Download or read book Perspective and problem for dynamic programming with uncertainty written by Masami Yasuda and published by . This book was released on 2001 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Techniques for Problem Solving in Uncertainty written by Tilahun, Surafel Luleseged and published by IGI Global. This book was released on 2018-06-22 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: When it comes to optimization techniques, in some cases, the available information from real models may not be enough to construct either a probability distribution or a membership function for problem solving. In such cases, there are various theories that can be used to quantify the uncertain aspects. Optimization Techniques for Problem Solving in Uncertainty is a scholarly reference resource that looks at uncertain aspects involved in different disciplines and applications. Featuring coverage on a wide range of topics including uncertain preference, fuzzy multilevel programming, and metaheuristic applications, this book is geared towards engineers, managers, researchers, and post-graduate students seeking emerging research in the field of optimization.
Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
Download or read book The Quadratic Assignment Problem written by E. Cela and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.
Download or read book Foundations of Non stationary Dynamic Programming with Discrete Time Parameter written by K. Hinderer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is an extended version of a manuscript of a course which the author taught at the University of Hamburg during summer 1969. The main purpose has been to give a rigorous foundation of stochastic dynamic programming in a manner which makes the theory easily applicable to many different practical problems. We mention the following features which should serve our purpose. a) The theory is built up for non-stationary models, thus making it possible to treat e.g. dynamic programming under risk, dynamic programming under uncertainty, Markovian models, stationary models, and models with finite horizon from a unified point of view. b) We use that notion of optimality (p-optimality) which seems to be most appropriate for practical purposes. c) Since we restrict ourselves to the foundations, we did not include practical problems and ways to their numerical solution, but we give (cf.section 8) a number of problems which show the diversity of structures accessible to non stationary dynamic programming. The main sources were the papers of Blackwell (65), Strauch (66) and Maitra (68) on stationary models with general state and action spaces and the papers of Dynkin (65), Hinderer (67) and Sirjaev (67) on non-stationary models. A number of results should be new, whereas most theorems constitute extensions (usually from stationary models to non-stationary models) or analogues to known results.
Download or read book Decision Making under Uncertainty in Financial Markets written by Jonas Ekblom and published by Linköping University Electronic Press. This book was released on 2018-09-13 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses the topic of decision making under uncertainty, with particular focus on financial markets. The aim of this research is to support improved decisions in practice, and related to this, to advance our understanding of financial markets. Stochastic optimization provides the tools to determine optimal decisions in uncertain environments, and the optimality conditions of these models produce insights into how financial markets work. To be more concrete, a great deal of financial theory is based on optimality conditions derived from stochastic optimization models. Therefore, an important part of the development of financial theory is to study stochastic optimization models that step-by-step better capture the essence of reality. This is the motivation behind the focus of this thesis, which is to study methods that in relation to prevailing models that underlie financial theory allow additional real-world complexities to be properly modeled. The overall purpose of this thesis is to develop and evaluate stochastic optimization models that support improved decisions under uncertainty on financial markets. The research into stochastic optimization in financial literature has traditionally focused on problem formulations that allow closed-form or `exact' numerical solutions; typically through the application of dynamic programming or optimal control. The focus in this thesis is on two other optimization methods, namely stochastic programming and approximate dynamic programming, which open up opportunities to study new classes of financial problems. More specifically, these optimization methods allow additional and important aspects of many real-world problems to be captured. This thesis contributes with several insights that are relevant for both financial and stochastic optimization literature. First, we show that the modeling of several real-world aspects traditionally not considered in the literature are important components in a model which supports corporate hedging decisions. Specifically, we document the importance of modeling term premia, a rich asset universe and transaction costs. Secondly, we provide two methodological contributions to the stochastic programming literature by: (i) highlighting the challenges of realizing improved decisions through more stages in stochastic programming models; and (ii) developing an importance sampling method that can be used to produce high solution quality with few scenarios. Finally, we design an approximate dynamic programming model that gives close to optimal solutions to the classic, and thus far unsolved, portfolio choice problem with constant relative risk aversion preferences and transaction costs, given many risky assets and a large number of time periods.
Download or read book Applied Mathematical Programming written by Stephen P. Bradley and published by Addison Wesley Publishing Company. This book was released on 1977 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission and composition of the U.S. merchant Marine fleet; network models; integer programming; design of a naval tender job shop; dynamic programming; large-scale systems; nonlinear programming; a system for bank portfolio planning; vectors and matrices; linear programming in matrix form; a labeling algorithm for the maximun-flow network problem.
Download or read book Robust Optimization written by Aharon Ben-Tal and published by Princeton University Press. This book was released on 2009-08-10 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
Download or read book High dimensional Adaptive Dynamic Programming with Mixed Integer Linear Programming written by Zirun Zhang and published by . This book was released on 2015 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming (DP, Bellman 1957) is a classic mathematical programming approach to solve multistage decision problems. The "Bellman equation" uses a recursive concept that includes both the current contribution and future contribution in the objective function of an optimization. The method has potential to represent dynamic decision-making systems, but an exact DP solution algorithm is limited to small problems with restrictions, such as problems with linear transitions and problems without uncertainty. Approximate dynamic programming (ADP) is a modern branch of DP that seeks to achieve numerical solutions via approximation. It is can be applied to real-world DP problems, but there are still challenges for high dimensions. This dissertation focuses on ADP value function approximation for a continuous-state space using the statistical perspective (Chen et al. 1999). Two directions of ADP methodology are developed: a sequential algorithm to explore the state space, and a sequential algorithm using mixed integer linear programming (MILP) and regression trees. The first component addresses exploration of the state space. A sequential state space exploration (SSSE) algorithm (Fan 2008) was developed using neural networks. Here it is considered the use of multivariate adaptive regression splines (Friedman 1991) in place of neural networks. In ADP, the value function approximation is defined over a specified state space region. In the real world, the relevant state space region is unknown. In particular, the ADP approach employed in this dissertation uses a statistical perspective that is analogous to design and analysis of computer experiments (DACE, Chen et al. 2006). In DACE, an experimental design is used to discretize the input space region, which is the state space region in ADP. Since the ADP state space region is unknown, SSSE uses the stochastic trajectories to sample future states and identify the potential range of system state. By reducing iterations without impacting solution quality, SSSE using MARS demonstrates improved efficiency over SSSE with neural networks. The second component of this dissertation addresses the optimization of a real world, complex, dynamic system. This work is motivated by a case study on the environmental impact of aircraft deicing activities at the Dallas-Fort Worth (D/FW) International Airport. For this case study, the state transitions are nonlinear, the objective function is nonconvex, and the decision (action) space is high-dimensional and discrete. To overcome these complexities, an ADP method is introduced using a piecewise linear value function approximation and MILP. The piecewise linear structure can be transformed for MILP by introducing binary variables. The treed regression value function approximation is flexible enough to approximate the nonlinear structure of the data and structured to be easily formulated in MILP. The proposed ADP approach is compared with a reinforcement learning (Murphy 2005) approach.
Download or read book Uncertain Optimal Control written by Yuanguo Zhu and published by Springer. This book was released on 2018-08-29 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.
Download or read book Some Applications of Competitive Prices to Problems of Dynamic Programming Under Uncertainty written by Jack Schechtman and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Learning and Approximate Dynamic Programming written by Jennie Si and published by John Wiley & Sons. This book was released on 2004-08-02 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete resource to Approximate Dynamic Programming (ADP), including on-line simulation code Provides a tutorial that readers can use to start implementing the learning algorithms provided in the book Includes ideas, directions, and recent results on current research issues and addresses applications where ADP has been successfully implemented The contributors are leading researchers in the field
Download or read book 11th International Conference on Theory and Application of Soft Computing Computing with Words and Perceptions and Artificial Intelligence ICSCCW 2021 written by Rafik A. Aliev and published by Springer Nature. This book was released on 2022-01-04 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 11th Conference on Theory and Applications of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence, ICSCCW-2021, held in Antalya, Turkey, on August 23–24, 2021. The general scope of the book covers uncertain computation, decision making under imperfect information, neuro-fuzzy approaches, natural language processing, and other areas. The topics of the papers include theory and application of soft computing, computing with words, image processing with soft computing, intelligent control, machine learning, fuzzy logic in data mining, soft computing in business, economics, engineering, material sciences, biomedical engineering, and health care. This book is a useful guide for academics, practitioners, and graduates in fields of soft computing and computing with words. It allows for increasing of interest in development and applying of these paradigms in various real-life fields.
Download or read book Robust Discrete Optimization and Its Applications written by Panos Kouvelis and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: • It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; • It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; • It accounts for the risk averse nature of decision makers; and • It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making.
Download or read book Research Perspectives in Hydraulics and Water Resources Engineering written by Rama Prasad and published by World Scientific. This book was released on 2002 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains ten state-of-the-art review articles on selected topics in hydraulics/fluid mechanics and water resources engineering.
Download or read book Dynamic Programming and Optimal Control written by Dimitri Bertsekas and published by Athena Scientific. This book was released on with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. Among its special features, the book 1) provides a unifying framework for sequential decision making, 2) treats simultaneously deterministic and stochastic control problems popular in modern control theory and Markovian decision popular in operations research, 3) develops the theory of deterministic optimal control problems including the Pontryagin Minimum Principle, 4) introduces recent suboptimal control and simulation-based approximation techniques (neuro-dynamic programming), which allow the practical application of dynamic programming to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model, 5) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume The electronic version of the book includes 29 theoretical problems, with high-quality solutions, which enhance the range of coverage of the book.
Download or read book Dynamical Aspects in Fuzzy Decision Making written by Yuji Yoshida and published by Physica. This book was released on 2013-06-05 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of fuzziness, inspired by Zadeh (1965), brings us fruitful results when it is applied to problems in decision making. Recently, problems in fuzzy decision making are getting more complex, and one of the most complex fac tors is dynamics in systems. Dynamical approach to fuzzy decision making has been proposed by Bellman and Zadeh's celebrated paper "Decision-making in a fuzzy environment" (1970). The idea has developed into fuzzy mathemati cal programming and has been applied in many fields including management science, operations research, control theory, engineering, systems analysis, computer science, mathematical finance etc. Dynamic programming, advo cated in Bellmans book "Dynamic programming" (1957), is one of the most powerful tools to deal with dynamics in systems, and Bellman and Zadeh has proposed the optimality principle in fuzzy decision making by (1970) introducing fuzzy dynamic programming. Fuzzy dynamic programming and fuzzy mathematical programming has been making remakable progress after they were given life by Bellman and Zadeh's paper (1970). In this volume, various kinds of dynamics, not only time but also structure of systems, are considered. This volume contains ten reviewed papers, which deal with dynamics in theory and applications and whose topics are poten tially related to dynamics and are expected to develope dynamical study in near future. first, fuzzy dynamic programming is reviewed from a viewpoint of its origin and consider its developement in theory and applications.
