This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability.
Author: Michele Conforti
Category: Business & Economics
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.
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer ...
Author: Alexander Schrijver
Publisher: John Wiley & Sons
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
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 ...
Author: Der-San Chen
Publisher: John Wiley & Sons
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.
The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers.
Author: Hamdy A. Taha
Publisher: Academic Press
Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming. Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers.
"Combines the theoretical and practical aspects of linear and integer programming.
Author: Gerard Sierksma
Publisher: CRC Press
"Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization."
Linear programming; Integer programming graphs; Enumeration methods; Cutting plane methods; The knapsack problem; Integer programming over cones; The set covering and partitioning problems; Approximate methods; Integer nonlinear programming ...
Author: Robert Garfinkel
Category: Integer programming
Linear programming; Integer programming graphs; Enumeration methods; Cutting plane methods; The knapsack problem; Integer programming over cones; The set covering and partitioning problems; Approximate methods; Integer nonlinear programming; Computational experience.
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 ...
Author: Laurence A. Wolsey
Publisher: John Wiley & Sons
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.
Constraint and Integer Programming presents some of the basic ideas of constraint programming and mathematical programming, explores approaches to integration, brings us up to date on heuristic methods, and attempts to discern future ...
Author: Michela Milano
Publisher: Springer Science & Business Media
Constraint and Integer Programming presents some of the basic ideas of constraint programming and mathematical programming, explores approaches to integration, brings us up to date on heuristic methods, and attempts to discern future directions in this fast-moving field.
Therefore any basic optimum solution of the modified linear program has integer
components and it is also the optimum solution to the original integer program .
The integer programming algorithms that will be presented below are just ...
Author: Te Chiang Hu
Category: Integer programming
Linear programming; Network flows; Integer programming.
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
Author: John K. Karlof
Publisher: CRC Press
Category: Technology & Engineering
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 on convergent Lagrangian techniques that use objective level-cut and domain-cut methods to solve separable nonlinear integer-programming problems, the book discusses the generalized assignment problem (GAP). The final theoretical chapter analyzes the use of decomposition methods to obtain bounds on the optimal value of solutions to integer linear-programming problems. The first application article contains models and solution algorithms for the rescheduling of airlines following the temporary closure of airports. The next chapters deal with the determination of an optimal mix of chartered and self-owned vessels needed to transport a product. The book then presents an application of integer programming that involves the capture, storage, and transmission of large quantities of data collected during testing scenarios involving military applications related to vehicles, medicine, equipment, missiles, and aircraft. The next article develops an integer linear-programming model to determine the assortment of products that must be carried by stores within a retail chain to maximize profit, and the final article contains an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILP). The authors purposefully include applications and theory that are usually not found in contributed books in order to appeal to a wide variety of researchers and practitioners.
Chapter 2 A test set for an integer program via Gröbner bases 2.1 The reduced
Gröbner basis of an integer program Consider an integer program of the form Min
cx : Ax = b , XE N where AEZM * " is a matrix of rank m , beZ " and CER " .
This book is primarily intended for undergraduate and postgraduate students of statistics, mathematics, operations research, and engineering. It provides the basic concepts and methods of linear and integer linear programming.
Author: Sanaullah Khan
Publisher: Cambridge Scholars Publishing
This book is primarily intended for undergraduate and postgraduate students of statistics, mathematics, operations research, and engineering. It provides the basic concepts and methods of linear and integer linear programming. The text begins with an introduction containing the mathematical background to the subject matter, and goes on to discuss advancements the field. Formulations of various problems in diverse fields in linear and integer programming formats are also presented here. The book’s presentation of the solution of various numerical problems makes the subject matter and the methods detailed in the text more lucid and easier to comprehend.
INTRODUCTION Linear programming has become a major tool used in business
planning and decision making . ... Integer or mixed integer programming in which
all or part of the variables are required to be in the solution only at unit values ...
ALL - INTEGER INTEGER PROGRAMMING ALGORITHM by Ralph E. Gomory
International Business Machines Corporation Research Center Yorktown Heights
, New York ABSTRACT : An all - integer integer programming algorithm is ...
LIST OF REFERENCES [ 1 ] Baugh , C. R. , T. Ibaraki , T. K. Liu , and S. Muroga ,
" Optimum Network Design Using NOR and NOR - AND Gates by Integer Programming , Report No. 293 , Department of Computer Science , University of