The book titled "Optimization Techniques" is based on optimization techniques and O.R. related courses for undergraduate and postgraduate engineering and mathematics students of various universities as well as for researchers working on optimization problems. The main objective of the book is to acquaint and familiarize the readers with different types of optimization techniques, solving optimization problems, implementing computational techniques, abstracting mathematical results and proofs etc. The book gives a clear appreciation and good grasp over most of the currently available optimization techniques. Each method developed has been illustrated with solved examples. A set of exercises for self practice is given at the end of each chapter. A set of brief answer review questions relating to the finer detail of the topics discussed in each chapter preceding the set of exercises has been added to facilitate learning and enhance the value of the book.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB (R), this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB (R), Python, Julia, and R - available on databookuw.com.

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Feature Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems

Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)-arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R. With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going into implementation. Algebraic representation allows for clear understanding and generalization of large applications, and writing formulations is necessary to explain and convey the modeling decisions made. Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B. This book: * Provides and explains code so examples are relatively clear and self-contained. * Emphasizes creating algebraic formulations before implementing. * Focuses on application rather than algorithmic details. * Embodies the philosophy of reproducible research. * Uses open-source tools to ensure access to powerful optimization tools. * Promotes open-source: all materials are available on the author's github repository. * Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R. * Provides code readers can adapt to their own applications . This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

This book provides different approaches used to analyze, draw attention, and provide an understanding of the advancements in the optimization field across the globe. It brings all of the latest methodologies, tools, and techniques related to optimization and industrial engineering into a single volume to build insights towards the latest advancements in various domains. Applications of Advanced Optimization Techniques in Industrial Engineering includes the basic concept of optimization, techniques, and applications related to industrial engineering. Concepts are introduced in a sequential way along with explanations, illustrations, and solved examples. The book goes on to explore applications of operations research and covers empirical properties of a variety of engineering disciplines. It presents network scheduling, production planning, industrial and manufacturing system issues, and their implications in the real world. The book caters to academicians, researchers, professionals in inventory analytics, business analytics, investment managers, finance firms, storage-related managers, and engineers working in engineering industries and data management fields.

Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature-notably in the area of convex analysis-essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.

The Science of Deep Learning emerged from courses taught by the author that have provided thousands of students with training and experience for their academic studies, and prepared them for careers in deep learning, machine learning, and artificial intelligence in top companies in industry and academia. The book begins by covering the foundations of deep learning, followed by key deep learning architectures. Subsequent parts on generative models and reinforcement learning may be used as part of a deep learning course or as part of a course on each topic. The book includes state-of-the-art topics such as Transformers, graph neural networks, variational autoencoders, and deep reinforcement learning, with a broad range of applications. The appendices provide equations for computing gradients in backpropagation and optimization, and best practices in scientific writing and reviewing. The text presents an up-to-date guide to the field built upon clear visualizations using a unified notation and equations, lowering the barrier to entry for the reader. The accompanying website provides complementary code and hundreds of exercises with solutions.

Problems in network optimization arise in all areas of technology and industrial management. The topic of network flows has applications in diverse fields such as chemistry, engineering, management science, scheduling and transportation, to name a few.

This book is for those interested in number systems, abstract algebra, and analysis. It provides an understanding of negative and fractional numbers with theoretical background and explains rationale of irrational and complex numbers in an easy to understand format. This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way.

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable.

Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Reviews the literature of the Moth-Flame Optimization algorithm; Provides an in-depth analysis of equations, mathematical models, and mechanisms of the Moth-Flame Optimization algorithm; Proposes different variants of the Moth-Flame Optimization algorithm to solve binary, multi-objective, noisy, dynamic, and combinatorial optimization problems; Demonstrates how to design, develop, and test different hybrids of Moth-Flame Optimization algorithm; Introduces several applications areas of the Moth-Flame Optimization algorithm focusing in sustainability.

This book describes the fundamental and theoretical concepts of optimization algorithms in a systematic manner, along with their potential applications and implementation strategies in mining engineering. It explains basics of systems engineering, linear programming, and integer linear programming, transportation and assignment algorithms, network analysis, dynamic programming, queuing theory and their applications to mine systems. Reliability analysis of mine systems, inventory management in mines, and applications of non-linear optimization in mines are discussed as well. All the optimization algorithms are explained with suitable examples and numerical problems in each of the chapters. Features include: * Integrates operations research, reliability, and novel computerized technologies in single volume, with a modern vision of continuous improvement of mining systems. * Systematically reviews optimization methods and algorithms applied to mining systems including reliability analysis. * Gives out software-based solutions such as MATLAB (R), AMPL, LINDO for the optimization problems. * All discussed algorithms are supported by examples in each chapter. * Includes case studies for performance improvement of the mine systems. This book is aimed primarily at professionals, graduate students, and researchers in mining engineering.

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 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

the handbook is a valuable reference to researchers from industry and academia, as well as Masters and PhD students around the globe working in the metaheuristics and applications domain includes contributions from a variety of academics/researchers in the field of metaheuristics

Operations research (OR) is a core discipline in military and defense management. Coming to the forefront initially during World War II, OR provided critical contributions to logistics, supply chains, and strategic simulation, while enabling superior decision-making for Allied forces. OR has grown to include analytics and many applications, including artificial intelligence, cybersecurity, and big data, and is the cornerstone of management science in manufacturing, marketing, telecommunications, and many other fields. The Handbook of Military and Defense Operations Research presents the voices leading OR and analytics to new heights in security through research, practical applications, case studies, and lessons learned in the field. Features Applies the experiences of educators and practitioners working in the field Employs the latest technology developments in case studies and applications Identifies best practices unique to the military, security, and national defense problem space Highlights similarities and dichotomies between analyses and trends that are unique to military, security, and defense problems

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.

Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations. Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses. Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion

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.

Metaheuristic optimization is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. This is usually applied when two or more objectives are to be optimized simultaneously. This book is presented with two major objectives. Firstly, it features chapters by eminent researchers in the field providing the readers about the current status of the subject. Secondly, algorithm-based optimization or advanced optimization techniques, which are applied to mostly non-engineering problems, are applied to engineering problems. This book will also serve as an aid to both research and industry. Usage of these methodologies would enable the improvement in engineering and manufacturing technology and support an organization in this era of low product life cycle. Features: Covers the application of recent and new algorithms Focuses on the development aspects such as including surrogate modeling, parallelization, game theory, and hybridization Presents the advances of engineering applications for both single-objective and multi-objective optimization problems Offers recent developments from a variety of engineering fields Discusses Optimization using Evolutionary Algorithms and Metaheuristics applications in engineering

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

The rich, multi-faceted and multi-disciplinary field of matching-based market design is an active and important one due to its highly successful applications with economic and sociological impact. Its home is economics, but with intimate connections to algorithm design and operations research. With chapters contributed by over fifty top researchers from all three disciplines, this volume is unique in its breadth and depth, while still being a cohesive and unified picture of the field, suitable for the uninitiated as well as the expert. It explains the dominant ideas from computer science and economics underlying the most important results on market design and introduces the main algorithmic questions and combinatorial structures. Methodologies and applications from both the pre-Internet and post-Internet eras are covered in detail. Key chapters discuss the basic notions of efficiency, fairness and incentives, and the way market design seeks solutions guided by normative criteria borrowed from social choice theory.

This book includes over 500 most challenging exercises and problems in calculus. Topical problems and exercises are discussed on set theory, numbers, functions, limits and continuity, derivative, integral calculus, Rolle's theorem, mean value theorem, optimization problems, sequences and series. All the seven chapters recall important definitions, theorems and concepts, making this book immensely valuable to undergraduate students of engineering, mathematics, statistics, computer science and basic sciences.