The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

This book describes the modelling and optimisation of vibration reduction systems in an integrated fashion using nonlinear equations of motion. It proposes an effective optimisation method for determining the basic characteristics of the non-linear visco-elastic elements used in passive vibration reduction systems. In the case of semi-active and active vibration isolators, a design process of the advanced control systems is proposed that makes possible to optimise the controller settings relatively to the selected vibro-isolation criteria. The approach developed here is subsequently tested by means of experimental investigations conducted on various sample vibration reduction systems: passive, semi-active and active. The book presents a biomechanical modelling approach that allows users to select the properties of vibro-isolation systems for different types of oscillation and different optimisation criteria - and can significantly reduce the harmful vibrations that can affect the human body in the process. Further, the book equips readers to evaluate the viscoelastic characteristics of passive systems and design control systems for semi-active and active systems. Modelling and Control Design of Vibration Reduction Systems offers a valuable guide for researchers and practitioners alike. It also provides students and academics with systematic information on the procedures to be followed in the design process for semi-active or active vibration reduction systems.

This 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.

The detailed survey on constraint handling techniques specifically penalty function approach is presented in the book; presents the Cohort Intelligence (CI) algorithm incorporated with a novel self-adaptive penalty function (SAPF) approach which helped in avoiding preliminary trials of selecting penalty parameter. The approach is referred to as CI-SAPF; CI-SAPF is further hybridized with Colliding Bodies Optimization (CBO) algorithm to promote a parameter less metaheuristic algorithm; presents solutions to several problems from discrete truss structure domain, mixed variable design engineering domain, and linear & nonlinear domain validating the CI-SAPF and CI-SAPF-CBO; behavior of SAPF approach on pseudo objective function, constraint violations, penalty function and penalty parameter have been analyzed and discussed in very detail; presents the in-depth analysis and comparison of the CI-SAPF, CI-SAPF-CBO and CBO algorithms with other contemporary techniques; provides the solution to real-world manufacturing problems of optimizing multi pass milling and turning processes using CI-SPF, CI-SAPF and CI-SAPF-CBO approaches.

This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items,  generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

"Nonconvex Optimal Control and Variational Problems "is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems.

Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with good functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author.

This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community."

In today's world, with an increase in the breadth and scope of real-world engineering optimization problems as well as with the advent of big data, improving the performance and efficiency of algorithms for solving such problems has become an indispensable need for specialists and researchers. In contrast to conventional books in the field that employ traditional single-stage computational, single-dimensional, and single-homogeneous optimization algorithms, this book addresses multiple newfound architectures for meta-heuristic music-inspired optimization algorithms. These proposed algorithms, with multi-stage computational, multi-dimensional, and multi-inhomogeneous structures, bring about a new direction in the architecture of meta-heuristic algorithms for solving complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data. The architectures of these new algorithms may also be appropriate for finding an optimal solution or a Pareto-optimal solution set with higher accuracy and speed in comparison to other optimization algorithms, when feasible regions of the solution space and/or dimensions of the optimization problem increase. This book, unlike conventional books on power systems problems that only consider simple and impractical models, deals with complicated, techno-economic, real-world, large-scale models of power systems operation and planning. Innovative applicable ideas in these models make this book a precious resource for specialists and researchers with a background in power systems operation and planning. Provides an understanding of the optimization problems and algorithms, particularly meta-heuristic optimization algorithms, found in fields such as engineering, economics, management, and operations research; Enhances existing architectures and develops innovative architectures for meta-heuristic music-inspired optimization algorithms in order to deal with complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data; Addresses innovative multi-level, techno-economic, real-world, large-scale, computational-logical frameworks for power systems operation and planning, and illustrates practical training on implementation of the frameworks using the meta-heuristic music-inspired optimization algorithms.

Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative. The volume, which includes new methods as well as review contributions will benefit a wide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.

This book provides several inventory models for making the right decision in inventory management under different environments. Basically, the optimal ordering policies are determined for situations with and without shortages in production-inventory systems. The chapters in the book include various features of inventory modeling i.e., inflation, deterioration, supply chain, learning, credit financing, carbon emission policy, stock-dependent demand, among others. The book is a useful resource for academicians, researchers, students, practitioners, and managers who can be benefited with the policies provided in the chapters of the book.

This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization - it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields."Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.

This book will cover heuristic optimization techniques and applications in engineering problems. The book will be divided into three sections that will provide coverage of the techniques, which can be employed by engineers, researchers, and manufacturing industries, to improve their productivity with the sole motive of socio-economic development. This will be the first book in the category of heuristic techniques with relevance to engineering problems and achieving optimal solutions. Features Explains the concept of optimization and the relevance of using heuristic techniques for optimal solutions in engineering problems Illustrates the various heuristics techniques Describes evolutionary heuristic techniques like genetic algorithm and particle swarm optimization Contains natural based techniques like ant colony optimization, bee algorithm, firefly optimization, and cuckoo search Offers sample problems and their optimization, using various heuristic techniques

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.

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a "hands-on" treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

Statistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems. It introduces state-of-the-art practical decision making through twenty-one case studies from real-life applications. The case studies cover a broad area of topics and the authors include links with source code and data, a very helpful tool for the reader. In its core, the text demonstrates how to use different factors to formulate statistical decision problems arising in various risk management applications, such as optimal hedging, portfolio optimization, cash flow matching, classification, and more. The presentation is organized into three parts: selected concepts of statistical decision theory, statistical decision problems, and case studies with portfolio safeguard. The text is primarily aimed at practitioners in the areas of risk management, decision making, and statistics. However, the inclusion of a fair bit of mathematical rigor renders this monograph an excellent introduction to the theory of general error, deviation, and risk measures for graduate students. It can be used as supplementary reading for graduate courses including statistical analysis, data mining, stochastic programming, financial engineering, to name a few. The high level of detail may serve useful to applied mathematicians, engineers, and statisticians interested in modeling and managing risk in various applications.

This book brings together the current state of-the-art research in Self Organizing Migrating Algorithm (SOMA) as a novel population-based evolutionary algorithm, modeled on the predator-prey relationship, by its leading practitioners. As the first ever book on SOMA, this book is geared towards graduate students, academics and researchers, who are looking for a good optimization algorithm for their applications. This book presents the methodology of SOMA, covering both the real and discrete domains, and its various implementations in different research areas. The easy-to-follow and implement methodology used in the book will make it easier for a reader to implement, modify and utilize SOMA.

This basic book has been used at the middle schools in Shanghai, China for more than 10 years. The book presents carefully-selected contents in order to achieve the roles of enlightenment and popularization. It mainly includes: Chapter 1: Human Brains, Computers and Fuzzy Mathematics; Chapter 2: Matrix, Fuzzy Relations and Fuzzy Matrix; Chapter 3: Fuzzy Control; Chapter 4: Fuzzy Statistics and Fuzzy Probability and Chapter 5: Fuzzy Linear Programming. It includes at the end of each chapter concise, interesting and profound reading and thinking materials, and a certain amount of exercises so as to make it an informative and interesting textbook. This book can be used not only as a textbook in senior middle schools, and in vocational colleges, but also as a primer for individually learning fuzzy mathematics.

Small satellite technology is opening up a new era in space exploration offering reduced cost of launch and maintenance, operational flexibility with on-orbit reconfiguration, redundancy etc. The true power of such missions can be harnessed only from close and precise formation flying of satellites. Formation flying missions support diverse application areas such as reconnaissance, remote sensing, solar observatory, deep space observatories, etc. A key component involved in formation flying is the guidance algorithm that should account for system nonlinearities and unknown disturbances. The main focus of this book is to present various nonlinear optimal control and adaptive guidance ideas to ensure precise close formation flying in presence of such difficulties. In addition to in-depth discussion of the relevant topics, MATLAB program files for the results included are also provided for the benefit of the readers. Since this book has concise information about the various guidance techniques, it will be useful reference for researchers and practising engineers in the space field.

This book provides a literature review of techniques used to pass from continuous to combinatorial space, before discussing a detailed example with individual steps of how cuckoo search (CS) can be adapted to solve combinatorial optimization problems. It demonstrates the application of CS to three different problems and describes their source code. The content is divided into five chapters, the first of which provides a technical description, together with examples of combinatorial search spaces. The second chapter summarizes a diverse range of methods used to solve combinatorial optimization problems. In turn, the third chapter presents a description of CS, its formulation and characteristics. In the fourth chapter, the application of discrete cuckoo search (DCS) to solve three POCs (the traveling salesman problem, quadratic assignment problem and job shop scheduling problem) is explained, focusing mainly on a reinterpretation of the terminology used in CS and its source of inspiration. In closing, the fifth chapter discusses random-key cuckoo search (RKCS) using random keys to represent positions found by cuckoo search in the TSP and QAP solution space.

This unique book describes how the General Algebraic Modeling System (GAMS) can be used to solve various power system operation and planning optimization problems. This book is the first of its kind to provide readers with a comprehensive reference that includes the solution codes for basic/advanced power system optimization problems in GAMS, a computationally efficient tool for analyzing optimization problems in power and energy systems. The book covers theoretical background as well as the application examples and test case studies. It is a suitable reference for dedicated and general audiences including power system professionals as well as researchers and developers from the energy sector and electrical power engineering community and will be helpful to undergraduate and graduate students.

- 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

Written by experts from all over the world, the book comprises the latest applications of mathematical and models in food engineering and fermentation. It provides the fundamentals on statistical methods to solve standard problems associated with food engineering and fermentation technology. Combining theory with a practical, hands-on approach, this book covers key aspects of food engineering. Presenting cuttingedge information, the book is an essential reference on the fundamental concepts associated with food engineering.

This book offers a timely review of cutting-edge applications of computational intelligence to business management and financial analysis. It covers a wide range of intelligent and optimization techniques, reporting in detail on their application to real-world problems relating to portfolio management and demand forecasting, decision making, knowledge acquisition, and supply chain scheduling and management.

The book provides a collection of recent applications of nature inspired optimization in industrial fields. Different optimization techniques have been deployed, and different problems have been effectively analyzed. The valuable contributions from researchers focus on three ultimate goals (i) improving the accuracy of these techniques, (ii) achieving higher speed and lower computational complexity, and (iii) working on their proposed applications. The book is helpful for active researchers and practitioners in the field.

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.