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Scheduling Using Relaxation And Decomposition
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Author :Stanford University. Department of Operations Research. Systems Optimization Laboratory Publisher : ISBN 13 : Total Pages :26 pages Book Rating :4.F/5 ( download)
Book Synopsis Scheduling Using Relaxation and Decomposition by : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Download or read book Scheduling Using Relaxation and Decomposition written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1995 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming by : Ivo Nowak
Download or read book Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming written by Ivo Nowak and published by Springer Science & Business Media. This book was released on 2005-08-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.
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 Intermittent Production Scheduling by : Charles A. Holloway
Download or read book Intermittent Production Scheduling written by Charles A. Holloway and published by . This book was released on 1977 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Integer Programming and Decomposition to Scheduling Problems by : Orlando Rivera letelier
Download or read book Applications of Integer Programming and Decomposition to Scheduling Problems written by Orlando Rivera letelier and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In scheduling problems, the goal is to assign time slots to a set of activities. In these problems, there are typically precedence constraints between activities that dictate the order in which they can be carried out and resource constraints that limit the number that can simultaneously be executed. In this thesis, we develop mixed integer programming methodologies, based on decomposition methods, for two very different classes of scheduling problems. These are the Strategic Open Pit Mine Planning Problem (SOPMP) and the Bin Packing Problem with Time Lags.Given a discretized representation of an orebody known as a block model, the SOPMP that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. These problems are known to be very difficult due to the large size of real mine planning problems (eg, millions of blocks, dozens of years). They are also very important in the mining industry. Every major mining operation in the world must solve this problem, at the very least, on a yearly basis.In this thesis, we tackle the SOPMP in Chapters 2 and 3.In Chapter 2 we begin by studying a lagrangean algorithm developed by Dan Bienstock and Mark Zuckerberg (henceforth, the BZ algorithm) in 2009 for solving the LP relaxation of large instances of SOPMP. In this study we generalize the classes of problems that can be solved with the BZ algorithm, and show that it can be cast as a special type of column generation algorithm. We prove, for general classes of mixed integer programming problems, that the BZ relaxation provides a bound that lies between the LP relaxation and Dantzig-Wolfe bounds. We further develop computational speed-ups that improve the performance of the BZ algorithm in practice, and test these on a large collection of data-sets.In Chapter 3 we deal with the problem of computing integer-feasible solution to SOPMP. Using the BZ algorithm developed in Chapter 2, we develop heuristics for this. In addition, we develop pre-procesing algorithms that reduce problem size, and embed the BZ algorithm in a branch-and-cut framework that makes use of two new classes of cutting planes. When comparing the value of the heuristics to the LP relaxation bound, the average gap computed is close to 10%. However, when applying the pre-processing techniques and cutting planes, this is reduced to 1.5% at the root node. Four hours of branching further reduces this to 0.6%.In Chapter 4, the BPPTL is presented. This is a generalization of the Bin Packing Problem in which bins must be assigned to time slots, while satisfying precedence constraints with lags. Two integer programming formulations are proposed: a compact formulation that models the problem exactly, and an extended formulation that models a relaxation. For two special cases of the problem, the case with unlimited bins per period and the case with one bin per period and non-negative time lags, we strengthen the extended formulation with a special family of constraints. We propose a branch-cut-and-price (BCP) algorithm to solve this formulation, with separation of integer and fractional solutions, and a strong diving heuristic. Computational experiments confirm that the BCP algorithm outperforms solving the compact formulation with a commercial solver. Using this approach we were able to optimally solve 70% of a class of previously open instances of this problem.
Book Synopsis Metaheuristics for Scheduling in Industrial and Manufacturing Applications by : Fatos Xhafa
Download or read book Metaheuristics for Scheduling in Industrial and Manufacturing Applications written by Fatos Xhafa and published by Springer. This book was released on 2008-08-22 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decades scheduling has been among the most studied op- mization problemsanditisstillanactiveareaofresearch!Schedulingappears in many areas of science, engineering and industry and takes di?erent forms depending on the restrictions and optimization criteria of the operating en- ronments [8]. For instance, in optimization and computer science, scheduling has been de?ned as “the allocation of tasks to resources over time in order to achieve optimality in one or more objective criteria in an e?cient way” and in production as “production schedule, i. e. , the planning of the production or the sequence of operations according to which jobs pass through machines and is optimal with respect to certain optimization criteria. ” Although there is a standardized form of stating any scheduling problem, namely “e?cient allocation ofn jobs onm machines –which can process no more than one activity at a time– with the objective to optimize some - jective function of the job completion times”, scheduling is in fact a family of problems. Indeed, several parameters intervene in the problem de?nition: (a) job characteristics (preemptive or not, precedence constraints, release dates, etc. ); (b) resource environment (single vs. parallel machines, un- lated machines, identical or uniform machines, etc. ); (c) optimization criteria (minimize total tardiness, the number of late jobs, makespan, ?owtime, etc. ; maximize resource utilization, etc. ); and, (d) scheduling environment (static vs. dynamic,intheformerthenumberofjobstobeconsideredandtheirready times are available while in the later the number of jobs and their charact- istics change over time).
Book Synopsis Chemical Production Scheduling by : Christos T. Maravelias
Download or read book Chemical Production Scheduling written by Christos T. Maravelias and published by Cambridge University Press. This book was released on 2021-05-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Beginning with basic principles and an overview of linear and mixed-integer programming, this unified treatment introduces the fundamental ideas underpinning most modeling approaches, and will allow you to easily develop your own models. With more than 150 figures, the basic concepts and ideas behind the development of different approaches are clearly illustrated. Addresses a wide range of problems arising in diverse industrial sectors, from oil and gas to fine chemicals, and from commodity chemicals to food manufacturing. A perfect resource for engineering and computer science students, researchers working in the area, and industrial practitioners.
Book Synopsis The Planning and Scheduling of Production Systems by : Abdelhakim Artiba
Download or read book The Planning and Scheduling of Production Systems written by Abdelhakim Artiba and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: If one accepts the premise that there is no wealth without production, whether at the individual or national level, one is immediately led to the conclusion that the study of productive systems lies at the forefront of subjects that should be intensively, as well as rationally and extensively, studied to achieve the desired 'sustainable growth' of society, where the latter is defined as growth in the quality of life that does not waste the available resources in the long run. Since the end of World War II there has been a remarkable evolution in thinking about production, abetted to a large measure by the nascent field of informatics: the computer technology and the edifices that have been built around it, such as information gathering and dissemination worldwide through communication networks, software products, peripheral interfaces, etc. Additionally, the very thought processes that guide and motivate studies in production have undergone fundamental changes which verge on being revolutionary, thanks to developments in operations research and cybernetics.
Book Synopsis Mathematical Optimization Theory and Operations Research by : Michael Khachay
Download or read book Mathematical Optimization Theory and Operations Research written by Michael Khachay and published by Springer. This book was released on 2019-06-12 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 48 full papers presented in this volume were carefully reviewed and selected from 170 submissions. MOTOR 2019 is a successor of the well-known International and All-Russian conference series, which were organized in Ural, Siberia, and the Far East for a long time. The selected papers are organized in the following topical sections: mathematical programming; bi-level optimization; integer programming; combinatorial optimization; optimal control and approximation; data mining and computational geometry; games and mathematical economics.
Book Synopsis 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering by :
Download or read book 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering written by and published by Elsevier. This book was released on 2015-07-14 with total page 2667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 25th European Symposium on Computer-Aided Process Engineering contains the papers presented at the 12th Process Systems Engineering (PSE) and 25th European Society of Computer Aided Process Engineering (ESCAPE) Joint Event held in Copenhagen, Denmark, 31 May - 4 June 2015. The purpose of these series is to bring together the international community of researchers and engineers who are interested in computing-based methods in process engineering. This conference highlights the contributions of the PSE/CAPE community towards the sustainability of modern society. Contributors from academia and industry establish the core products of PSE/CAPE, define the new and changing scope of our results, and future challenges. Plenary and keynote lectures discuss real-world challenges (globalization, energy, environment, and health) and contribute to discussions on the widening scope of PSE/CAPE versus the consolidation of the core topics of PSE/CAPE. Highlights how the Process Systems Engineering/Computer-Aided Process Engineering community contributes to the sustainability of modern society Presents findings and discussions from both the 12th Process Systems Engineering (PSE) and 25th European Society of Computer-Aided Process Engineering (ESCAPE) Events Establishes the core products of Process Systems Engineering/Computer Aided Process Engineering Defines the future challenges of the Process Systems Engineering/Computer Aided Process Engineering community
Download or read book Metaheuristics written by Luca Di Gaspero and published by Springer Nature. This book was released on 2023-02-22 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Conference on Metaheuristics, MIC 2022, held in Syracuse, Italy, in July 2022. The 48 full papers together with 17 short papers presented were carefully reviewed and selected from 72 submissions. The papers detail metaheuristic techniques. Chapter “Evaluating the Effects of Chaos in Variable Neighbourhood Search” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Operations Research by : Jay E. Aronson
Download or read book Operations Research written by Jay E. Aronson and published by IAP. This book was released on 2009-04-01 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawn from a conference honoring Gerald L. Thompson, the pioneer of operations research, this volume brings together some of the latest writings of major figures in the field. The volume is divided into four parts: the first part reviews the career and significance of Thompson, the second concentrates on linear and nonlinear optimization, the third looks at network and integer programming, and the fourth provides examples of applications-oriented research in manufacturing. This volume will be an invaluable resource for all scholars and researchers involved in theory and methodology in operations research and management science.
Book Synopsis Optimization Theory for Large Systems by : Leon S. Lasdon
Download or read book Optimization Theory for Large Systems written by Leon S. Lasdon and published by Courier Corporation. This book was released on 2013-01-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.
Author :Crouzeix, Jean-Pierre Publisher :Montréal : Centre for Research on Transportation = Centre de recherche sur les transports ISBN 13 : Total Pages :42 pages Book Rating :4.:/5 (222 download)
Book Synopsis Vehicle Scheduling Problem : Lagrangean Decomposition and Duality Gap by : Crouzeix, Jean-Pierre
Download or read book Vehicle Scheduling Problem : Lagrangean Decomposition and Duality Gap written by Crouzeix, Jean-Pierre and published by Montréal : Centre for Research on Transportation = Centre de recherche sur les transports. This book was released on 1989 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Lagrangean decomposition and Lagrangean relaxation are used to deal with the vehicle scheduling problem with multiple vehicle types and time windows. Relying on general results about Langrangean decomposition, it is shown that for many vehicle scheduling problems, lower bounds generated with Lagrangean decomposition and Lagrangean relaxation are identical. Furthermore, applying general results about duality gap to our problem, it is shown that it can be reduced to zero by using augmented versions of Lagrangean decomposition and relaxation."
Book Synopsis Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by : Mohit Tawarmalani
Download or read book Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming written by Mohit Tawarmalani and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.
Book Synopsis Computational Modeling and Problem Solving in the Networked World by : Hemant K. Bhargava
Download or read book Computational Modeling and Problem Solving in the Networked World written by Hemant K. Bhargava and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of a selected subset of research articles presented at the Eighth INFORMS Computing Society Conference, held in Chandler, Arizona, from January 8 to 10, 2003. The articles in this book represent the diversity and depth of the interface between ORiMS (operations research and the management sciences) and CS/AI (computer science and artificial intelligence ). This volume starts with two papers that represent the reflective and integrative thinking that is critical to any scientific discipline. These two articles present philosophical perspectives on computation, covering a variety of traditional and newer methods for modeling, solving, and explaining mathematical models. The next set includes articles that study machine learning and computational heuristics, and is followed by articles that address issues in performance testing of solution algorithms and heuristics. These two sets of papers demonstrate the richness of thought that takes place at the ORiMS and CSI AI interface. The final set of articles demonstrates the usefulness of these and other methods at the interface towards solving problems in the real world, covering e-commerce, workflow, electronic negotiation, music, parallel computation, and telecommunications. The articles in this collection represent the results of cross-fertilization between ORiMS and CSI AI, making possible advances that could have not been achieved in isolation. The continuing aim ofthe INFORMS Computing Society and this research conference is to invigorate and further develop this interface.
Book Synopsis Electric Power System Applications of Optimization by : James A. Momoh
Download or read book Electric Power System Applications of Optimization written by James A. Momoh and published by CRC Press. This book was released on 2017-12-19 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the demand for energy continues to grow, optimization has risen to the forefront of power engineering research and development. Continuing in the bestselling tradition of the first edition, Electric Power System Applications of Optimization, Second Edition presents the theoretical background of optimization from a practical power system point of view, exploring advanced techniques, new directions, and continuous application problems. The book provides both the analytical formulation of optimization and various algorithmic issues that arise in the application of various methods in power system planning and operation. The second edition adds new functions involving market programs, pricing, reliability, and advances in intelligent systems with implemented algorithms and illustrative examples. It describes recent developments in the field of Adaptive Critics Design and practical applications of approximate dynamic programming. To round out the coverage, the final chapter combines fundamental theories and theorems from functional optimization, optimal control, and dynamic programming to explain new Adaptive Dynamic Programming concepts and variants. With its one-of-a-kind integration of cornerstone optimization principles with application examples, this second edition propels power engineers to new discoveries in providing optimal supplies of energy.
