rely on intuitive reasoning and examples, whenever practical, instead of theorems and proofs.