This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book's major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.

This book offers a rigorous mathematical analysis of fuzzy geometrical ideas. It demonstrates the use of fuzzy points for interpreting an imprecise location and for representing an imprecise line by a fuzzy line. Further, it shows that a fuzzy circle can be used to represent a circle when its description is not known precisely, and that fuzzy conic sections can be used to describe imprecise conic sections. Moreover, it discusses fundamental notions on fuzzy geometry, including the concepts of fuzzy line segment and fuzzy distance, as well as key fuzzy operations, and includes several diagrams and numerical illustrations to make the topic more understandable. The book fills an important gap in the literature, providing the first comprehensive reference guide on the fuzzy mathematics of imprecise image subsets and imprecise geometrical objects. Mainly intended for researchers active in fuzzy optimization, it also includes chapters relevant for those working on fuzzy image processing and pattern recognition. Furthermore, it is a valuable resource for beginners interested in basic operations on fuzzy numbers, and can be used in university courses on fuzzy geometry, dealing with imprecise locations, imprecise lines, imprecise circles, and imprecise conic sections.

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.

This book introduces readers to the use of R codes for optimization problems. First, it provides the necessary background to understand data envelopment analysis (DEA), with a special emphasis on fuzzy DEA. It then describes DEA models, including fuzzy DEA models, and shows how to use them to solve optimization problems with R. Further, it discusses the main advantages of R in optimization problems, and provides R codes based on real-world data sets throughout. Offering a comprehensive review of DEA and fuzzy DEA models and the corresponding R codes, this practice-oriented reference guide is intended for masters and Ph.D. students in various disciplines, as well as practitioners and researchers.

This book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.

Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions. As an application, the author derives results for single minmax location problems formulated by means of extended perturbed minimal time functions as well as for multi-facility minmax location problems defined by gauges. In addition, he provides formulae of projections onto the epigraphs of gauges to solve these kinds of location problems numerically by using parallel splitting algorithms. Numerical comparisons of recent methods show the excellent performance of the proposed solving technique. About the Author: Dr. Oleg Wilfer received his PhD at the Faculty of Mathematics of Chemnitz University of Technology, Germany. He is currently working as a development engineer in the automotive industry.

This Springer brief discusses the use of control engineering methods to plan a cancer therapy which tends to reduce tumour size in patients, striking a balance that minimizes the toxic effects of the treatment. The authors address the design and computation of impulsive control therapies, a methodology previously underexplored in the application of control methods to medical modelling. This allows simulation of such discrete events as taking a pill rather than relying on the supply of therapy being continuous and steady. The book begins with an introduction to the topic, before moving onto pharmacokinetic, pharmacodynamical and tumour-growth models and explaining how they describe the relationship between a certain therapy plan and the evolution of cancer. This is placed firmly in the context of work introducing impulsive differential equations. The final chapter summarizes the research presented and suggests future areas of research to encourage readers in taking the subject forward. This book is of interest to biomedical engineers, researchers and students, particularly those with a background in systems and control engineering.

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

This book presents a new meta-heuristic algorithm, inspired by the self-defense mechanisms of plants in nature. Numerous published works have demonstrated the various self-defense mechanisms (survival strategies) plants use to protect themselves against predatory organisms, such as herbivorous insects. The proposed algorithm is based on the predator-prey mathematical model originally proposed by Lotka and Volterra, consisting of two nonlinear first-order differential equations, which allow the growth of two interacting populations (prey and predator) to be modeled. The proposed meta-heuristic is able to produce excellent results in several sets of benchmark optimization problems. Further, fuzzy logic is used for dynamic parameter adaptation in the algorithm.

This book explores key examples concerning the implementation of information technology and mathematical modeling to solve issues concerning environmental sustainability. The examples include using fuzzy weighted multivariate regression to predict the water quality index at Perak River in Malaysia; using wireless sensor networks (WSNs) for a remote river water pollution monitoring system; deriving biomass activated carbon from oil palm shell; and assessing the performance of a PV/T air solar collector. The book offers a valuable resource for all graduate students and researchers who are working in this rapidly growing area.

This Festschrift is in honor of Chris Hankin, Professor at the Imperial College in London, UK, on the Occasion of His 65th Birthday.Chris Hankin is a Fellow of the Institute for Security Science and Technology and a Professor of Computing Science. His research is in cyber security, data analytics and semantics-based program analysis. He leads multidisciplinary projects focused on developing advanced visual analytics and providing better decision support to defend against cyber attacks. This Festschrift is a collection of scientific contributions related to the topics that have marked the research career of Professor Chris Hankin. The contributions have been written to honour Chris' career and on the occasion of his retirement.

This self-contained book describes social influence from a computational point of view, with a focus on recent and practical applications, models, algorithms and open topics for future research. Researchers, scholars, postgraduates and developers interested in research on social networking and the social influence related issues will find this book useful and motivating. The latest research on social computing is presented along with and illustrations on how to understand and manipulate social influence for knowledge discovery by applying various data mining techniques in real world scenarios. Experimental reports, survey papers, models and algorithms with specific optimization problems are depicted. The main topics covered in this book are: chrematistics of social networks, modeling of social influence propagation, popular research problems in social influence analysis such as influence maximization, rumor blocking, rumor source detection, and multiple social influence competing.

This book highlights state-of-the-art research on renewable energy integration technology and suitable and efficient power generation, discussing smart grids, renewable energy grid integration, prediction control models, and econometric models for predicting the global solar radiation and factors that affect solar radiation, performance evaluation of photovoltaic systems, and improved energy consumption prediction models. It discusses several methods, algorithms, environmental data-based performance analyses, and experimental results to help readers gain a detailed understanding of the pros and cons of technologies in this rapidly growing area. Accordingly, it offers a valuable resource for students and researchers working on renewable energy optimization models.

This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares - that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance. The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLAB (R), and data sets accompanying the book online. Suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques - e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms - as valuable tools for analyzing and solving Ky Fan inequalities.

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs) . As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Describes how evolutionary algorithms (EAs) can be used to identify, model, and minimize day-to-day problems that arise for researchers in optimization and mobile networking

Mobile ad hoc networks (MANETs), vehicular networks (VANETs), sensor networks (SNs), and hybrid networks--each of these require a designer's keen sense and knowledge of evolutionary algorithms in order to help with the common issues that plague professionals involved in optimization and mobile networking.

This book introduces readers to both mobile ad hoc networks and evolutionary algorithms, presenting basic concepts as well as detailed descriptions of each. It demonstrates how metaheuristics and evolutionary algorithms (EAs) can be used to help provide low-cost operations in the optimization process--allowing designers to put some "intelligence" or sophistication into the design. It also offers efficient and accurate information on dissemination algorithms, topology management, and mobility models to address challenges in the field.

"Evolutionary Algorithms for Mobile Ad Hoc Networks" Instructs on how to identify, model, and optimize solutions to problems that arise in daily researchPresents complete and up-to-date surveys on topics like network and mobility simulatorsProvides sample problems along with solutions/descriptions used to solve each, with performance comparisonsCovers current, relevant issues in mobile networks, like energy use, broadcasting performance, device mobility, and more

"Evolutionary Algorithms for Mobile Ad Hoc Networks" is an ideal book for researchers and students involved in mobile networks, optimization, advanced search techniques, and multi-objective optimization.

This SpringerBrief bridges the gap between the areas of simulation studies on the one hand, and optimization with natural computing on the other. Since natural computing methods have been applied with great success in several application areas, a review concerning potential benefits and pitfalls for simulation studies is merited. The brief presents such an overview and combines it with an introduction to natural computing and selected major approaches, as well as with a concise treatment of general simulation-based optimization. As such, it is the first review which covers both the methodological background and recent application cases. The brief is intended to serve two purposes: First, it can be used to gain more information concerning natural computing, its major dialects, and their usage for simulation studies. It also covers the areas of multi-objective optimization and neuroevolution. While the latter is only seldom mentioned in connection with simulation studies, it is a powerful potential technique. Second, the reader is provided with an overview of several areas of simulation-based optimization which range from logistic problems to engineering tasks. Additionally, the brief focuses on the usage of surrogate and meta-models. The brief presents recent application examples.

This volume consists of selected essays by participants of the workshop Control at Large Scales: Energy Markets and Responsive Grids held at the Institute for Mathematics and its Applications, Minneapolis, Minnesota, U.S.A. from May 9-13, 2016. The workshop brought together a diverse group of experts to discuss current and future challenges in energy markets and controls, along with potential solutions. The volume includes chapters on significant challenges in the design of markets and incentives, integration of renewable energy and energy storage, risk management and resilience, and distributed and multi-scale optimization and control. Contributors include leading experts from academia and industry in power systems and markets as well as control science and engineering. This volume will be of use to experts and newcomers interested in all aspects of the challenges facing the creation of a more sustainable electricity infrastructure, in areas such as distributed and stochastic optimization and control, stability theory, economics, policy, and financial mathematics, as well as in all aspects of power system operation.

This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.

This book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search. Algorithms are analyzed from a wide spectrum of theories and frameworks to offer insight to the main characteristics of algorithms and understand how and why they work for solving optimization problems. In-depth mathematical analyses are carried out for different perspectives, including complexity theory, fixed point theory, dynamical systems, self-organization, Bayesian framework, Markov chain framework, filter theory, statistical learning, and statistical measures. Students and researchers in optimization, operations research, artificial intelligence, data mining, machine learning, computer science, and management sciences will see the pros and cons of a variety of algorithms through detailed examples and a comparison of algorithms.

This authored monograph presents a study on fundamental limits and robustness of stability and stabilization of time-delay systems, with an emphasis on time-varying delay, robust stabilization, and newly emerged areas such as networked control and multi-agent systems. The authors systematically develop an operator-theoretic approach that departs from both the traditional algebraic approach and the currently pervasive LMI solution methods. This approach is built on the classical small-gain theorem, which enables the author to draw upon powerful tools and techniques from robust control theory. The book contains motivating examples and presents mathematical key facts that are required in the subsequent sections. The target audience primarily comprises researchers and professionals in the field of control theory, but the book may also be beneficial for graduate students alike.

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.

This book develops a new approach called parameter advising for finding a parameter setting for a sequence aligner that yields a quality alignment of a given set of input sequences. In this framework, a parameter advisor is a procedure that automatically chooses a parameter setting for the input, and has two main ingredients: (a) the set of parameter choices considered by the advisor, and (b) an estimator of alignment accuracy used to rank alignments produced by the aligner. On coupling a parameter advisor with an aligner, once the advisor is trained in a learning phase, the user simply inputs sequences to align, and receives an output alignment from the aligner, where the advisor has automatically selected the parameter setting. The chapters first lay out the foundations of parameter advising, and then cover applications and extensions of advising. The content * examines formulations of parameter advising and their computational complexity, * develops methods for learning good accuracy estimators, * presents approximation algorithms for finding good sets of parameter choices, and * assesses software implementations of advising that perform well on real biological data. Also explored are applications of parameter advising to * adaptive local realignment, where advising is performed on local regions of the sequences to automatically adapt to varying mutation rates, and * ensemble alignment, where advising is applied to an ensemble of aligners to effectively yield a new aligner of higher quality than the individual aligners in the ensemble. The book concludes by offering future directions in advising research.

This book presents the topology optimization theory for laminar flows with low and moderate Reynolds numbers, based on the density method and level-set method, respectively. The density-method-based theory offers efficient convergence, while the level-set-method-based theory can provide anaccurate mathematical expression of the structural boundary. Unsteady, body-force-driven and two-phase properties are basic characteristics of the laminar flows. The book discusses these properties, which are typical of microfluidics and one of the research hotspots in the area of Micro-Electro-Mechanical Systems (MEMS), providing an efficient inverse design approach for microfluidic structures. To demonstrate the applications of this topology optimization theory in the context of microfluidics, it also investigates inverse design for the micromixer, microvalve and micropump, which are key elements in lab-on-chip devices.