Download or read book A BENDER S APPROACH TO DISJUNCTIVE PROGRAMMING written by James C. Bean and published by . This book was released on 1992 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Disjunctive Programming written by Egon Balas and published by Springer. This book was released on 2018-11-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business.

Download or read book Disjunctive Programming written by Egon Balas and published by . This book was released on 1977 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper reviews some recent developments in the convex analysis approach to integer programming. These developments are based on viewing integer programs as disjunctive programs. i.e., linear programs with disjunctive constraints, an approach which seems to be fruitful for 0-1 programming both theoretically and practically. On the theoretical side, it provides structural characterizations which offer new insights. On the practical side, it produces a variety of cutting planes with desirable properties and offers new ways of combining cutting planes with enumerative techniques. (Author).

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

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 Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems written by Jean-Charles Régin and published by Springer Science & Business Media. This book was released on 2004-04-07 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2004, held in Nice, France in April 2004. The 23 revised full papers and 7 revised short papers presented together with an invited talk were carefully reviewed and selected from 56 submissions. Methodological and foundational issues from AI, OR, and algorithmics are presented as well as applications to the solution of combinatorial optimization problems in various fields via constraint programming.

Download or read book Computational Stochastic Programming written by Lewis Ntaimo and published by Springer Nature. This book was released on with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Integer Programming written by and published by . This book was released on 2005 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book FINITE DISJUNCTIVE PROGRAMMING METHODS FOR GENERAL MIXED INTEGER LINEAR PROGRAMS written by Binyuan Chen and published by . This book was released on 2011 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, a finitely convergent disjunctive programming procedure, the Convex Hull Tree (CHT) algorithm, is proposed to obtain the convex hull of a general mixed & ndash;integer linear program with bounded integer variables. The CHT algorithm constructs a linear program that has the same optimal solution as the associated mixed-integer linear program. The standard notion of sequential cutting planes is then combined with ideasunderlying the CHT algorithm to help guide the choice of disjunctions to use within a new cutting plane method, the Cutting Plane Tree (CPT) algorithm. We show that the CPT algorithm converges to an integer optimal solution of the general mixed-integer linear program with bounded integer variables in finitely many steps. We also enhance the CPT algorithm with several techniques including a & ldquo;round-of-cuts & rdquo; approach and an iterative method for solving the cut generation linear program (CGLP). Two normalization constraints are discussed in detail for solving the CGLP. For moderately sized instances, our study shows that the CPT algorithm provides significant gap closures with a pure cutting plane method.

Download or read book Integer Programming and Combinatorial Optimization written by Karen Aardal and published by Springer Nature. This book was released on 2022-05-27 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 23rd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2022, held in Eindhoven, The Netherlands, in June 2022. The 33 full papers presented were carefully reviewed and selected from 93 submissions addressing key techniques of document analysis. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting the latest results of theory and practice of the various aspects of discrete optimization.

Download or read book Logic Based Benders Decomposition written by John Hooker and published by Springer Nature. This book was released on 2023-12-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growing variety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

Download or read book Global Optimization and Constraint Satisfaction written by Christophe Jermann and published by Springer Science & Business Media. This book was released on 2005-05-24 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the throughly refereed post-proceedings of the Second International Workshop on Global Optimization and Constraint Satisfaction, COCOS 2003, held in Lausanne, Switzerland in Nowember 2003. The 13 revised full papers presented were carefully selected and went through two rounds of reviewing and improvement. The papers are devoted to theoretical, algorithmic, and application-oriented issues in global constrained optimization and constraint satisfaction; they are organized in topical sections on constraint satisfaction problems, global optimization, and applications.

Download or read book Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems written by Egon Balas and published by . This book was released on 1983 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses a new conceptual framework for the convexification of discrete optimization problems, and a general technique for obtaining approximations to the convex hull of the feasible set. The concepts come from disjunctive programming and the key tool is a description of the convex hull of a union of polyhedra in terms of a higher dimensional polyhedron. Although this description was known for several years, only recently was it shown by Jeroslow and Lowe to yield improved representations of discrete optimization problem as the intersection (conjunction) of unions of polyhedra, and define an operation that takes one such expression into another, equivalent one, with fewer conjuncts. Then introduced is a class of relaxations based on replacing each conjunct (union of polyhdera) by its convex hull. The strength of the relaxation increases as the number of conjuncts decreases, and the class of relaxations forms a hierarchy that spans the spectrum between the common linear programming relaxation, and the convex hull of the feasible set itself. Instances where this approach presents advantages include critical path problems in disjunctive graphs, network synthesis problems, certain fixed charge network flow problems, etc. The author illustrates the approach on the first of these problems, which is a model for machine sequencing. (Author).

Download or read book Handbooks in Operations Research and Management Science written by K. Aardal and published by Elsevier. This book was released on 2005-12-08 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this Handbook volume cover nine main topics that are representative of recent theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on the early history of the field. The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization.

Download or read book Handbook of Constraint Programming written by Francesca Rossi and published by Elsevier. This book was released on 2006-08-18 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.- Covers the whole field of constraint programming- Survey-style chapters- Five chapters on applications

Download or read book Large Scale Optimization with Applications written by and published by Springer Science & Business Media. This book was released on 1997 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Logic Based Methods for Optimization written by John Hooker and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling and solutiontechniques. Designed to be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more