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Optimal Control Problems Arising in Forest Management (SpringerBriefs in Optimization)
by Alexander J. ZaslavskiThis book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.
Optimal Control Problems Related to the Robinson–Solow–Srinivasan Model (Monographs in Mathematical Economics #4)
by Alexander J. ZaslavskiThis book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson–Solow–Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2–6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.
Optimal Control Theory: Applications to Management Science and Economics (Springer Texts in Business and Economics)
by Suresh P. SethiThis new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.
Optimal Control Theory and Static Optimization in Economics
by Daniel Leonard Ngo Van LongOptimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. Economic intuition is emphasized, examples and problem sets covering a wide range of applications in economics are provided, theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with the simple formulations and progressing to advanced topics. Optimal control theory is introduced directly, without recourse to the calculus of variations, and the connection with the latter and with dynamic programming is explained in a separate chapter. Also, the book draws the parallel between optimal control theory and static optimization. No previous knowledge of differential equations is required.
Optimal Covariate Designs
by Premadhis Das Ganesh Dutta Nripes Kumar Mandal Bikas Kumar SinhaThis book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for the construction of optimum designs using Hadamard matrices, the Kronecker product, Rao-Khatri product, mixed orthogonal arrays to name a few.
Optimal Coverage in Wireless Sensor Networks (Springer Optimization and Its Applications #162)
by Weili Wu Zhao Zhang Wonjun Lee Ding-Zhu DuThis book will serve as a reference, presenting state-of-the-art research on theoretical aspects of optimal sensor coverage problems. Readers will find it a useful tool for furthering developments on theory and applications of optimal coverage; much of the content can serve as material for advanced topics courses at the graduate level. The book is well versed with the hottest research topics such as Lifetime of Coverage, Weighted Sensor Cover, k-Coverage, Heterogeneous Sensors, Barrier, Sweep and Partial Coverage, Mobile Sensors, Camera Sensors and Energy-Harvesting Sensors, and more. Topics are introduced in a natural order from simple covers to connected covers, to the lifetime problem. Later, the book begins revisiting earlier problems ranging from the introduction of weights to coverage by k sensors and partial coverage, and from sensor heterogeneity to novel problems such as the barrier coverage problem. The book ends with coverage of mobile sensors, camera sensors, energy-harvesting sensors, underwater sensors, and crowdsensing.
Optimal Design of Control Systems: Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221)
by Gennadii E. Kolosov"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."
Optimal Design through the Sub-Relaxation Method
by Pablo PedregalThis book provides a comprehensive guide to analyzing and solving optimal design problems in continuous media by means of the so-called sub-relaxation method. Though the underlying ideas are borrowed from other, more classical approaches, here they are used and organized in a novel way, yielding a distinct perspective on how to approach this kind of optimization problems. Starting with a discussion of the background motivation, the book broadly explains the sub-relaxation method in general terms, helping readers to grasp, from the very beginning, the driving idea and where the text is heading. In addition to the analytical content of the method, it examines practical issues like optimality and numerical approximation. Though the primary focus is on the development of the method for the conductivity context, the book's final two chapters explore several extensions of the method to other problems, as well as formal proofs. The text can be used for a graduate course in optimal design, even if the method would require some familiarity with the main analytical issues associated with this type of problems. This can be addressed with the help of the provided bibliography.
Optimal Districting and Territory Design (International Series in Operations Research & Management Science #284)
by Roger Z. Ríos-MercadoThis book highlights recent advances in the field of districting, territory design, and zone design. Districting problems deal essentially with tactical decisions, and involve mainly dividing a set of geographic units into clusters or territories subject to some planning requirements. This book presents models, theory, algorithms (exact or heuristic), and applications that would bring research on districting systems up-to-date and define the state-of-the-art. Although papers have addressed real-world problems that require districting or territory division decisions, this is the first comprehensive book that directly addresses these problems. The chapters capture the diverse nature of districting applications, as the book is divided into three different areas of research. Part I covers recent up-to-date surveys on important areas of districting such as police districting, health care districting, and districting algorithms based on computational geometry. Part II focuses on recent advances on theory, modeling, and algorithms including mathematical programming and heuristic approaches, and finally, Part III contains successful applications in real-world districting cases.
Optimal Estimation of Dynamic Systems (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
by John L. Crassidis John L. JunkinsAn ideal self-study guide for practicing engineers as well as senior undergraduate and beginning graduate students, this book highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking. With more than 100 pages of new material, this reorganized and expanded edition incorporates new theoretical results, a new chapter on advanced sequential state estimation, and additional examples and exercises. MATLAB codes are available on the book's website.
Optimal Experimental Design: A Concise Introduction for Researchers (Lecture Notes in Statistics #226)
by Jesús López-FidalgoThis textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.
Optimal Experimental Design for Non-Linear Models
by Christos P. KitsosThis book tackles the Optimal Non-Linear Experimental Design problem from an applications perspective. At the same time it offers extensive mathematical background material that avoids technicalities, making it accessible to non-mathematicians: Biologists, Medical Statisticians, Sociologists, Engineers, Chemists and Physicists will find new approaches to conducting their experiments. The book is recommended for Graduate Students and Researchers.
Optimal Fractional-order Predictive PI Controllers: For Process Control Applications with Additional Filtering (Studies in Infrastructure and Control)
by Arun Mozhi Panneer Selvam Fawnizu Azmadi Hussin Rosdiazli Ibrahim Kishore Bingi Nagarajapandian M.This book presents the study to design, develop, and implement improved PI control techniques using dead-time compensation, structure enhancements, learning functions and fractional ordering parameters. Two fractional-order PI controllers are proposed and designed: fractional-order predictive PI and hybrid iterative learning based fractional-order predictive PI controller. Furthermore, the proposed fractional-order control strategies and filters are simulated over first- and second-order benchmark process models and further validated using the real-time experimentation of the pilot pressure process plant. In this book, five chapters are structured with a proper sequential flow of details to provide a better understanding for the readers. A general introduction to the controllers, filters and optimization techniques is presented in Chapter 1. Reviews of the PI controllers family and their modifications are shown in the initial part of Chapter 2, followed by the development of the proposed fractional-order predictive PI (FOPPI) controller with dead-time compensation ability. In the first part of chapter 3, a review of the PI based iterative learning controllers, modified structures of the ILC and their modifications are presented. Then, the design of the proposed hybrid iterative learning controller-based fractional-order predictive PI controller based on the current cyclic feedback structure is presented. Lastly, the results and discussion of the proposed controller on benchmark process models and the real-time experimentation of the pilot pressure process plant are given. Chapter 4 presents the development of the proposed filtering techniques and their performance comparison with the conventional methods. Chapter 5 proposes the improvement of the existing sine cosine algorithm (SCA) and arithmetic optimization algorithm (AOA) to form a novel arithmetic-trigonometric optimization algorithm (ATOA) to accelerate the rate of convergence in lesser iterations with mitigation towards getting caught in the same local position. The performance analysis of the optimization algorithm will be carried out on benchmark test functions and the real-time pressure process plant.
The Optimal Homotopy Asymptotic Method
by Vasile Marinca Nicolae HerisanuThis book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book "Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches", published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Optimal Impulsive Control: The Extension Approach (Lecture Notes in Control and Information Sciences #477)
by Fernando Lobo Pereira Dmitry Karamzin Aram ArutyunovOptimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints.The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.
Optimal Impulsive Control for Cancer Therapy (SpringerBriefs in Electrical and Computer Engineering)
by João P. Belfo João M. LemosThis Springer brief discusses the use of control engineering methods to plan a cancer therapy which tends to reduce tumour size in patients, striking a balance that minimizes the toxic effects of the treatment. The authors address the design and computation of impulsive control therapies, a methodology previously underexplored in the application of control methods to medical modelling. This allows simulation of such discrete events as taking a pill rather than relying on the supply of therapy being continuous and steady.The book begins with an introduction to the topic, before moving onto pharmacokinetic, pharmacodynamical and tumour-growth models and explaining how they describe the relationship between a certain therapy plan and the evolution of cancer. This is placed firmly in the context of work introducing impulsive differential equations. The final chapter summarizes the research presented and suggests future areas of research to encourage readers in taking the subject forward. This book is of interest to biomedical engineers, researchers and students, particularly those with a background in systems and control engineering.
Optimal Interconnection Trees in the Plane
by Marcus Brazil Martin ZachariasenThis book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions. Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.
Optimal Investment
by L. C. RogersReaders of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.
Optimal Learning
by Warren B. Powell Ilya O. RyzhovLearn the science of collecting information to make effective decisionsEveryday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting information is time-consuming and expensive. Designed for readers with an elementary background in probability and statistics, the book presents effective and practical policies illustrated in a wide range of applications, from energy, homeland security, and transportation to engineering, health, and business.This book covers the fundamental dimensions of a learning problem and presents a simple method for testing and comparing policies for learning. Special attention is given to the knowledge gradient policy and its use with a wide range of belief models, including lookup table and parametric and for online and offline problems. Three sections develop ideas with increasing levels of sophistication:Fundamentals explores fundamental topics, including adaptive learning, ranking and selection, the knowledge gradient, and bandit problemsExtensions and Applications features coverage of linear belief models, subset selection models, scalar function optimization, optimal bidding, and stopping problems Advanced Topics explores complex methods including simulation optimization, active learning in mathematical programming, and optimal continuous measurementsEach chapter identifies a specific learning problem, presents the related, practical algorithms for implementation, and concludes with numerous exercises. A related website features additional applications and downloadable software, including MATLAB and the Optimal Learning Calculator, a spreadsheet-based package that provides an introduction to learning and a variety of policies for learning.
Optimal Lightweight Construction Principles
by Federico Maria Ballo Massimiliano Gobbi Giampiero Mastinu Giorgio PreviatiThis book presents simple design paradigms related to lightweight design, that are derived from an in-depth and theoretically sound analysis based on Pareto theory. It uses numerous examples, including torsion and inflated tubes, to fully explain the theories discussed. Lightweight Construction Principles begins by defining terms in relation to engineering design and optimal design of complex mechanical systems. It then discusses the analytical derivation of the Pareto-optimal set, before applying analytical formulae to optimal design of bent beams. The book moves through numerous case studies of different beam and tube construction including beams subject to bending, thin walled tubes under torsion and truss structures. This book will be of interest to researchers and graduate students in the field of structural optimisation and multi-objective optimization, as well as to practitioners such as design engineers.
Optimal Operation and Control of Power Systems Using an Algebraic Modelling Language (Green Energy and Technology)
by Nnamdi Nwulu Saheed Lekan GbadamosiThis book presents mathematical models of demand-side management programs, together with operational and control problems for power and renewable energy systems. It reflects the need for optimal operation and control of today’s electricity grid at both the supply and demand spectrum of the grid. This need is further compounded by the advent of smart grids, which has led to increased customer/consumer participation in power and renewable energy system operations. The book begins by giving an overview of power and renewable energy systems, demand-side management programs and algebraic modeling languages. The overview includes detailed consideration of appliance scheduling algorithms, price elasticity matrices and demand response incentives. Furthermore, the book presents various power system operational and control mathematical formulations, incorporating demand-side management programs. The mathematical formulations developed are modeled and solved using the Advanced Interactive Multidimensional Modeling System (AIMMS) software, which offers a powerful yet simple algebraic modeling language for solving optimization problems. The book is extremely useful for all power system operators and planners who are concerned with optimal operational procedures for managing today’s complex grids, a context in which customers are active participants and can curb/control their demand. The book details how AIMMS can be a useful tool in optimizing power grids and also offers a valuable research aid for students and academics alike.
Optimal Power Flow Using FACTS Devices: Soft Computing Techniques
by L. Ashok Kumar K. Mohana SundaramOptimal Power Flow Using FACTS Devices: Soft Computing Techniques develops intelligent algorithms to analyze optimal power flow (OPF) and to enhance the power transfer capability of the transmission line with reduced congestion. By providing elaborate studies on FACTS devices and by using soft computing metaheuristics algorithms such as Firefly, Cuckoo, Flower Pollination, and others., this book enables readers to know about algorithms in real-time power system applications and damping of subsynchronous resonance (SSR) oscillations. Key features of this book include: Offers comprehensive review of FACTS devices and the importance of soft computing techniques for solving OPF. Describes the various problems associated with power system operation and control. Addresses issues of SSR in power systems and proposes soft techniques for SSR analysis in power systems. Demonstrates of the importance of SSR and congestion management using intelligent FACTS devices as part of OPF. Covers power systems’ reliability, quality, cost-effectiveness, effects on customer goodwill, and pollution limits, including the deregulation of markets and different intelligent controllers. Optimal Power Flow Using FACTS Devices: Soft Computing Techniques is aimed at researchers and professionals in the field of power systems.
Optimal Quantification and Symmetry (Behaviormetrics: Quantitative Approaches to Human Behavior #12)
by Shizuhiko NishisatoThis book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life—for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers.Mathematical symmetry is well known, as can be inferred from Hirschfeld’s simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato’s dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
Optimal Resource Allocation
by Igor A. UshakovA UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATIONOptimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems.Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features:An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biologyNumerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protectionThe applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problemsPractical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithmsOptimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.
Optimal Search for Moving Targets
by Lawrence D. Stone Johannes O. Royset Alan R. WashburnThisbook begins with a review of basic results in optimal search for a stationarytarget. It then develops the theory of optimal search for a moving target,providing algorithms for computing optimal plans and examples of their use. Next it develops methods for computing optimal search plans involving multipletargets and multiple searchers with realistic operational constraints on searchmovement. These results assume that the target does not react to the search. Inthe final chapter there is a brief overview of mostly military problems wherethe target tries to avoid being found as well as rescue or rendezvous problemswhere the target and the searcher cooperate. Larry Stone wrote his definitive book Theory of Optimal Search in1975, dealing almost exclusively with the stationary target search problem. Since then the theory has advanced to encompass search for targets that moveeven as the search proceeds, and computers have developed sufficient capabilityto employ the improved theory. In this book, Stone joins Royset and Washburn todocument and explain this expanded theory of search. The problem of how tosearch for moving targets arises every day in military, rescue, lawenforcement, and border patrol operations.