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Optimal Bound And Scan Algorithm For Integer Linear Programming
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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 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 Accelerated Bound and Scan Algorithm for Integer Programming by : Stanford University. Department of Operations Research
Download or read book Accelerated Bound and Scan Algorithm for Integer Programming written by Stanford University. Department of Operations Research and published by . This book was released on 1972 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a new implicit enumeration algorithm for solving the pure integer linear programming problem. The theory of equivalent integer programming problems is first used to reformulate the problem. A technique, originally used with particular success in the bound-and-scan algorithm to deal with only a subset of the variables, is extended to all of the variables in the restructured problem. In addition to the resulting basic enumeration scheme, the algorithm includes a scanning procedure and a method for identifying constraints which become redundant during the course of the algorithm. Computational experience on standard test problems is reported.
Book Synopsis Efficient Suboptimal Algorithms for Integer Linear Programming with an Interior by : Stanford University. Department of Industrial Engineering
Download or read book Efficient Suboptimal Algorithms for Integer Linear Programming with an Interior written by Stanford University. Department of Industrial Engineering and published by . This book was released on 1966 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper presents and evaluates some new suboptimal algorithms for the pure integer linear programming problem having only inequality constraints. The computation time required by these algorithms (after obtaining the optimal noninteger solution) has been only a small fraction of that required by the simplex method. Furthermore, the solution obtained by the better algorithms consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these algorithms also are outlines. A companion paper presents an optimal 'bound-and-scan' algorithm that would be used in conjuection with these suboptimal algorithms. (Author).
Book Synopsis A further investigation of efficient heuristic procedures for integer linear programming with an interior by : Stanford University. Systems Optimization Laboratory
Download or read book A further investigation of efficient heuristic procedures for integer linear programming with an interior written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1981 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some heuristic procedures for seeking a good approximate solution of any pure integer linear programming problem are evaluated. It was found that the procedures are extremely efficient, being computationally feasible for problems having hundreds of variables and constraints. Furthermore, they proved to be very effective in identifying good solutions, often obtaining optimal ones. Thus, the procedures provide a way of dealing with the frequently encountered integer programming problems that are beyond the computational capability of existing algorithms. For smaller problems, they also provide an advanced start for accelerating certain primal algorithms, including the author's Bound-and-Scan algorithm and Faaland and Hillier's Accelerated Bound-and-Scan algorithm. In addition, Jeroslow and Smith have found that imbedding the first part of one of these procedures inside the iterative step of a branch-and-bound algorithm can greatly improve the latter's efficiency in locating solutions whose objective function value is within a specified percentage of that for the optimal solution.
Book Synopsis Interior Path Methods for Heuristic Integer Programming Procedures by : Stanford University. Department of Operations Research
Download or read book Interior Path Methods for Heuristic Integer Programming Procedures written by Stanford University. Department of Operations Research and published by . This book was released on 1977 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers heuristic procedures for general mixed integer linear programming with inequality constraints. It focuses on the question of how to most effectively initialize such procedures by constructing an interior path from which to search for good feasible solutions. These paths lead from an optimal solution for the corresponding linear programming problem (i.e., deleting integrality restrictions) into the interior of the feasible region for this problem. Previous methods for constructing linear paths of this kind are analyzed from a statistical viewpoint, which motivates a promising new method. These methods are then extended to piecewise linear paths in order to improve the direction of search in certain cases where constraints that are not binding on the optimal linear programming solution become particularly relevant. Computational experience is reported. (Author).
Book Synopsis Estimates and Bounds on Computational Effort in the Accelerated Bound and Scan Algorithm by : Stanford University. Department of Operations Research
Download or read book Estimates and Bounds on Computational Effort in the Accelerated Bound and Scan Algorithm written by Stanford University. Department of Operations Research and published by . This book was released on 1972 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for obtaining estimates and bounds on computational effort in the Accelerated bound-and-scan algorithm are presented. The basic tools of analysis used are various results from the theory of partitions of numbers, and central-limit theorem, and geometric interpretations of the algorithm. The results of the analysis are used to provide partial answers to questions such as (a) What is the greatest amount of time the algorithm could require to solve a given problem. (b) What is the expected computation time. (c) How should the variables and constraints be ordered. (d) How does the computation time depend on the number of variables. and (E) How is the computation time affected by the quality of the starting solution.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integer Programming and Related Areas by : C. Kastning
Download or read book Integer Programming and Related Areas written by C. Kastning and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integer Prograw~ing is one of the most fascinating and difficult areas in the field of Mathematical Optimization. Due to this fact notable research contributions to Integer Programming have been made in very different branches of mathematics and its applications. Since these publications are scattered over many journals, proceedings volumes, monographs, and working papers, a comprehensive bibliography of all these sources is a helpful tool even for specialists in this field. I initiated this compilation of literature in 1970 at the Institut fur ~konometrie und Operations Research, University of Bonn. Since then many collaborators have contributed to and worked on it. Among them Dipl.-Math. Claus Kastning has done the bulk of the work. With great perseverance and diligence he has gathered all the material and checked it with the original sources. The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers. Without the invaluable and dedicated engagement of Claus Kastning the bibliography would never have reached this final version. For this reason he must be considered its responsible editor. As with any other collection this literature list has a subjective viewpoint and may be in some sense incomplete. We have however tried to be as complete as possible. The bibliography contains 4704 different publications by 6767 authors which were classified by 11839 descriptor entries.
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).
Book Synopsis U.S. Government Research & Development Reports by :
Download or read book U.S. Government Research & Development Reports written by and published by . This book was released on 1966-11 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1982 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Integer Programming and Combinatorial Optimization by : Gerard Cornuejols
Download or read book Integer Programming and Combinatorial Optimization written by Gerard Cornuejols and published by Springer. This book was released on 2007-03-05 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Integer Programming and Combinatorial Optimization, IPCO'99, held in Graz, Austria, in June 1999. The 33 revised full papers presented were carefully reviewed and selected from a total of 99 submissions. Among the topics addressed are theoretical, computational, and application-oriented aspects of approximation algorithms, branch and bound algorithms, computational biology, computational complexity, computational geometry, cutting plane algorithms, diaphantine equations, geometry of numbers, graph and network algorithms, online algorithms, polyhedral combinatorics, scheduling, and semidefinite programs.
Download or read book Discrete Optimization I written by and published by Elsevier. This book was released on 2000-04-01 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Optimization I
Book Synopsis Efficient Heuristic Procedures for Integer Linear Programming with an Interior by : Stanford University. Department of Operations Research
Download or read book Efficient Heuristic Procedures for Integer Linear Programming with an Interior written by Stanford University. Department of Operations Research and published by . This book was released on 1969 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods (after obtaining the optimal noninteger solution by the simplex method) has generally been only a small fraction of that used by the simplex method for the problems tested (which have 15 to 300 original variables). Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. There are numerous important problems in logistics that can be formulated as integer linear programming problems. These algorithms enable one to obtain good solutions to large problems of this kind. (Author).
Book Synopsis A Linear Programming Based Branch and Bound Algorithm for Mixed Integer Generalized Network Problems by : Raymond Neil McCollum
Download or read book A Linear Programming Based Branch and Bound Algorithm for Mixed Integer Generalized Network Problems written by Raymond Neil McCollum and published by . This book was released on 1981 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
