Download or read book Fundamental Algorithmics written by Gilles Brassard and published by Prentice Hall. This book was released on 1998 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Branch and Bound Methods for Combinatorial Problems written by John D C Little and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial problems arise in a wide variety of fields, from computer science to operations research to engineering. This book provides an in-depth introduction to the branch and bound method, a powerful algorithmic technique for solving combinatorial optimization problems. With clear explanations, detailed examples, and practical advice, John D. C. Little's work is an essential resource for anyone seeking to understand this important area of research. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Download or read book State of the Art in Global Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.

Download or read book Branch and Bound Applications in Combinatorial Data Analysis written by Michael J. Brusco and published by Springer Science & Business Media. This book was released on 2005-11-30 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides clear explanatory text, illustrative mathematics and algorithms, demonstrations of the iterative process, pseudocode, and well-developed examples for applications of the branch-and-bound paradigm to important problems in combinatorial data analysis. Supplementary material, such as computer programs, are provided on the world wide web. Dr. Brusco is an editorial board member for the Journal of Classification, and a member of the Board of Directors for the Classification Society of North America.

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.

Download or read book Computational Combinatorial Optimization written by Michael Jünger and published by Springer Science & Business Media. This book was released on 2001-11-21 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.

Download or read book Combinatorial Optimization written by Christos H. Papadimitriou and published by Courier Corporation. This book was released on 2013-04-26 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Download or read book Optimization Techniques and Applications with Examples written by Xin-She Yang and published by John Wiley & Sons. This book was released on 2018-09-19 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniques in optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint-handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book’s exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: Offers an accessible and state-of-the-art introduction to the main optimization techniques Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques Presents a balance of theory, algorithms, and implementation Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniques in optimization.

Download or read book Exact and Heuristic Methods in Combinatorial Optimization written by Rafael Martí and published by Springer Nature. This book was released on 2022-03-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, algorithmic advances as well as hardware and software improvements have provided an excellent environment to create and develop solving methods to hard optimization problems. Modern exact and heuristic techniques are dramatically enhancing our ability to solve significant practical problems. This monograph sets out state-of-the-art methodologies for solving combinatorial optimization problems, illustrating them with two well-known problems. This second edition of the book extends the first one by adding to the ‘linear ordering problem’ (LOP), included in the first edition, the ‘maximum diversity problem’ (MDP). In this way, we provide the reader with the background, elements and strategies to tackle a wide range of different combinatorial optimization problems. The exact and heuristic techniques outlined in these pages can be put to use in any number of combinatorial optimization problems. While the authors employ the LOP and the MDP to illustrate cutting-edge optimization technologies, the book is also a tutorial on how to design effective and successful implementations of exact and heuristic procedures alike. This monograph provides the basic principles and fundamental ideas that will enable students and practitioners to create valuable applications based on both exact and heuristic technologies. Specifically, it is aimed at engineers, scientists, operations researchers, and other applications specialists who are looking for the most appropriate and recent optimization tools to solve particular problems. The book provides a broad spectrum of advances in search strategies with a focus on its algorithmic and computational aspects.

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).

Download or read book Recent Advances and Historical Development of Vector Optimization written by Johannes Jahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.

Download or read book Combinatorial And Global Optimization written by Rainer E Burkard and published by World Scientific. This book was released on 2002-04-05 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans-Williamson relaxation of the maximum cut problem, and the Du-Hwang solution of the Gilbert-Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece.

Download or read book Combinatorial Optimization Problems Molecular Unfolding written by N.B. Singh and published by N.B. Singh. This book was released on with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the fascinating world of protein folding and unfolding with "Combinatorial Optimization Problems: Molecular Unfolding." This book is the perfect starting point for absolute beginners looking to understand the intricate processes behind molecular dynamics. It seamlessly integrates fundamental principles with essential optimization techniques, offering readers clear explanations and practical insights. Whether you're a student, researcher, or simply curious about molecular biology, this accessible guide will deepen your understanding of how proteins transition between various states. Embark on a journey into the captivating realm of molecular biology and computational methods—grab your copy today and unlock the secrets of molecular unfolding!

Download or read book Decision Diagrams for Optimization written by David Bergman and published by Springer. This book was released on 2016-11-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]

Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2010-01-12 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.

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.