Optimization

Algorithms and Applications

Author: Rajesh Kumar Arora

Publisher: CRC Press

ISBN: 149872115X

Category: Business & Economics

Page: 466

View: 7700

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Choose the Correct Solution Method for Your Optimization Problem Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve non-convex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures—one of the first optimization books to do so—and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory’s cutting plane method, the branch-and-bound method, and Balas’ algorithm for integer programming problems. The author follows a step-by-step approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book’s CRC Press web page.
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Stochastic Optimization

Algorithms and Applications

Author: Stanislav Uryasev,Panos M. Pardalos

Publisher: Springer Science & Business Media

ISBN: 1475765940

Category: Technology & Engineering

Page: 435

View: 8214

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Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.
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Parallel Optimization

Theory, Algorithms, and Applications

Author: Department of Mathematics and Computer Science Yair Censor,Yair Censor,Stavros Andrea Zenios

Publisher: Oxford University Press on Demand

ISBN: 9780195100624

Category: Computers

Page: 539

View: 5324

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This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.
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Practical Bilevel Optimization

Algorithms and Applications

Author: Jonathan F. Bard

Publisher: Springer Science & Business Media

ISBN: 9780792354581

Category: Business & Economics

Page: 473

View: 6589

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The focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology. What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field. Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists.
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Multilevel Optimization: Algorithms and Applications

Author: A. Migdalas,Panos M. Pardalos,Peter Värbrand

Publisher: Springer Science & Business Media

ISBN: 9780792346937

Category: Computers

Page: 384

View: 6305

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In many decision processes there is an hierarchy of decision-makers and decisions are taken at different levels in this hierarchy. Multilevel programming focuses on the whole hierarchy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of optimization problems which must be solved in a predetermined sequence. The field of multilevel optimization has become a well-known and important research field. Hierarchical structures can be found in scientific disciplines such as environment, ecology, biology, chemical engineering, mechanics, classification theory, databases, network design, transportation, game theory and economics. Moreover, new applications are constantly being introduced. This has stimulated the development of new theory and efficient algorithms. This volume contains 16 chapters written by various leading researchers and presents a cohesive authoritative overview of developments and applications in their emerging field of optimization. Audience: Researchers whose work involves the application of mathematical programming and optimization to hierarchical structures.
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Introduction to Nonlinear Optimization

Theory, Algorithms, and Applications with MATLAB

Author: Amir Beck

Publisher: SIAM

ISBN: 1611973643

Category: Mathematics

Page: 282

View: 873

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This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
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Glowworm Swarm Optimization

Theory, Algorithms, and Applications

Author: Krishnanand N. Kaipa,Debasish Ghose

Publisher: Springer

ISBN: 3319515950

Category: Computers

Page: 248

View: 5193

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This book provides a comprehensive account of the glowworm swarm optimization (GSO) algorithm, including details of the underlying ideas, theoretical foundations, algorithm development, various applications, and MATLAB programs for the basic GSO algorithm. It also discusses several research problems at different levels of sophistication that can be attempted by interested researchers. The generality of the GSO algorithm is evident in its application to diverse problems ranging from optimization to robotics. Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. The book is a valuable resource for researchers as well as graduate and undergraduate students in the area of swarm intelligence and computational intelligence and working on these topics.
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Biogeography-Based Optimization: Algorithms and Applications

Author: Yujun Zheng,Xueqin Lu,Minxia Zhang,Shengyong Chen

Publisher: Springer

ISBN: 9789811325854

Category: Computers

Page: 221

View: 3134

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This book introduces readers to the background, general framework, main operators, and other basic characteristics of biogeography-based optimization (BBO), which is an emerging branch of bio-inspired computation. In particular, the book presents the authors’ recent work on improved variants of BBO, hybridization of BBO with other algorithms, and the application of BBO to a variety of domains including transportation, image processing, and neural network learning. The content will help to advance research into and application of not only BBO but also the whole field of bio-inspired computation. The algorithms and applications are organized in a step-by-step manner and clearly described with the help of pseudo-codes and flowcharts. The readers will learn not only the basic concepts of BBO but also how to apply and adapt the algorithms to the engineering optimization problems they actually encounter.
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