This book describes the development of innovative non-centralized optimization-based control schemes to solve economic dispatch problems of large-scale energy systems. Particularly, it focuses on communication and cooperation processes of local controllers, which are integral parts of such schemes. The economic dispatch problem, which is formulated as a convex optimization problem with edge-based coupling constraints, is solved by using methodologies in distributed optimization over time-varying networks, together with distributed model predictive control, and system partitioning techniques. At first, the book describes two distributed optimization methods, which are iterative and require the local controllers to exchange information with each other at each iteration. In turn, it shows that the sequence produced by these methods converges to an optimal solution when some conditions, which include how the controllers must communicate and cooperate, are satisfied. Further, it proposes an information exchange protocol to cope with possible communication link failures. Finally, the proposed distributed optimization methods are extended to the cases with random communication networks and asynchronous updates. Overall, this book presents a set of improved predictive control and distributed optimization methods, together with a rigorous mathematical analysis of each proposed algorithms. It describes a comprehensive approach to cope with communication and cooperation issues of non-centralized control schemes and show how the improved schemes can be successfully applied to solve the economic dispatch problems of large-scale energy systems.

This book presents essential concepts of traditional Flower Pollination Algorithm (FPA) and its recent variants and also its application to find optimal solution for a variety of real-world engineering and medical problems. Swarm intelligence-based meta-heuristic algorithms are extensively implemented to solve a variety of real-world optimization problems due to its adaptability and robustness. FPA is one of the most successful swarm intelligence procedures developed in 2012 and extensively used in various optimization tasks for more than a decade. The mathematical model of FPA is quite straightforward and easy to understand and enhance, compared to other swarm approaches. Hence, FPA has attracted attention of researchers, who are working to find the optimal solutions in variety of domains, such as N-dimensional numerical optimization, constrained/unconstrained optimization, and linear/nonlinear optimization problems. Along with the traditional bat algorithm, the enhanced versions of FPA are also considered to solve a variety of optimization problems in science, engineering, and medical applications.

This proceedings volume highlights the state-of-the-art knowledge related to optimization, decisions science and problem solving methods, as well as their application in industrial and territorial systems. It includes contributions tackling these themes using models and methods based on continuous and discrete optimization, network optimization, simulation and system dynamics, heuristics, metaheuristics, artificial intelligence, analytics, and also multiple-criteria decision making. The number and the increasing size of the problems arising in real life require mathematical models and solution methods adequate to their complexity. There has also been increasing research interest in Big Data and related challenges. These challenges can be recognized in many fields and systems which have a significant impact on our way of living: design, management and control of industrial production of goods and services; transportation planning and traffic management in urban and regional areas; energy production and exploitation; natural resources and environment protection; homeland security and critical infrastructure protection; development of advanced information and communication technologies. The chapters in this book examine how to deal with new and emerging practical problems arising in these different fields through the presented methodologies and their applications. The chapter topics are applicable for researchers and practitioners working in these areas, but also for the operations research community. The contributions were presented during the international conference "Optimization and Decision Science" (ODS2017), held at Hilton Sorrento Palace Conference Center, Sorrento, Italy, September 4 - 7, 2017. ODS 2017, was organized by AIRO, Italian Operations Research Society, in cooperation with DIETI (Department of Electrical Engineering and Information Technology) of University "Federico II" of Naples.

Unique in that it focuses on formulation and case studies rather than solutions procedures covering applications for pure, generalized and integer networks, equivalent formulations plus successful techniques of network models. Every chapter contains a simple model which is expanded to handle more complicated developments, a synopsis of existing applications, one or more case studies, at least 20 exercises and invaluable references.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 49 examples, 110 exercises, 66 algorithms, 24 interactive JavaScript programs, 77 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.

This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization.* Provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts.* Demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rank-one update.* Highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration.* Gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results.

An introduction to game theory and its application to the study of politics, designed by a leading authority for students without advanced mathematical training.

This book presents a wide range of optimization methods and their applications to various electrical power system problems such as economical load dispatch, demand supply management in microgrids, levelized energy pricing, load frequency control and congestion management, and reactive power management in radial distribution systems. Problems related to electrical power systems are often highly complex due to the massive dimensions, nonlinearity, non-convexity and discontinuity associated with objective functions. These systems also have a large number of equality and inequality constraints, which give rise to optimization problems that are difficult to solve using classical numerical methods. In this regard, nature inspired optimization algorithms offer an effective alternative, due to their ease of use, population-based parallel search mechanism, non-dependence on the nature of the problem, and ability to accommodate non-differentiable, non-convex problems. The analytical model of nature inspired techniques mimics the natural behaviors and intelligence of life forms. These techniques are mainly based on evolution, swarm intelligence, ecology, human intelligence and physical science.

This book presents a selection of advanced case studies that cover a substantial range of issues and real-world challenges and applications in space engineering. Vital mathematical modeling, optimization methodologies and numerical solution aspects of each application case study are presented in detail, with discussions of a range of advanced model development and solution techniques and tools. Space engineering challenges are discussed in the following contexts: *Advanced Space Vehicle Design *Computation of Optimal Low Thrust Transfers *Indirect Optimization of Spacecraft Trajectories *Resource-Constrained Scheduling, *Packing Problems in Space *Design of Complex Interplanetary Trajectories *Satellite Constellation Image Acquisition *Re-entry Test Vehicle Configuration Selection *Collision Risk Assessment on Perturbed Orbits *Optimal Robust Design of Hybrid Rocket Engines *Nonlinear Regression Analysis in Space Engineering *Regression-Based Sensitivity Analysis and Robust Design *Low-Thrust Multi-Revolution Orbit Transfers *Modeling and Optimization of Balance Layout Problems *Pilot-Induced Oscillations Alleviation *Modeling and Optimization of Hybrid Transfers to Near-Earth Objects *Probabilistic Safety Analysis of the Collision Between Space Debris and Satellite *Flatness-based Low-thrust Trajectory Optimization for Spacecraft Proximity Operations The contributing authors are expert researchers and practitioners in either the space engineering and/or in the applied optimization fields. Researchers and practitioners working in various applied aspects of space engineering will find this book practical and informative. Academics, graduate and post-graduate students in aerospace engineering, applied mathematics, operations research, optimization, and optimal control, will find this book useful.

This book presents the latest insights and developments in the field of socio-cultural inspired algorithms. Akin to evolutionary and swarm-based optimization algorithms, socio-cultural algorithms belong to the category of metaheuristics (problem-independent computational methods) and are inspired by natural and social tendencies observed in humans by which they learn from one another through social interactions. This book is an interesting read for engineers, scientists, and students studying/working in the optimization, evolutionary computation, artificial intelligence (AI) and computational intelligence fields.

This proceedings volume convenes selected, peer-reviewed papers presented at the 3rd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2022, which was held on July 4-7, 2022 by the Technical University of Civil Engineering of Bucharest, Romania. Works in this volume cover new developments in applications of mathematics in science and engineering, with emphasis on mathematical and computational modeling of real-world problems. Topics range from the use of differential equations to model mechanical structures to the employ of number theory in the development of information security and cryptography. Educational issues specific to the acquisition of mathematical competencies by engineering and science students at all university levels are also touched on. Researchers and university students are the natural audiences for this book, which can be equally appealing to practitioners seeking up-to-date techniques in mathematical applications to different contexts and disciplines.

The satellite range scheduling (SRS) problem, an important operations research problem in the aerospace industry consisting of allocating tasks among satellites and Earth-bound objects, is examined in this book. SRS principles and solutions are applicable to many areas, including: Satellite communications, where tasks are communication intervals between sets of satellites and ground stations Earth observation, where tasks are observations of spots on the Earth by satellites Sensor scheduling, where tasks are observations of satellites by sensors on the Earth. This self-contained monograph begins with a structured compendium of the problem and moves on to explain the optimal approach to the solution, which includes aspects from graph theory, set theory, game theory and belief networks. This book is accessible to students, professionals and researchers in a variety of fields, including: operations research, optimization, scheduling theory, dynamic programming and game theory. Taking account of the distributed, stochastic and dynamic variants of the problem, this book presents the optimal solution to the fixed interval SRS problem and how to migrate results into more complex cases. Reference algorithms and traditional algorithms for solving the scheduling problems are provided and compared with examples and simulations in practical scenarios.

Most textbooks on modern heuristics provide the reader with detailed descriptions of the functionality of single examples like genetic algorithms, genetic programming, tabu search, simulated annealing, and others, but fail to teach the underlying concepts behind these different approaches.

The author takes a different approach in this textbook by focusing on the users' needs and answering three fundamental questions: First, he tells us which problems modern heuristics are expected to perform well on, and which should be left to traditional optimization methods. Second, he teaches us to systematically design the "right" modern heuristic for a particular problem by providing a coherent view on design elements and working principles. Third, he shows how we can make use of problem-specific knowledge for the design of efficient and effective modern heuristics that solve not only small toy problems but also perform well on large real-world problems.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

In 2014, winner of "Outstanding Book Award" by The Japan Society for Fuzzy Theory and Intelligent Informatics. Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins by outlining the history and development of the fuzzy random variable before detailing numerous optimization models and applications that include the design of system controls for a dam.

This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In the last decade, there has been an explosive growth of research on complex real-world networks, a theme that is becoming pervasive in many disciplines, ranging from mathematics and computer science to the social and biological sciences. Optimization of complex communication networks requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network. Although there are a few books addressing social networks or complex networks, none of them has specially focused on the optimization perspective of studying these networks. This book provides the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex networks. A wide range of applications and optimization problems derived from research areas such as cellular and molecular chemistry, operations research, brain physiology, epidemiology, and ecology.

Throughout the evolutionary history of this planet, biological systems have been able to adapt, survive and ?ourish despite the turmoils and upheavals of the environment. This ability has long fascinated and inspired people to emulate and adapt natural processes for application in the arti?cial world of human endeavours. The realm of optimisation problems is no exception. In fact, in recent years biological systems have been the inspiration of the majority of meta-heuristic search algorithms including, but not limited to, genetic algorithms, particle swarmoptimisation, ant colony optimisation and extremal optimisation. This book presentsa continuum ofbiologicallyinspired optimisation, from the theoretical to the practical. We begin with an overview of the ?eld of biologically-inspired optimisation, progress to presentation of theoretical analysesandrecentextensionstoavarietyofmeta-heuristicsand?nallyshow application to a number of real-worldproblems. As such, it is anticipated the book will provide a useful resource for reseachers and practitioners involved in any aspect of optimisation problems. The overviewof the ?eld is provided by two works co-authored by seminal thinkers in the ?eld. Deb's "Evolution's Niche in Multi-Criterion Problem Solving," presents a very comprehensive and complete overview of almost all major issues in Evolutionary Multi-objective Optimisation (EMO). This chapter starts with the original motivation for developing EMO algorithms and provides an account of some successful problem domains on which EMO has demonstrated a clear edge over their classical counterparts.

Give Your Students the Proper Groundwork for Future Studies in Optimization A First Course in Optimization is designed for a one-semester course in optimization taken by advanced undergraduate and beginning graduate students in the mathematical sciences and engineering. It teaches students the basics of continuous optimization and helps them better understand the mathematics from previous courses. The book focuses on general problems and the underlying theory. It introduces all the necessary mathematical tools and results. The text covers the fundamental problems of constrained and unconstrained optimization as well as linear and convex programming. It also presents basic iterative solution algorithms (such as gradient methods and the Newton-Raphson algorithm and its variants) and more general iterative optimization methods. This text builds the foundation to understand continuous optimization. It prepares students to study advanced topics found in the author's companion book, Iterative Optimization in Inverse Problems, including sequential unconstrained iterative optimization methods.

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author's own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book's main subject: applications to problems in mathematics and physics. These include topics such as Schroedinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.

DLP denotes a dynamic-linear modeling and optimization approach to computational decision support for resource planning problems that arise, typically, within the natural resource sciences and the disciplines of operations research and operational engineering. It integrates techniques of dynamic programming (DP) and linear programming (LP) and can be realized in an immediate, practical and usable way. Simultaneously DLP connotes a broad and very general modeling/ algorithmic concept that has numerous areas of application and possibilities for extension. Two motivating examples provide a linking thread through the main chapters, and an appendix provides a demonstration program, executable on a PC, for hands-on experience with the DLP approach.

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.

Evolutionary algorithms are very powerful techniques used to find solutions to real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.Comrephensive coverage of this growing area of research.Carefully introduces each algorithm with examples and in-depth discussion.Includes many applications to real-world problems, including engineering design and scheduling.Includes discussion of advanced topics and future research.Accessible to those with limited knowledge of multi-objective optimization and evolutionary algorithms

Provides an extensive discussion on the principles of multi-objective optimization and on a number of classical approaches.

This integrated presentation of theory, algorithms and examples will benefit those working in the areas of optimization, optimal design and evolutionary computing.

Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design-such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints-are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The authors address all of these issues through many examples in the book.

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.