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 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 Adaptive Dynamic Programming for High dimensional Multicollinear State Spaces written by Bancha Ariyajunya and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming (DP) is a mathematical programming method for optimizing a system changing over time and has been used to solve multi-stage optimization problems in manufacturing systems, environmental engineering, and many other fields. Exact solutions are only possible for small problems or under very limiting restrictions, but computationally practical approximate DP methods now exist. Most continuous-state problems require discretization of the state space. A design and analysis of computer experiments (DACE) approach for approximate DP uses experimental design and statistical modeling to approximate the value function in continuous-state problems. However, ideal experimental designs are orthogonal, and when the state variables are correlated, ideal experimental designs will not appropriately represent the state space. In this dissertation, the Atlanta ozone pollution problem, which is known for having a multicollinear state space, is selected as our case study. For complex applications like air quality, the state transitions are not given as closed form equations. Rather, an advanced photochemical air quality, such as the Atlanta Urban Airshed Model (UAM), can represent state transitions. However, the UAM is computationally impractical to be used directly in DP. Therefore, in adaptive DP (ADP), statistical metamodels are developed to provide computationally practical surrogates for state transitions. In the dissertation, three types of state transition metamodels for the Atlanta UAM are developed and implemented in ADP. The first type ignores the inherent collinearity between ozone concentrations at different times and monitoring sites and constructs metamodels that have deliberately high variance inflation factors (VIFs). The second type addresses the multicollinearity using classical regression analysis techniques to yield low VIFs. Finally, the third type develops metamodels that orthogonalize the state space. Results are compared under the base case of the Atlanta case study and 50 random hypothetical scenarios.
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 Applied Dynamic Programming written by Richard E. Bellman and published by Princeton University Press. This book was released on 2015-12-08 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive study of dynamic programming applied to numerical solution of optimization problems. It will interest aerodynamic, control, and industrial engineers, numerical analysts, and computer specialists, applied mathematicians, economists, and operations and systems analysts. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Adaptive Dynamic Programming with Eligibility Traces and Complexity Reduction of High dimensional Systems written by Seaar Jawad Kadhim Al-Dabooni and published by . This book was released on 2018 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This dissertation investigates the application of a variety of computational intelligence techniques, particularly clustering and adaptive dynamic programming (ADP) designs especially heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Moreover, a one-step temporal-difference (TD(0)) and n-step TD (TD([lambda])) with their gradients are utilized as learning algorithms to train and online-adapt the families of ADP. The dissertation is organized into seven papers. The first paper demonstrates the robustness of model order reduction (MOR) for simulating complex dynamical systems. Agglomerative hierarchical clustering based on performance evaluation is introduced for MOR. This method computes the reduced order denominator of the transfer function by clustering system poles in a hierarchical dendrogram. Several numerical examples of reducing techniques are taken from the literature to compare with our work. In the second paper, a HDP is combined with the Dyna algorithm for path planning. The third paper uses DHP with an eligibility trace parameter ([lambda]) to track a reference trajectory under uncertainties for a nonholonomic mobile robot by using a first-order Sugeno fuzzy neural network structure for the critic and actor networks. In the fourth and fifth papers, a stability analysis for a model-free action-dependent HDP([lambda]) is demonstrated with batch- and online-implementation learning, respectively. The sixth work combines two different gradient prediction levels of critic networks. In this work, we provide a convergence proofs. The seventh paper develops a two-hybrid recurrent fuzzy neural network structures for both critic and actor networks. They use a novel n-step gradient temporal-difference (gradient of TD([lambda])) of an advanced ADP algorithm called value-gradient learning (VGL([lambda])), and convergence proofs are given. Furthermore, the seventh paper is the first to combine the single network adaptive critic with VGL([lambda])."--Abstract, page iv.
Download or read book Dynamic Programming written by Art Lew and published by Springer Science & Business Media. This book was released on 2006-10-09 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a practical introduction to computationally solving discrete optimization problems using dynamic programming. From the examples presented, readers should more easily be able to formulate dynamic programming solutions to their own problems of interest. We also provide and describe the design, implementation, and use of a software tool that has been used to numerically solve all of the problems presented earlier in the book.
Download or read book Nonlinear and Dynamic Programming written by S. Dano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide an introductory text of Nonlinear and Dynamic Programming for students of managerial economics and operations research. The author also hopes that engineers, business executives, managers, and others responsible for planning of industrial operations may find it useful as a guide to the problems and methods treated, with a view to practical applications. The book may be considered as a sequel to the author's Linear Programming in Industry (1960, 4th revised and enlarged edition 1974), but it can be used independently by readers familiar with the elements of linear programming models and techniques. The two volumes con stitute an introduction to the methods of mathematical programming and their application to industrial optimization problems. The author feels that the vast and ever-increasing literature on mathematical programming has not rendered an introductory exposition super fluous. The general student often tends to feel somewhat lost if he goes straight to the special literature; he will be better equipped for tackling real problems and using computer systems if he has acquired some previous training in constructing small-scale programming models and applying standard algorithms for solving them by hand. The book is intended to provide this kind of training, keeping the mathematics at the necessary minimum. The text contains numerous exercises. The reader should work out these problems for himself and check with the answers given at the end of the book. The text is based on lectures given at the University of Copenhagen.
Download or read book Adaptive Dynamic Programming Single and Multiple Controllers written by Ruizhuo Song and published by Springer. This book was released on 2018-12-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a class of novel optimal control methods and games schemes based on adaptive dynamic programming techniques. For systems with one control input, the ADP-based optimal control is designed for different objectives, while for systems with multi-players, the optimal control inputs are proposed based on games. In order to verify the effectiveness of the proposed methods, the book analyzes the properties of the adaptive dynamic programming methods, including convergence of the iterative value functions and the stability of the system under the iterative control laws. Further, to substantiate the mathematical analysis, it presents various application examples, which provide reference to real-world practices.
Download or read book Robust Adaptive Dynamic Programming written by Yu Jiang and published by John Wiley & Sons. This book was released on 2017-04-13 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at state-of-the-art ADP theory and real-world applications This book fills a gap in the literature by providing a theoretical framework for integrating techniques from adaptive dynamic programming (ADP) and modern nonlinear control to address data-driven optimal control design challenges arising from both parametric and dynamic uncertainties. Traditional model-based approaches leave much to be desired when addressing the challenges posed by the ever-increasing complexity of real-world engineering systems. An alternative which has received much interest in recent years are biologically-inspired approaches, primarily RADP. Despite their growing popularity worldwide, until now books on ADP have focused nearly exclusively on analysis and design, with scant consideration given to how it can be applied to address robustness issues, a new challenge arising from dynamic uncertainties encountered in common engineering problems. Robust Adaptive Dynamic Programming zeros in on the practical concerns of engineers. The authors develop RADP theory from linear systems to partially-linear, large-scale, and completely nonlinear systems. They provide in-depth coverage of state-of-the-art applications in power systems, supplemented with numerous real-world examples implemented in MATLAB. They also explore fascinating reverse engineering topics, such how ADP theory can be applied to the study of the human brain and cognition. In addition, the book: Covers the latest developments in RADP theory and applications for solving a range of systems’ complexity problems Explores multiple real-world implementations in power systems with illustrative examples backed up by reusable MATLAB code and Simulink block sets Provides an overview of nonlinear control, machine learning, and dynamic control Features discussions of novel applications for RADP theory, including an entire chapter on how it can be used as a computational mechanism of human movement control Robust Adaptive Dynamic Programming is both a valuable working resource and an intriguing exploration of contemporary ADP theory and applications for practicing engineers and advanced students in systems theory, control engineering, computer science, and applied mathematics.
Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2011-09-20 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 Applied Dynamic Programming for Optimization of Dynamical Systems written by Rush D. Robinett III and published by SIAM. This book was released on 2005-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized.
Download or read book A Design and Analysis of Computer Experiments based Approach to Approximate Infinite Horizon Dynamic Programming with Continuous State Spaces written by Asama Kulvanitchaiyanunt and published by . This book was released on 2014 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming (DP) is an optimization approach that transforms a complex problem into a sequence of simpler sub-problems at different points in stage. The original DP approach used Bellman's equation to compute the "cost-to-go" function. This method is useful when considering a few states and decisions. However, when dealing with high-dimensional data set with continuous state space, the limit called 'curse of dimensionality' obstructs the solution as the size of the state space grows exponentially. Given recent advances in computational power, approximate dynamic programming (ADP) is introduced by not seeking to compute the future value function exactly and at each point of the state space; rather opting for an approximation of the future value function in the domain of the state space. Two main components of ADP method which have been challenged among existing ADP studies are discretization of the state space and estimation of the cost-to-go or future value function. The first part of this dissertation research seeks to develop a solution method to solve an infinite horizon dynamic programming called Design and Analysis of Computer Experiment (DACE)-based Approach to ADP. Multivariate Adaptive Regression Splines (MARS) which is a flexible, nonparametric statistical modeling tool is used to approximate future value functions in stochastic dynamic programming (SDP) problems with continuous state variables. The training data set is updated sequentially based on the conditions. This sequential grid discretization explores the state space and provides a statistically parsimonious ADP methodology which 'adaptively' captures the important variables from the state space. There are 3 different algorithms presented in this dissertation based on the conditions of sampling process of the training data set. Comparisons are presented on a forward simulation with 12 time periods. The second part of the dissertation research is to develop a batch mode Reinforcement Learning (RL) using MARS as an approximator to solve the same problem with the first part. The main difference between these two methods is the input variables to approximate future value function. In batch mode RL method, the state-action space is used, thus the estimated function (output) is a function of both state and action variables. By contrast, DACE-based ADP used only state variable and the estimated future function is based only on state variables. The study on state-action discretization is presented in this dissertation. Two different designs are used, including Monte Carlo sampling and Sobol' sequence design. Comparisons are presented on the same forward simulation. The third part is to develop a two-stage framework for Adaptive Design for Controllability of a System of Plug-in Hybrid Electric Vehicle Charging Stations Case Study. The second-stage dynamic control problem is formulated and initially solved by mean value problem using linear programming. After that a DACE approach is used to develop a metamodel of the second stage solution based on the possible solution from the first stage. Then the metamodel will be turned into the first stage and at this point the final solution will be made. DACE helps reduce time-consuming computer models by replacing the loop between first and second stage with a constraint generated from the gradient of the approximation function. Moreover, the metamodel can give more accessible description to the second stage.
Download or read book Supply Chain Optimization Part II written by and published by John Wiley & Sons. This book was released on 2007-11-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the leading authority in the field, the Centre for Process Systems Engineering at Imperial College London, this book includes theoretical developments, algorithms, methodologies and tools in process systems engineering and applications from the chemical, energy, molecular, biomedical and other areas. It spans a whole range of length scales seen in manufacturing industries, from molecular and nanoscale phenomena to enterprise-wide optimization and control. As such, this will appeal to a broad readership, since the topic applies not only to all technical processes but also due to the interdisciplinary expertise required to solve the challenge. The ultimate reference work for years to come.
Download or read book Mathematical Programming for Industrial Engineers written by Mordecai Avriel and published by CRC Press. This book was released on 1996-05-16 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Setting out to bridge the gap between the theory of mathematical programming and the varied, real-world practices of industrial engineers, this work introduces developments in linear, integer, multiobjective, stochastic, network and dynamic programing. It details many relevant industrial-engineering applications.;College or university bookstores may order five or more copies at a special student price, available upon request from Marcel Dekker, Inc.
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.
Download or read book A Reformulation Linearization Technique for Solving Discrete and Continuous Nonconvex Problems written by Hanif D. Sherali and published by Springer Science & Business Media. This book was released on 1998-12-31 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sets out a new method for generating tight linear or convex programming relaxations for discrete and continuous nonconvex programming problems, featuring a model that affords a useful representation and structure, further strengthened with an automatic reformulation and constraint generation technique. Offers a unified treatment of discrete and continuous nonconvex programming problems, bridging these two types of nonconvexities with a polynomial representation of discrete constraints, and discusses special applications to discrete and continuous nonconvex programs. Material comprises original work of the authors compiled from several journal publications. No index. Annotation copyrighted by Book News, Inc., Portland, OR
