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Heuristics are strategies using readily accessible, loosely applicable information to control problem solving. Algorithms, for example, are a type of heuristic. By contrast, Metaheuristics are methods used to design Heuristics and may coordinate the usage of several Heuristics toward the formulation of a single method. GRASP (Greedy Randomized Adaptive Search Procedures) is an example of a Metaheuristic. To the layman, heuristics may be thought of as ‘rules of thumb’ but despite its imprecision, heuristics is a very rich field that refers to experience-based techniques for problem-solving, learning, and discovery. Any given solution/heuristic is not guaranteed to be optimal but heuristic methodologies are used to speed up the process of finding satisfactory solutions where optimal solutions are impractical. The introduction to this Handbook provides an overview of the history of Heuristics along with main issues regarding the methodologies covered. This is followed by Chapters containing various examples of local searches, search strategies and Metaheuristics, leading to an analyses of Heuristics and search algorithms. The reference concludes with numerous illustrations of the highly applicable nature and implementation of Heuristics in our daily life. Each chapter of this work includes an abstract/introduction with a short description of the methodology. Key words are also necessary as part of top-matter to each chapter to enable maximum search engine optimization. Next, chapters will include discussion of the adaptation of this methodology to solve a difficult optimization problem, and experiments on a set of representative problems.

Algorithms. --- Mathematical optimization. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer science—Mathematics. --- Computer software. --- Optimization. --- Analysis. --- Mathematical and Computational Engineering. --- Math Applications in Computer Science. --- Mathematical Software.

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This book provides beginning graduate or senior-level undergraduate students in materials disciplines with a primer of the fundamental and quantitative ideas on kinetic processes in solid materials. Kinetics is concerned with the rate of change of the state of existence of a material system under thermodynamic driving forces. Kinetic processes in materials typically involve chemical reactions and solid state diffusion in parallel or in tandem. Thus, mathematics of diffusion in continuum is first dealt with in some depth, followed by the atomic theory of diffusion and a brief review of chemical reaction kinetics. Chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions are examined. Through this course of learning, a student will become able to predict quantitatively how fast a kinetic process takes place, to understand the inner workings of the process, and to design the optimal process of material state change. Provides students with the tools to predict quantitatively how fast a kinetic process takes place and solve other diffusion related problems; Learns fundamental and quantitative ideas on kinetic processes in solid materials; Examines chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions, among others; Contains end-of chapter exercise problems to help reinforce students' grasp of the concepts presented within each chapter.

Materials --- Mechanical properties. --- Mechanical behavior of materials --- Mechanical properties of materials --- Mechanics --- Mechanical behavior --- Materials science. --- Statistical physics. --- Mathematical physics. --- Chemometrics. --- Characterization and Evaluation of Materials. --- Statistical Physics and Dynamical Systems. --- Mathematical Applications in the Physical Sciences. --- Math. Applications in Chemistry. --- Chemistry, Analytic --- Analytical chemistry --- Chemistry --- Physical mathematics --- Physics --- Mathematical statistics --- Material science --- Physical sciences --- Mathematics --- Measurement --- Statistical methods

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This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Computer mathematics. --- Computer science—Mathematics. --- Optical data processing. --- Computational Mathematics and Numerical Analysis. --- Math Applications in Computer Science. --- Image Processing and Computer Vision. --- Mathematical Applications in Computer Science. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Computer mathematics --- Electronic data processing --- Mathematics --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment --- Computer science --- Mathematics.

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This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

Mathematical physics. --- Functional analysis. --- Numerical analysis. --- Partial differential equations. --- Computer science—Mathematics. --- Mathematical Applications in the Physical Sciences. --- Functional Analysis. --- Numerical Analysis. --- Partial Differential Equations. --- Math Applications in Computer Science. --- Partial differential equations --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Physics --- Mathematics --- Shape theory (Topology) --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces

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Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering. .

Artificial intelligence --- Mathematics. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Artificial intelligence. --- Computer science—Mathematics. --- Matrix theory. --- Algebra. --- Artificial Intelligence. --- Math Applications in Computer Science. --- Linear and Multilinear Algebras, Matrix Theory. --- Mathematics --- Mathematical analysis --- Computer science --- Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Computer mathematics