- Includes industrial case studies - Includes chapters on cyber physical systems, machine learning, deep learning, cyber security, robotics, smart manufacturing and predictive analytics - surveys current trends and challenges in metaheuristics and industry 4.0

Linear and Nonlinear Programming is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. The new co-author, Yinyu Ye, has written chapters and chapter material on a number of these areas including Interior Point Methods.

The Routledge Companion to Philosophy of Physics is a comprehensive and authoritative guide to the state of the art in the philosophy of physics. It comprisess 54 self-contained chapters written by leading philosophers of physics at both senior and junior levels, making it the most thorough and detailed volume of its type on the market - nearly every major perspective in the field is represented. The Companion's 54 chapters are organized into 12 parts. The first seven parts cover all of the major physical theories investigated by philosophers of physics today, and the last five explore key themes that unite the study of these theories. I. Newtonian Mechanics II. Special Relativity III. General Relativity IV. Non-Relativistic Quantum Theory V. Quantum Field Theory VI. Quantum Gravity VII. Statistical Mechanics and Thermodynamics VIII. Explanation IX. Intertheoretic Relations X. Symmetries XI. Metaphysics XII. Cosmology The difficulty level of the chapters has been carefully pitched so as to offer both accessible summaries for those new to philosophy of physics and standard reference points for active researchers on the front lines. An introductory chapter by the editors maps out the field, and each part also begins with a short summary that places the individual chapters in context. The volume will be indispensable to any serious student or scholar of philosophy of physics.

Metaheuristics for Resource Deployment under Uncertainty in Complex Systems analyzes how to set locations for the deployment of resources to incur the best performance at the lowest cost. Resources can be static nodes and moving nodes while services for a specific area or for customers can be provided. Theories of modeling and solution techniques are used with uncertainty taken into account and real-world applications used. The authors present modeling and metaheuristics for solving resource deployment problems under uncertainty while the models deployed are related to stochastic programming, robust optimization, fuzzy programming, risk management, and single/multi-objective optimization. The resources are heterogeneous and can be sensors and actuators providing different tasks. Both separate and cooperative coverage of the resources are analyzed. Previous research has generally dealt with one type of resource and considers static and deterministic problems, so the book breaks new ground in its analysis of cooperative coverage with heterogeneous resources and the uncertain and dynamic properties of these resources using metaheuristics. This book will help researchers, professionals, academics, and graduate students in related areas to better understand the theory and application of resource deployment problems and theories of uncertainty, including problem formulations, assumptions, and solution methods.

The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others. This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.

This book presents the essential concepts of operations research and engineering management in a structured manner. Starting with the basic functions of management - planning, organizing, leading and controlling - it introduces the reader to the process of strategic decision-making, covering the essentials of technological invention management, innovation and entrepreneurship, with ample examples of decision-making under certainty, uncertainty and risk conditions. It also exposes the reader to the fundamentals of managing projects and professional communication. In order to reinforce the theory used, practical case studies taken from relevant disciplines are introduced. For instance, case studies from the retail sector have been appended to the assignment problem and cases related to traffic have been introduced for queuing formulation. The concept of game theory is discussed in greater detail with an introduction to topics such as incentive compatibility, Bayesian representations for different games, budget balance, auctions and a broad coverage of mechanism design. While a few of these problems have been solved in the book, a few others have been left un-solved to promote readers' understanding. The mix of theoretical and practical examples reveals to the reader the underlying complexities and highlights the challenges entailed by field implementation.

Focuses on the latest research in the field of differential equations in engineering applications Discusses the most recent research findings that are occurring across different institutions Identifies the gaps in the knowledge of differential equations Presents the most fruitful areas for further research in advanced processes Offers the most forthcoming studies in modeling and simulation along with real-world case studies

This book both summarizes the basic theory of evolutionary games and explains their developing applications, giving special attention to the 2-player, 2-strategy game. This game, usually termed a "2x2 game" in the jargon, has been deemed most important because it makes it possible to posit an archetype framework that can be extended to various applications for engineering, the social sciences, and even pure science fields spanning theoretical biology, physics, economics, politics, and information science. The 2x2 game is in fact one of the hottest issues in the field of statistical physics. The book first shows how the fundamental theory of the 2x2 game, based on so-called replicator dynamics, highlights its potential relation with nonlinear dynamical systems. This analytical approach implies that there is a gap between theoretical and reality-based prognoses observed in social systems of humans as well as in those of animal species. The book explains that this perceived gap is the result of an underlying reciprocity mechanism called social viscosity. As a second major point, the book puts a sharp focus on network reciprocity, one of the five fundamental mechanisms for adding social viscosity to a system and one that has been a great concern for study by statistical physicists in the past decade. The book explains how network reciprocity works for emerging cooperation, and readers can clearly understand the existence of substantial mechanics when the term "network reciprocity" is used. In the latter part of the book, readers will find several interesting examples in which evolutionary game theory is applied. One such example is traffic flow analysis. Traffic flow is one of the subjects that fluid dynamics can deal with, although flowing objects do not comprise a pure fluid but, rather, are a set of many particles. Applying the framework of evolutionary games to realistic traffic flows, the book reveals that social dilemma structures lie behind traffic flow.

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed.

The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options. "

Winner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA) A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations. Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theory Uses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structures Applies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack games Contains an extended case study based on a real application in railway security, which provides a blueprint for how to perform ARA in similar security situations Includes exercises at the end of most chapters, with selected solutions at the back of the book The book shows decision makers how to build Bayesian models for the strategic calculation of their opponents, enabling decision makers to maximize their expected utility or minimize their expected loss. This new approach to risk analysis asserts that analysts should use Bayesian thinking to describe their beliefs about an opponent's goals, resources, optimism, and type of strategic calculation, such as minimax and level-k thinking. Within that framework, analysts then solve the problem from the perspective of the opponent while placing subjective probability distributions on all unknown quantities. This produces a distribution over the actions of the opponent and enables analysts to maximize their expected utilities.

Stealth technology is a crucial pre-requisite in the combat zone, where swiftness, surprise and initiative are the decisive elements for survivability. The supreme goal here is to reduce the visibility of military vehicles by shaping, application of radar absorbing materials, passive cancellation, active cancellation etc. With respect to multilayered radar absorbing structures (RAS), this book presents an efficient algorithm based on particle swarm optimization (PSO), for the material selection as well as optimization of thickness of multilayered RAS models considering both normal as well as oblique incidence cases. It includes a thorough overview of the theoretical background required for the analysis of multilayered RAS as well as the step-by-step procedure for the implementation of PSO-based algorithm. The accuracy and computational efficiency of the indigenously developed code is also clearly established using relevant validations and case studies. FEATURES Provides step-by-step procedure for the implementation of particle swarm optimization (PSO) based algorithm in the context of multilayered radar absorbing structures (RAS) design Helps to understand the EM design, analysis and optimization of multilayered RAS Describes the theoretical background required for the analysis of multilayered RAS Illustrates in detail the theoretical formulation supported by intuitive ray diagrams and comprehensive flowcharts to implement the algorithm with ease Includes elaborate validations and case studies This book will serve as a valuable resource for students, researchers, scientists, and engineers involved in the electromagnetic design and development of multi-layered radar absorbing structures.

* A valuable teaching resource, replete with exercises, for any course of gambling mathematics * Suitable for a wide audience of professionals, researchers and students * Many practical applications for the gambling industry

This volume consists of 14 contributed chapters written by leading experts, offering in-depth discussions of the mathematical modeling and algorithmic aspects for tackling a range of space engineering applications. This book will be of interest to researchers and practitioners working in the field of space engineering. Since it offers an in-depth exposition of the mathematical modelling, algorithmic and numerical solution aspects of the topics covered, the book will also be useful to aerospace engineering graduates and post-graduate students who wish to expand their knowledge by studying real-world applications and challenges that they will encounter in their profession. Readers will obtain a broad overview of some of the most challenging space engineering operational scenarios of today and tomorrow: this will be useful for managers in the aerospace field, as well as in other industrial sectors. The contributed chapters are mainly focused on space engineering practice. Researchers and practitioners in mathematical systems modelling, operations research, optimization, and optimal control will also benefit from the case studies presented in this book. The model development and optimization approaches discussed can be extended towards other application areas that are not directly related to space engineering. Therefore, the book can be a useful reference to assist in the development of new modelling and optimization applications.

This textbook approaches optimization from a multi-aspect, multi-criteria perspective. By using a Multiple Criteria Decision Making (MCDM) approach, it avoids the limits and oversimplifications that can come with optimization models with one criterion. The book is presented in a concise form, addressing how to solve decision problems in sequences of intelligence, modelling, choice and review phases, often iterated, to identify the most preferred decision variant. The approach taken is human-centric, with the user taking the final decision is a sole and sovereign actor in the decision making process. To ensure generality, no assumption about the Decision Maker preferences or behavior is made. The presentation of these concepts is illustrated by numerous examples, figures, and problems to be solved with the help of downloadable spreadsheets. This electronic companion contains models of problems to be solved built in Excel spreadsheet files. Optimization models are too often oversimplifications of decision problems met in practice. For instance, modeling company performance by an optimization model in which the criterion function is short-term profit to be maximized, does not fully reflect the essence of business management. The company's managing staff is accountable not only for operational decisions, but also for actions which shall result in the company ability to generate a decent profit in the future. This calls for management decisions and actions which ensure short-term profitability, but also maintaining long-term relations with clients, introducing innovative products, financing long-term investments, etc. Each of those additional, though indispensable actions and their effects can be modeled separately, case by case, by an optimization model with a criterion function adequately selected. However, in each case the same set of constraints represents the range of company admissible actions. The aim and the scope of this textbook is to present methodologies and methods enabling modeling of such actions jointly.

This book studies R. Buckminster Fuller's World Game and similar world games, past and present. Proposed by Fuller in 1964 and first played in colleges and universities across North America at a time of growing ecological crisis, the World Game attempted to turn data analysis, systems modelling, scenario building, computer technology, and information design to more egalitarian ends to meet human needs. It challenged players to redistribute finite planetary resources more equitably, to 'make the world work'. Criticised and lauded in equal measure, the World Game has evolved through several formats and continues today in correspondence with debates on planetary stewardship, gamification, data management, and the democratic deficit. This book looks again at how the World Game has been played, focusing on its architecture, design, and gameplay. With hindsight, the World Game might appear naive, utopian, or technocratic, but we share its problems, if not necessarily its solutions. Such a study will be of interest to scholars working in art history, design history, game studies, media studies, architecture, and the environmental humanities.

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

Adopting a variational approach, this self-contained textbook presents the basic principles of optimal control governed by ODEs. Inside, readers will encounter the fundamental issues of existence of optimal solutions, optimality conditions, and numerical approximation from a variational perspective, academic and real-world examples testing the book's variational approach, and a unified treatment that requires no prior expertise in variational problems or numerical approximation. A Variational Approach to Optimal Control of ODEs is for applied analysts, applied mathematicians, and control engineers. It can be used in courses on Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters are an outgrowth of presentations from the 11th International Symposium on Dynamic Games and Applications.

Key topics covered include:

* stochastic and differential games

* dynamic games and their applications in various areas, such as ecology and economics

* numerical methods and algorithms in dynamic games

* zero- and nonzero-sum games

* pursuit-evasion games

* evolutionary game theory and applications

The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including adaptive observations, sensitivity analysis, parameter estimation and AI applications. The book is useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

In 1781, Gaspard Monge defined the problem of ""optimal transportation"", or the transferring of mass with the least possible amount of work, with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is at once an introduction to the field of optimal transportation and a survey of the research on the topic over the last 15 years. The book is intended for graduate students and researchers, and it covers both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB(R), and Maple(TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

This book covers the issues related to optimization of engineering and management problems using soft computing techniques with an industrial outlook. It covers a broad area related to real life complex decision making problems using a heuristics approach. It also explores a wide perspective and future directions in industrial engineering research on a global platform/scenario. The book highlights the concept of optimization, presents various soft computing techniques, offers sample problems, and discusses related software programs complete with illustrations. Features Explains the concept of optimization and relevance to soft computing techniques towards optimal solution in engineering and management Presents various soft computing techniques Offers problems and their optimization using various soft computing techniques Discusses related software programs, with illustrations Provides a step-by-step tutorial on how to handle relevant software for obtaining the optimal solution to various engineering problems

A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems. It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.