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Solving Set Partitioning Problems Using Lagrangian Relaxation
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Book Synopsis Solving Set Partitioning Problems Using Lagrangian Relaxation by : Maria Gertruda Cornelia van Blanc- van Krieken
Download or read book Solving Set Partitioning Problems Using Lagrangian Relaxation written by Maria Gertruda Cornelia van Blanc- van Krieken and published by . This book was released on 2006 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Lagrangean Relaxation Based Algorithm for Solving Set Partitioning Problems by : Maria Gertruda Cornelia Krieken
Download or read book A Lagrangean Relaxation Based Algorithm for Solving Set Partitioning Problems written by Maria Gertruda Cornelia Krieken and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Dual Algorithm for Large Scale Set Partitioning by : Marshall L. Fisher
Download or read book A Dual Algorithm for Large Scale Set Partitioning written by Marshall L. Fisher and published by . This book was released on 1986 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Searching for Optimal Integer Solutions to Set Partitioning Problems Using Column Generation by : David Bredstrom
Download or read book Searching for Optimal Integer Solutions to Set Partitioning Problems Using Column Generation written by David Bredstrom and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a new approach to produce integer feasible columns to a set partitioning problem directly in solving the linear programming (LP) relaxation using column generation. Traditionally, column generation is aimed to solve the LP relaxation as quick as possible without any concern of the integer properties of the columns formed. In our approach we aim to generate the columns forming the optimal integer solution while simultaneously solving the LP relaxation. By this we can remove column generation in the branch and bound search. The basis is a subgradient technique applied to a Lagrangian dual formulation of the set partitioning problem extended with an additional surrogate constraint. This extra constraint is not relaxed and is used to better control the subgradient evaluations. The column generation is then directed, via the multipliers, to construct columns that form feasible integer solutions. Computational experiments show that we can generate the optimal integer columns in a large set of well known test problems as compared to both standard and stabilized column generation and simultaneously keep the number of columns smaller than standard column generation.
Book Synopsis Integer and Combinatorial Optimization by : Laurence A. Wolsey
Download or read book Integer and Combinatorial Optimization written by Laurence A. Wolsey and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.
Book Synopsis Exploiting Consecutive Ones Structure in the Set Partitioning Problem by : Mehmet Ayik
Download or read book Exploiting Consecutive Ones Structure in the Set Partitioning Problem written by Mehmet Ayik and published by . This book was released on 2000-12-01 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Set Partitioning Problem (SPP) is one of the most extensively researched models in integer optimization, and is widely applied in operations research. SPP is used for crew scheduling, vehicle routing, stock cutting, production scheduling, and many other combinatorial problems. The power and generality of SPP come at a price: An SPP can be very difficult to solve. A real-world SPP often has columns, or rows, with long strings of consecutive ones. We exploit this with a new preprocessing reduction that can eliminate some variables. We also introduce a column-splitting technique to render a model that can be solved directly or used to bound SPP with Lagrangian relaxation or an exterior penalty method. We develop an SPP row- splitting method that yields a special model that Bender's decomposition may then solve faster than the monolithic SPP. We demonstrate these techniques with well-known test problems from airlines and other researchers. We also contribute a new U.S. Navy aircraft carrier long-term deployment scheduling model, using our new techniques to plan with weekly fidelity over a ten-year planning horizon. This improved time fidelity increases planned deployment coverage of areas of responsibility by about ten carrier weeks.
Book Synopsis A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by : Hanif D. Sherali
Download or read book A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems written by Hanif D. Sherali and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
Book Synopsis Column Generation by : Guy Desaulniers
Download or read book Column Generation written by Guy Desaulniers and published by Springer Science & Business Media. This book was released on 2006-03-20 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
Book Synopsis Handbook of Constraint Programming by : Francesca Rossi
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
Book Synopsis Naval Research Logistics Quarterly by :
Download or read book Naval Research Logistics Quarterly written by and published by . This book was released on 1979 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Lagrangian Relaxation and Branch-and-bound Procedure for Solving Problems with Workload Balancing Constraints by : James Pirie Hart
Download or read book A Lagrangian Relaxation and Branch-and-bound Procedure for Solving Problems with Workload Balancing Constraints written by James Pirie Hart and published by . This book was released on 1984 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantitative Problem Solving Methods in the Airline Industry by : Cynthia Barnhart
Download or read book Quantitative Problem Solving Methods in the Airline Industry written by Cynthia Barnhart and published by Springer Science & Business Media. This book was released on 2011-12-22 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews Operations Research theory, applications and practice in seven major areas of airline planning and operations. In each area, a team of academic and industry experts provides an overview of the business and technical landscape, a view of current best practices, a summary of open research questions and suggestions for relevant future research. There are several common themes in current airline Operations Research efforts. First is a growing focus on the customer in terms of: 1) what they want; 2) what they are willing to pay for services; and 3) how they are impacted by planning, marketing and operational decisions. Second, as algorithms improve and computing power increases, the scope of modeling applications expands, often re-integrating processes that had been broken into smaller parts in order to solve them in the past. Finally, there is a growing awareness of the uncertainty in many airline planning and operational processes and decisions. Airlines now recognize the need to develop ‘robust’ solutions that effectively cover many possible outcomes, not just the best case, “blue sky” scenario. Individual chapters cover: Customer Modeling methodologies, including current and emerging applications. Airline Planning and Schedule Development, with a look at many remaining open research questions. Revenue Management, including a view of current business and technical landscapes, as well as suggested areas for future research. Airline Distribution -- a comprehensive overview of this newly emerging area. Crew Management Information Systems, including a review of recent algorithmic advances, as well as the development of information systems that facilitate the integration of crew management modeling with airline planning and operations. Airline Operations, with consideration of recent advances and successes in solving the airline operations problem. Air Traffic Flow Management, including the modeling environment and opportunities for both Air Traffic Flow Management and the airlines.
Author :Christodoulos A. Floudas Publisher :Springer Science & Business Media ISBN 13 :0387747583 Total Pages :4646 pages Book Rating :4.3/5 (877 download)
Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas
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".
Book Synopsis Handbook of Approximation Algorithms and Metaheuristics by : Teofilo F. Gonzalez
Download or read book Handbook of Approximation Algorithms and Metaheuristics written by Teofilo F. Gonzalez and published by CRC Press. This book was released on 2018-05-15 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.
Book Synopsis The Logic of Logistics by : David Simchi-Levi
Download or read book The Logic of Logistics written by David Simchi-Levi and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state-of-the-art in the science of logistics management. As a result, the authors have written a timely and authoritative survey of this field that many practitioners and researchers will find makes an invaluable companion to their work.
Book Synopsis Models for Practical Routing Problems in Logistics by : S. P. Anbuudayasankar
Download or read book Models for Practical Routing Problems in Logistics written by S. P. Anbuudayasankar and published by Springer. This book was released on 2014-07-08 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with complex variants of Travelling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) within the manufacturing and service industries. The objective is to develop heuristics for these supply chain problems in order to offer practical solutions to improve operational efficiency. These heuristics are evaluated using benchmark and derived data-sets. Case studies pertaining to logistics in different industries including textile machinery manufacturing and banking are also included to demonstrate the created heuristics. High competition in today’s global market has forced the organizations to invest in and focus on their logistics system. The critical function of logistics is the transportation within and across various supply chain entities. Both supply and distribution procedure require effective transportation management. A small improvement in routing problems can lead to huge logistics savings in absolute terms. This book should appeal to executives, researchers and consultants seeking supply chain management solutions.
Book Synopsis Pro-active Dynamic Vehicle Routing by : Francesco Ferrucci
Download or read book Pro-active Dynamic Vehicle Routing written by Francesco Ferrucci and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with transportation processes denoted as the Real-time Distribution of Perishable Goods (RDOPG). The book presents three contributions that are made to the field of transportation. First, a model considering the minimization of customer inconvenience is formulated. Second, a pro-active real-time control approach is proposed. Stochastic knowledge is generated from past request information by a new forecasting approach and is used in the pro-active approach to guide vehicles to request-likely areas before real requests arrive there. Various computational results are presented to show that in many cases the pro-active approach is able to achieve significantly improved results. Moreover, a measure for determining the structural quality of request data sets is also proposed. The third contribution of this book is a method that is presented for considering driver inconvenience aspects which arise from vehicle en-route diversion activities. Specifically, this method makes it possible to restrict the number of performed vehicle en-route diversion activities.
