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An Algorithm For The Bounded Variable Integer Programming Problem
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Book Synopsis An Algorithm for the Bounded Variable Integer Programming Problem by : L. E Trotter (Jr)
Download or read book An Algorithm for the Bounded Variable Integer Programming Problem written by L. E Trotter (Jr) and published by . This book was released on 1973 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: TSR-1355DA-31-124-ARO(D)-462*Mathematical programming, Linear programming, Computer programming, Computations, Algorithms*Integer programmingAn algorithm is proposed for the bounded variable pure integer programming problem which treats general integer variables directly in an implicit enumeration procedure closely related to that advanced by Balas and Geoffrion for binary programming problems. Means of obtaining near optimum solutions through a slight modification of the algorithm are discussed. Techniques which use bounds on variables to improve algorithmic efficiency are developed and examined computationally. Further computational results indicate that direct treatment of general integer variables is significantly more effective than binary expansion. (Author).
Book Synopsis Integer Programming by : Hamdy A. Taha
Download or read book Integer Programming written by Hamdy A. Taha and published by Academic Press. This book was released on 2014-05-10 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bound and Scan Algorithm for Pure Integer Linear Programming with General Variables by : Stanford University. Department of Operations Research
Download or read book Bound and Scan Algorithm for Pure Integer Linear Programming with General Variables written by Stanford University. Department of Operations Research and published by . This book was released on 1969 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report presents the theory underlying the bound-and-scan algorithm for solving the pure integer linear programming problem with general integer variables. This algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. New encouraging computational experience is reported which suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems (including the mixed-integer case) also are outlined. The report also gives a listing of a new FORTRAN code for the algorithm and 30 new test problems.
Book Synopsis The Bounded Variable Algorithm for Solving Integer Linear Programming Problems by : Patrick Dennis Krolak
Download or read book The Bounded Variable Algorithm for Solving Integer Linear Programming Problems written by Patrick Dennis Krolak and published by . This book was released on 1968 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Integer Programming by : Der-San Chen
Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Linear Programming with Applications by : Bernard Kolman
Download or read book Elementary Linear Programming with Applications written by Bernard Kolman and published by Elsevier. This book was released on 2014-05-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful.
Book Synopsis The Compact Bounded Variable Algorithm for Solving Pure Integer Linear Programming Problems by : Chia-Man Wan
Download or read book The Compact Bounded Variable Algorithm for Solving Pure Integer Linear Programming Problems written by Chia-Man Wan and published by . This book was released on 1974 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approaches to Integer Programming by : M. L. Balinski
Download or read book Approaches to Integer Programming written by M. L. Balinski and published by . This book was released on 1974 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Branch and bound experiments in 0-1 programming; A subadditive approach to the group problem of integer programming; Two computationaly difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems; Lagrangean relaxation for integer programming; A heuristic algorithm for mixed-integer programming problems; On the group problem for mixed integer programming; Experiments in the formulation of integer programming problems.
Book Synopsis Optimal Bound and Scan Algorithm for Integer Linear Programming by : Stanford University. Department of Industrial Engineering
Download or read book Optimal Bound and Scan Algorithm for Integer Linear Programming written by Stanford University. Department of Industrial Engineering and published by . This book was released on 1966 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new algorithm for solving the pure integer linear programming problem is presented and evaluated. Roughly speaking this algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. Encouraging computational experience is reported that suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems also are outlined. (Author).
Book Synopsis Integer Programming by : Robert Garfinkel
Download or read book Integer Programming written by Robert Garfinkel and published by Wiley-Interscience. This book was released on 1972 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Integer Programming by : Harvey M. Salkin
Download or read book Foundations of Integer Programming written by Harvey M. Salkin and published by North Holland. This book was released on 1989 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Integer Programming by : Elias Munapo
Download or read book Linear Integer Programming written by Elias Munapo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated.
Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin
Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
Download or read book Studies in Integer Programming written by and published by Elsevier. This book was released on 2011-10-10 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Integer Programming
Book Synopsis Mixed Integer Nonlinear Programming by : Jon Lee
Download or read book Mixed Integer Nonlinear Programming written by Jon Lee and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
Book Synopsis Integer Programming by : Harvey M. Salkin
Download or read book Integer Programming written by Harvey M. Salkin and published by Addison Wesley Publishing Company. This book was released on 1975 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixed Integer Programming Algorithms for Site Selection and Other Fixed Charge Problems Having Capacity Constraints by : Paul Gray
Download or read book Mixed Integer Programming Algorithms for Site Selection and Other Fixed Charge Problems Having Capacity Constraints written by Paul Gray and published by . This book was released on 1967 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms for solving site-selection and similar fixed charge problems with upper bound constraints are presented. The basic approach is to formulate the problem as a mixed integer program and to solve these programs by decomposing them into a master integer program and a series of subproblems which are linear programs. To reduce the number of vertices to be examined to manageable proportions, the bound-and-scan algorithm by F.S. Hillier was adapted to the fixed charge problem. Algorithms are presented for four classes of problems: (1) Fixed charge problem with linear variable costs and a fixed charge for each variable at non-zero level. (2) Problem 1 with separable concave or convex variable costs. (3) A warehouse location problem in which variable costs and constraints are of the transportation type. A fixed charge is associated with each warehouse opened. (4) The fixed charge transportation problem in which a fixed charge is associated with each route rather than with each warehouse. Computational results for Problems 1, 2, and 4 are presented. (Author).
