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Special features of the book 1. A very comprehensive and accessible approach in the presentation of the material. 2. A variety of solved examples to illustrate the theoretical results. 3. A large number of unsolved exercises for the students are given for practice at the end of each section. 4. Solution to each unsolved examples are given at the end of each exercise.
The first edition of Integrated Methods for Optimization was published in January 2007. Because the book covers a rapidly developing field, the time is right for a second edition. The book provides a unified treatment of optimization methods. It brings ideas from mathematical programming (MP), constraint programming (CP), and global optimization (GO)into a single volume. There is no reason these must be learned as separate fields, as they normally are, and there are three reasons they should be studied together. (1) There is much in common among them intellectually, and to a large degree they can be understood as special cases of a single underlying solution technology. (2) A growing literature reports how they can be profitably integrated to formulate and solve a wide range of problems. (3) Several software packages now incorporate techniques from two or more of these fields. The book provides a unique resource for graduate students and practitioners who want a well-rounded background in optimization methods within a single course of study. Engineering students are a particularly large potential audience, because engineering optimization problems often benefit from a combined approach—particularly where design, scheduling, or logistics are involved. The text is also of value to those studying operations research, because their educational programs rarely cover CP, and to those studying computer science and artificial intelligence (AI), because their curric ula typically omit MP and GO. The text is also useful for practitioners in any of these areas who want to learn about another, because it provides a more concise and accessible treatment than other texts. The book can cover so wide a range of material because it focuses on ideas that arerelevant to the methods used in general-purpose optimization and constraint solvers. The book focuses on ideas behind the methods that have proved useful in general-purpose optimization and constraint solvers, as well as integrated solvers of the present and foreseeable future. The second edition updates results in this area and includes several major new topics: Background material in linear, nonlinear, and dynamic programming. Network flow theory, due to its importance in filtering algorithms. A chapter on generalized duality theory that more explicitly develops a unifying primal-dual algorithmic structure for optimization methods. An extensive survey of search methods from both MP and AI, using the primal-dual framework as an organizing principle. Coverage of several additional global constraints used in CP solvers. The book continues to focus on exact as opposed to heuristic methods. It is possible to bring heuristic methods into the unifying scheme described in the book, and the new edition will retain the brief discussion of how this might be done.
For first courses in operations research, operations management Optimization in Operations Research, Second Edition covers a broad range of optimization techniques, including linear programming, network flows, integer/combinational optimization, and nonlinear programming. This dynamic text emphasizes the importance of modeling and problem formulation andhow to apply algorithms to real-world problems to arrive at optimal solutions. Use a program that presents a better teaching and learning experience-for you and your students. Prepare students for real-world problems: Students learn how to apply algorithms to problems that get them ready for their field. Use strong pedagogy tools to teach: Key concepts are easy to follow with the text's clear and continually reinforced learning path. Enjoy the text's flexibility: The text features varying amounts of coverage, so that instructors can choose how in-depth they want to go into different topics.
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms. Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the “story” of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book’s various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with MapleTM and MATLAB® content for the discussed calculations. Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations Research is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.
Simulation-Based Optimization: Parametric Optimization Techniques and Reinforcement Learning introduce the evolving area of static and dynamic simulation-based optimization. Covered in detail are model-free optimization techniques – especially designed for those discrete-event, stochastic systems which can be simulated but whose analytical models are difficult to find in closed mathematical forms. Key features of this revised and improved Second Edition include: · Extensive coverage, via step-by-step recipes, of powerful new algorithms for static simulation optimization, including simultaneous perturbation, backtracking adaptive search and nested partitions, in addition to traditional methods, such as response surfaces, Nelder-Mead search and meta-heuristics (simulated annealing, tabu search, and genetic algorithms) · Detailed coverage of the Bellman equation framework for Markov Decision Processes (MDPs), along with dynamic programming (value and policy iteration) for discounted, average, and total reward performance metrics · An in-depth consideration of dynamic simulation optimization via temporal differences and Reinforcement Learning: Q-Learning, SARSA, and R-SMART algorithms, and policy search, via API, Q-P-Learning, actor-critics, and learning automata · A special examination of neural-network-based function approximation for Reinforcement Learning, semi-Markov decision processes (SMDPs), finite-horizon problems, two time scales, case studies for industrial tasks, computer codes (placed online) and convergence proofs, via Banach fixed point theory and Ordinary Differential Equations Themed around three areas in separate sets of chapters – Static Simulation Optimization, Reinforcement Learning and Convergence Analysis – this book is written for researchers and students in the fields of engineering (industrial, systems, electrical and computer), operations research, computer science and applied mathematics.
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice. - Presents optimization techniques clearly, including worked-out examples, from traditional to advanced - Maps out the relations between optimization and other mathematical topics and disciplines - Provides systematic coverage of algorithms to facilitate computer coding - Gives MATLAB© codes in relation to optimization techniques and their use in computer-aided design - Presents nature-inspired optimization techniques including genetic algorithms and artificial neural networks
Basic text on deterministic optimization methods. Techniques of modeling real world decision making problems, modeling examples that illustrate the use of modeling techniques, and a variety of problem classes are presented. Various types of algorithms with explanations of how each algorithm works and what conclusion can be drawn from its output, and a review of Matrix Algebra and Geometry and a chapter on Heuristic Methods.
The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.