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Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen. Features Vast collection of examples Simple. accessible presentation Suitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineers Examples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example. Simon Serovajsky is a professor of mathematics at Al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.

This up-to-date overview of Bayesian nonparametric statistics provides both an introduction to the field and coverage of recent research topics, including deep neural networks, high-dimensional models and multiple testing, Bernstein-von Mises theorems and variational Bayes approximations, many of which have previously only been accessible through research articles. Although Bayesian posterior distributions are widely applied in astrophysics, inverse problems, genomics, machine learning and elsewhere, their theory is still only partially understood, especially in complex settings such as nonparametric or semiparametric models. Here, the available theory on the frequentist analysis of posterior distributions is outlined in terms of convergence rates, limiting shape results and uncertainty quantification. Based on lecture notes for a course given at the St-Flour summer school in 2023, the book is aimed at researchers and graduate students in statistics and probability.

This textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field. With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization problems under application-relevant conditions sets a new accent that enriches the stock of previous textbooks on optimization. Using the theory and algorithms of smooth convex optimization, the book illustrates that the global solution of a class of optimization problems frequently encountered in practice is efficiently possible, while for the more difficult-to-handle non-convex problems itdevelops in detail the ideas of branch-and-bound methods. This book is the English translation of the 2nd edition of “Grundzüge der Globalen Optimierung” (Springer, 2021) written in German. The translation was done with the help of artificial intelligence. A subsequent revision was performed by the author to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness. It may, however, read stylistically different from a conventional translation.

This book addresses the analysis of functions of a real variable and transitions from the standard calculus sequence to mathematical analysis. The author presents the limits and convergence of sequences of functions, illustrates the limitations of the Riemann integral, and discusses the need for a new integral: the Lebesgue integral. The fundamental concepts of the theory of calculus of one variable is presented in addition to limits, continuity, derivatives and its applications, and integrals and their applications. The tone and language of the book is kept as informal as possible along with the descriptions and examples to aid learning. The book is concise and presents single variable advanced calculus leading up to Fourier analysis. In addition, the book sets up sufficient background for a course in measure theory and Lebesgue integration.

This thesis deals with an optimization problem from the field of theoretical plasma physics. Specifically, it deals with the question of how the accelerated electrons are spatially arranged in a plasma wave generated by a laser pulse. An internal structure of this so-called witness beam is of interest for the radiation characteristics of such electron beams, in particular with regard to the coherence of the generated radiation. The resulting internal structure of the electron beam is a result of the interaction of the electrons with each other and the electric fields of the wakefield, therefore it is determined by solving a minimization problem. The thesis builds on previous results in this field and aims to find suggestions for improved algorithms to determine the minimum sought.

This book provides a comprehensive review of the latest developments in optimization based learning algorithms within the field of electrical engineering. It covers various power system applications including efficient power system operation, load forecasting, fault analysis, home automation and efficient smart grid management. Each application is accompanied by case studies and a literature review in self-contained chapters. The book is dedicated to study the effectiveness of intelligent methods in addressing the power system problems and its mitigation using optimization algorithms. It discusses several optimization algorithms such as random forest algorithm, metaheuristic algorithm, scaled conjugate gradient descent algorithm, artificial bee colony algorithm etc. and their usability in intelligent decision makers for the various optimization problems in electrical engineering. This timely book serves as a practical guide and reference sources for students, researchers and professionals.

This book provides models and methods for the optimal management of electrical vehicles through an interdisciplinary approach that brings together knowledge from the sectors of transportation, manufacturing and smart grids. Optimization of Electric-Vehicle Charging explores several optimization models for the scheduling of electric vehicles in a smart grid. Both discrete-time and discrete-event approaches are considered to minimize tardiness, charging and production costs, on the basis of information like release time, due date, deadline, energy request, and availability of energy generated from renewable sources. Transportation demand is assessed, as well as user-equilibrium-based approaches, for the location of charging stations and for the assignment of users to multiple charging stations. Employing illustrations, tables and examples to elucidate the ideas presented, this book will be of value to researchers and practitioners in the fields of electrical engineering and transportation, as well as to graduate and PhD students.

This contributed volume guides researchers and practitioners on resource collaborative management of supply chains and manufacturing enterprises within an industrial internet technological environment. The book comprises 10 chapters that cover two major topics in the subject of logistics 4.0, namely the utilization of both disruptive technologies and optimization techniques in smart logistic management. With global research on the book's topic expanding rapidly across various directions and disciplines, it provides a structured framework for international experts to showcase outstanding work and unique approaches. Researchers and students will find the comprehensive outline on collaborative optimization and management of smart manufacturing and production, warehousing, inventory, logistics, transportation, integrated supply chain, and supply network within the industrial internet platform a beneficial guide to understanding current and future practical problems that arise in manufacturing and supply chain management.

This book is interdisciplinary and unites several areas of applied probability, statistics, and computational mathematics including computer experiments, optimal experimental design, and global optimization. The bulk of the book is based on several recent papers by the authors but also contains new results. Considering applications, this brief highlights multistart and other methods of global optimizations requiring efficient exploration of the domain of optimization. This book is accessible to a wide range of readers; the prerequisites for reading the book are rather low, and many numerical examples are provided that pictorially illustrate the main ideas, methods, and conclusions. The main purpose of this book is the construction of efficient exploration strategies of high-dimensional sets. In high dimensions, the asymptotic arguments could be practically misleading and hence the emphasis on the non-asymptotic regime. An important link with global optimization stems from the observation that approximate covering is one of the key concepts associated with multistart and other key random search algorithms. In addition to global optimization, important applications of the results are computer experiments and machine learning. It is demonstrated that the asymptotically optimal space-filling designs, such as pure random sampling or low-discrepancy point nets, could be rather inefficient in the non-asymptotic regime and the authors suggest ways of increasing the efficiency of such designs. The range of techniques ranges from experimental design, Monte Carlo, and asymptotic expansions in the central limit theorem to multivariate geometry, theory of lattices, and numerical integration. This book could be useful to a wide circle of readers, especially those specializing in global optimization, numerical analysis, computer experiments, and computational mathematics. As specific recipes for improving set exploration schemes are formulated, the book can also be used by the practitioners interested in applications only.

Dieses Buch betont die grundlegenden Konzepte des CS-Algorithmus und seiner Varianten sowie deren Anwendung zur Lösung unterschiedlicher Optimierungsprobleme in medizinischen und ingenieurwissenschaftlichen Anwendungen. Evolutionäre metaheuristische Ansätze werden zunehmend zur Lösung komplexer Optimierungsprobleme in verschiedenen realen Anwendungen eingesetzt. Einer der erfolgreichsten Optimierungsalgorithmen ist die Cuckoo-Suche (CS), die zu einem aktiven Forschungsbereich geworden ist, um N-dimensionale und lineare/nichtlineare Optimierungsprobleme mithilfe einfacher mathematischer Prozesse zu lösen. CS hat die Aufmerksamkeit verschiedener Forscher auf sich gezogen, was zur Entstehung zahlreicher Varianten des grundlegenden CS mit verbesserten Leistungsmerkmalen seit 2019 geführt hat.

This book develops robust design and assessment of product and production from viewpoint of system theory, which is quantized with the introduction of brand new concept of preferable probability and its assessment. It aims to provide a new idea and novel way to robust design and assessment of product and production and relevant problems. Robust design and assessment of product and production is attractive to both customer and producer since the stability and insensitivity of a product's quality to uncontrollable factors reflect its value. Taguchi method has been used to conduct robust design and assessment of product and production for half a century, but its rationality is criticized by statisticians due to its casting of both mean value of a response and its dispersion into one index, which doesn't characterize the issue of simultaneous optimization of above two independent sub-responses sufficiently for robust design, so an appropriate approach is needed. The preference or role of a response in the evaluation is indicated by using preferable probability as the unique index. Thus, the rational approach for robust design and assessment of product and production is formulated by means of probabilistic multi-objective optimization, which reveals the simultaneous optimization of both mean value of a response and its dispersion in manner of joint probability. Besides, defuzzification and fuzzification measurements are involved as preliminary approaches for robust assessment, the latter provides miraculous treatment for the'target the best'case flexibly.

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.

This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

This comprehensive textbook covers both classical and geometric aspects of optimization using methods, deterministic and stochastic, in a single volume and in a language accessible to non-mathematicians. It will help serve as an ideal study material for senior undergraduate and graduate students in the fields of civil, mechanical, aerospace, electrical, electronics, and communication engineering.The book includes: Derivative-based Methods of Optimization. Direct Search Methods of Optimization. Basics of Riemannian Differential Geometry. Geometric Methods of Optimization using Riemannian Langevin Dynamics. Stochastic Analysis on Manifolds and Geometric Optimization Methods. This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.

The book is focused on latest developments and findings on engineering applications of AI and swarm intelligence. It provides comprehensive reviews and surveys on implementations and coding aspects of case studies and applications where appropriate. The book is useful for scholars, lecturers, and practitioners from academia and industrial applications. The readership of this book also includes Ph.D. students and researchers with a wide experience in the subject areas.

This book explores cutting-edge medical imaging advancements and their applications in clinical decision-making. The book contains various topics, methodologies, and applications, providing readers with a comprehensive understanding of the field's current state and prospects. It begins with exploring domain adaptation in medical imaging and evaluating the effectiveness of transfer learning to overcome challenges associated with limited labeled data. The subsequent chapters delve into specific applications, such as improving kidney lesion classification in CT scans, elevating breast cancer research through attention-based U-Net architecture for segmentation and classifying brain MRI images for neurological disorders. Furthermore, the book addresses the development of multimodal machine learning models for brain tumor prognosis, the identification of unique dermatological signatures using deep transfer learning, and the utilization of generative adversarial networks to enhance breast cancer detection systems by augmenting mammogram images. Additionally, the authors present a privacy-preserving approach for breast cancer risk prediction using federated learning, ensuring the confidentiality and security of sensitive patient data. This book brings together a global network of experts from various corners of the world, reflecting the truly international nature of its research.

In this book Lukas Graf studies dynamic network flows which are a model for individual car traffic in road networks. It is assumed that drivers choose their routes based on information about the current state of the network in such a way as to selfishly minimize their own arrival time at their destination. Whilst on their journey the drivers adapt their current route choices based on the changing state of the network. A dynamic flow wherein every (infinitesimally small) flow particle behaves in this way is then called an instantaneous dynamic equilibrium. After giving a mathematically precise definition of this equilibrium concept the author shows existence of those equilibrium flows, studies their computational complexity and derives bounds on their quality.

This book examines optimization problems that in practice involve random model parameters. It outlines the computation of robust optimal solutions, i.e., optimal solutions that are insensitive to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into corresponding deterministic problems.Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, and differentiation formulas for probabilities and expectations.The fourth edition of this classic text has been carefully and thoroughly revised. It includes new chapters on the solution of stochastic linear programs by discretization of the underlying probability distribution, and on solving deterministic optimization problems by means of controlled random search methods and multiple random search procedures. It also presents a new application of stochastic optimization methods to machine learning problems with different loss functions. For the computation of optimal feedback controls under stochastic uncertainty, besides the open-loop feedback procedures, a new method based on Taylor expansions with respect to the gain parameters is presented. The book is intended for researchers and graduate students who are interested in stochastics, stochastic optimization, and control. It will also benefit professionals and practitioners whose work involves technical, economicand/or operations research problems under stochastic uncertainty.

This book collects selected contributions of the “Optimization and Decision Science - ODS2023” international conference on the theme of optimization in green sustainability and ecological transition. ODS2023 was held in Ischia, 4–7 September 2023, and was organized by AIRO, the Italian Operations Research Society. The book offers new and original contributions on operations research, optimization, decision science, and prescriptive analytics from both a methodological and applied perspectives with a special focus on SDG related topics.It provides a state-of-the art on problem models and solving methods to address a widely class of real-world problems, arising in different application areas such as logistics, transportation, manufacturing, health, ICT and mobile networks, and emergency/disaster management. In addition, the scientific works collected in this book aim at providing significant contributions in the themes of sustainability, traffic and pollution reductions, and energy management.This book is aimed primarily at researchers and Ph.D. students in the Operations Research community. However, due to its interdisciplinary contents, this book is of high interest also for students and researchers from other disciplines, including artificial intelligence, computer sciences, finance, mathematics, and engineering as well as for practitioners facing complex decision-making problems in logistics, manufacturing production, and services.

Written by an experienced operations research practitioner with a strong applied mathematics background, this book offers practical insights into how to approach optimization problems, how to develop intelligent and efficient mathematical models and algorithms, and how to implement and deliver software products to customers. With a focus on revealing the similarities and differences between academia and industry in mathematical modeling, the book provides useful tips and advice based on the author's extensive experience as a principal developer working to solve real-world optimization problems for several major high-tech companies.The book offers valuable food for thought for researchers and practical guidance for graduate students preparing for their future projects in the industry. It is also an essential resource for practitioners working in the industrial, business, and service sectors.

This first book of conference proceedings contains selected papers presented at ICGEC 2023, the 15th International Conference on Genetic and Evolutionary Computing, held on October 6–8, 2023, in Kaohsiung, Taiwan. The conference is intended as an international forum for the researchers and professionals in all areas of genetic and evolutionary computing. And the readers know the up-to-date techniques of the mentioned topics, including swarm intelligence and its applications, operational technologies and networked multimedia applications, wearable computing and intelligent data hiding, image processing and intelligent applications, and intelligent multimedia tools and applications. It helps readers bring new ideas or apply the designed approaches from the collected papers to their professional jobs.

This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations. In this setting, problems become much more involved and, for this same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the modern calculus of variations and the analytical foundation associated with it. In particular, it covers an extended introduction to basic functional analysis and to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the need for further challenges beyond the topics addressed here will push students to more advanced horizons.

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education.Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy's inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages.It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

An unexpected take on how games work, what the stakes are for them, and how game designers can avoid the traps of optimization.The process of optimization in games seems like a good thing—who wouldn't want to find the most efficient way to play and win? As Christopher Paul argues in Optimizing Play, however, optimization can sometimes risk a tragedy of the commons, where actions that are good for individuals jeopardize the overall state of the game for everyone else. As he explains, players inadvertently limit play as they theorycraft, seeking optimal choices. The process of developing a meta, or the most effective tactic available, structures decision making, causing play to stagnate. A “stale” meta then creates a perception that a game is solved and may lead players to turn away from the game.Drawing on insights from game studies, rhetoric, the history of science, ecology, and game theory literature, Paul explores the problem of optimization in a range of video games, including Overwatch, FIFA/EA Sports FC, NBA 2K, Clash Royale, World of Warcraft, and League of Legends. He also pulls extensively from data analytics in sports, where the problem has progressed further and is even more intractable than it is in video games, given the money sports teams invest to find an edge. Finally, Paul offers concrete and specific suggestions for how games can be developed to avoid the trap set by optimization run amok.

The Water-Energy-Food Nexus: Optimization Models for Decision Making covers the discussion about water, energy, and food as a crucial resource for human well-being and for sustainable development. These resources are inextricable interrelated, therefore, to cover water, energy, and food demands in different sectors and at different scales, it must be considered several sources to produce resources even conventional or unconventional, and there must be considered the interlinkages of resources for a proper integration. This book will emphasize several issues that must be considered in the design of water-energy-food nexus systems such as the selection of technologies to produce water or energy, size of technologies and food required to cover nutritional demands. Therefore, in The Water-Energy-Food Nexus: Optimization Models for Decision Making, mathematical models are presented for the design of water-energy-food nexus systems involving several strategies to account for issues like sustainable development, security of resources, interest in conflicts from stakeholders, and efficient allocation of resources. - Includes different optimization models for the integration of water-energy-food nexus - Considers sustainability criteria in the presented models - Helps readers understand different approaches for trade-off solutions - Presents general software that can be used in solving different problems

Handbook of Whale Optimization Algorithm: Variants, Hybrids, Improvements, and Applications provides the most in-depth look at an emerging meta-heuristic that has been widely used in both science and industry. Whale Optimization Algorithm has been cited more than 5000 times in Google Scholar, thus solving optimization problems using this algorithm requires addressing a number of challenges including multiple objectives, constraints, binary decision variables, large-scale search space, dynamic objective function, and noisy parameters to name a few. This handbook provides readers with in-depth analysis of this algorithm and existing methods in the literature to cope with such challenges. The authors and editors also propose several improvements, variants and hybrids of this algorithm. Several applications are also covered to demonstrate the applicability of methods in this book. Provides in-depth analysis of equations, mathematical models and mechanisms of the Whale Optimization Algorithm Proposes different variants of the Whale Optimization Algorithm to solve binary, multiobjective, noisy, dynamic and combinatorial optimization problems Demonstrates how to design, develop and test different hybrids of Whale Optimization Algorithm Introduces several application areas of the Whale Optimization Algorithm, focusing on sustainability Includes source code from applications and algorithms that is available online

The formal optimization handbook is a comprehensive guide that covers a wide range of subjects. It includes a literature review, a mathematical formulation of optimization methods, flowcharts and pseudocodes, illustrations, problems and applications, results and critical discussions, and much more. The book covers a vast array of formal optimization fields, including mathematical and Bayesian optimization, neural networks and deep learning, genetic algorithms and their applications, hybrid optimization methods, combinatorial optimization, constraint handling in optimization methods, and swarm-based optimization. This handbook is an excellent reference for experts and non-specialists alike, as it provides stimulating material. The book also covers research trends, challenges, and prospective topics, making it a valuable resource for those looking to expand their knowledge in this field.

This monograph introduces a new mathematical model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. Its main feature is the expansion of the family of Lotka-Volterra systems by introducing a new term that defines aggression. Because the model is flexible, it can be applied to various scenarios in the context of human populations, such as strategy games, competition in the marketplace, and civil wars. Drawing from a variety of methodologies within dynamical systems, ODEs, and mathematical biology, the authors'approach focuses on the dynamical properties of the system. This is accomplished by detecting and describing all possible equilibria, and analyzing the strategies that may lead to the victory of the aggressive population. Techniques typical of two-dimensional dynamical systems are used, such as asymptotic behaviors regulated by the Poincaré–Bendixson Theorem. A New Lotka-Volterra Model of Competition With Strategic Aggression will appeal to researchers and students studying population dynamics and dynamical systems, particularly those interested in the cross section between mathematics and ecology.

This textbook is an introduction to nonlinear optimization, which treats mathematical concepts stringently on the one hand, but also motivates them in great detail and illustrates them with 42 figures. Therefore, the book is not only aimed at mathematicians, but also at natural scientists, engineers, and economists who want to understand and apply mathematically sound methods in their field. With just over two hundred pages, the book offers sufficient flexibility to serve as a foundation for various types of lectures on nonlinear optimization. Many geometric approaches for understanding both optimality conditions and numerical methods introduce a new perspective, enriching the existing literature on optimization. This is particularly evident in the detailed treatment of issues arising from different functional descriptions of the same geometry of feasible sets, and the thus motivated introduction of constraint qualifications for deriving derivative-based optimality conditions. This book is the English translation of the second edition of “Grundzüge der Nichtlinearen Optimierung” (Springer, 2021) written in German. The translation was done with the help of artificial intelligence. A subsequent revision was performed by the author to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness. It may, however, read stylistically different from a conventional translation.

The book introduces dependability (security metric) ideas, gives a general overview of the security analysis of Safety-Critical Systems (SCSs), explains why the study is necessary and defines key terms relevant to this research. It makes an effort to emphasize the significance of security in comparison to other dependability indicators and illustrates the key drivers of this research's purpose. The mathematical foundation of the security analysis process is briefly illustrated, and key mathematical terminology and concepts are presented that are crucial for the security evaluation of critical systems. This book's objective is to provide a thorough understanding of the security analysis process. It will be a research-focused book designed for undergraduate, graduate, and doctoral courses in software and cyber security. The fundamentals of reliability, security, metrics, and mathematical foundation have been covered in this book. Each technique's actual applications, along with benefits and drawbacks, are also shown. Applying each technique to the various case studies serves as a demonstration of how it works. By using the many case studies of safety-critical systems, the students can also learn different analysis approaches and how to model them. Students will be able to use these tools, in particular, on a case study of their choice to analyze system security. The book includes a comparison of various strategies and appropriate recommendations for further reading on these subjects. Moreover, this book's target audience includes software professionals who are interested in security analysis.

Tackle the most challenging problems in science and engineering with these cutting-edge algorithms Multi-objective optimization problems (MOPs) are those in which more than one objective needs to be optimized simultaneously. As a ubiquitous component of research and engineering projects, these problems are notoriously challenging. In recent years, evolutionary algorithms (EAs) have shown significant promise in their ability to solve MOPs, but challenges remain at the level of large-scale multi-objective optimization problems (LSMOPs), where the number of variables increases and the optimized solution is correspondingly harder to reach. Evolutionary Large-Scale Multi-Objective Optimization and Applications constitutes a systematic overview of EAs and their capacity to tackle LSMOPs. It offers an introduction to both the problem class and the algorithms before delving into some of the cutting-edge algorithms which have been specifically adapted to solving LSMOPs. Deeply engaged with specific applications and alert to the latest developments in the field, it's a must-read for students and researchers facing these famously complex but crucial optimization problems. The book's readers will also find: Analysis of multi-optimization problems in fields such as machine learning, network science, vehicle routing, and more Discussion of benchmark problems and performance indicators for LSMOPs Presentation of a new taxonomy of algorithms in the field Evolutionary Large-Scale Multi-Objective Optimization and Applications is ideal for advanced students, researchers, and scientists and engineers facing complex optimization problems.

As public awareness of social and environmental issues grew, more consumers began to support firms committed to developing and operating environmentally sustainable and socially responsible supply chains. Consumers, investors, and regulators began demanding transparency and accountability, pushing companies to address the environmental footprint of their products and operations. The book addresses essential questions, such as how a firm shifts its focus from being profit-focused to being triple-bottom-line driven and how a firm develops its supply chain with a conscience. Written by practice leaders and leading scholars, it sheds light on different paths a firm can take to embrace its role as a sustainability champion, paving the way for a future where profit and the planet coexist. The book is intended as a tribute to Professor Hau Lee's seminal contributions, elevating the triple bottom line to the forefront of the Operations Management (OM) research agenda. It stimulates practitioners and researchers to engage in deeper and broader discussions about ways to strike a better balance among profit, people, and the planet.

This textbook provides researchers, post-graduate students, and practitioners with a systematic framework for coping with uncertainty when making facility location decisions. In addition to in-depth coverage of models and solution techniques, application areas are discussed. The book guides readers through the field, showing how to successfully analyze new problems and handle new applications. Initially, the focus is on base models and concepts. Then, gradually, more comprehensive models and more involved solution algorithms are discussed. Throughout the book, two perspectives are intertwined: the paradigm for capturing uncertainty, and the facility location problem at hand. The former includes stochastic programming, robust optimization, chance-constrained programming, and distributional robust optimization; the latter includes classical facility location problems and those arising in many real-world applications such as hub location, location routing, andlocation inventory.

This textbook introduces readers to a comprehensive framework for the application of deterministic optimization strategies in the field of chemical processes, with a strong emphasis on sustainability.The book establishes a vital connection between fundamental deterministic optimization principles, optimization tools, and real-world application instances, all within the context of environmentally responsible practices. The approach put forth in this book is exceptionally versatile, allowing for the use of many optimization software and deterministic techniques.Contained in the book are many fundamental optimization concepts, encompassing linear programming, nonlinear programming, integer programming, and multi-objective optimization, all tailored to promote sustainable decision-making. Furthermore, the book provides practical examples illustrating the application of these techniques within sustainable chemical processes as tutorials.The textbook also explores the utilization of popular optimization software platforms such as GAMS, MATLAB, and Python, demonstrating how these tools can be leveraged for eco-friendly process optimization. Through this comprehensive framework, readers can not only acquire the skills needed to optimize a wide range of processes but also learn how to do so with sustainability at the forefront of their considerations. This approach streamlines the optimization process, eliminating unnecessary complications along the way and ensuring that environmental and ethical considerations are integral to the decision-making process.

This book explores optimization under uncertainty and related applications in agriculture, sustainable supply chains and the agrifood industry. Rapid changes in the primary sector are leading to more and more industrialized structures, which require optimization methods in order to cope with today's challenges. Addressing uncertainty in the agrifood industry may lead to more robust supply chain designs or to diversified risk. Sustainability requires interaction with the environmental or social sciences. This book bridges the gap between optimization theory, uncertainty, sustainability and primary-sector applications (mainly in the agriculture and food industry, but also fisheries, forestry and natural resources in general). Although it has been a major challenge for the operations research community, this urgently needed interdisciplinary collaboration is not adequately covered in most current curricula in applied mathematics, economics or (agronomic/industrial/forest) engineering. This book highlights research that can help fill this gap. The individual chapters cover applications of stochastic integer linear programming and multicriteria decision methods in agriculture. The topics addressed include uncertainty in areas such as the sugar cane industry, pig farming, and cold storage for perishable products. Large-scale sustainable food production is a growing concern; this book offers solutions to help meet global demand in agriculture by using and improving the methods of optimization theory and operations research.

In this book, various chaos maps are embedded in eleven efficient and well-known metaheuristics and a significant improvement in the optimization results is achieved. The two basic steps of metaheuristic algorithms consist of exploration and exploitation. The imbalance between these stages causes serious problems for metaheuristic algorithms, which are immature convergence and stopping in local optima. Chaos maps with chaotic jumps can save algorithms from being trapped in local optima and lead to convergence toward global optima. Embedding these maps in the exploration phase, exploitation phase, or both simultaneously corresponds to three efficient and useful scenarios. By creating competition between different modes and increasing diversity in the search space and creating sudden jumps in the search phase, improvements are achieved for chaotic algorithms. Four Chaotic Algorithms, including Chaotic Cyclical Parthenogenesis Algorithm, Chaotic Water Evaporation Optimization, Chaotic Tug-of-War Optimization, and Chaotic Thermal Exchange Optimization are developed.