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Books > Science & Mathematics > Mathematics > Optimization > General
In many decision problems, e.g. from the area of production and logistics manage ment, the evaluation of alternatives and the determination of an optimal or at least suboptimal solution is an important but dif?cult task. For most such problems no ef?cient algorithm is known and classical approaches of Operations Research like Mixed Integer Linear Programming or Dynamic Pro gramming are often of limited use due to excessive computation time. Therefore, dedicated heuristic solution approaches have been developed which aim at providing good solutions in reasonable time for a given problem. However, such methods have two major drawbacks: First, they are tailored to a speci?c prob lem and their adaption to other problems is dif?cult and in many cases even impos sible. Second, they are typically designed to "build" one single solution in the most effective way, whereas most decision problems have a vast number of feasible solu tions. Hence usually the chances are high that there exist better ones. To overcome these limitations, problem independent search strategies, in particular metaheuris tics, have been proposed. This book provides an elementary step by step introduction to metaheuristics focusing on the search concepts they are based on. The ?rst part demonstrates un derlying concepts of search strategies using a simple example optimization problem.
This book introduces readers to the "Jaya" algorithm, an advanced optimization technique that can be applied to many physical and engineering systems. It describes the algorithm, discusses its differences with other advanced optimization techniques, and examines the applications of versions of the algorithm in mechanical, thermal, manufacturing, electrical, computer, civil and structural engineering. In real complex optimization problems, the number of parameters to be optimized can be very large and their influence on the goal function can be very complicated and nonlinear in character. Such problems cannot be solved using classical methods and advanced optimization methods need to be applied. The Jaya algorithm is an algorithm-specific parameter-less algorithm that builds on other advanced optimization techniques. The application of Jaya in several engineering disciplines is critically assessed and its success compared with other complex optimization techniques such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Artificial Bee Colony (ABC), and other recently developed algorithms.
In recent decades, it has become possible to turn the design process into computer algorithms. By applying different computer oriented methods the topology and shape of structures can be optimized and thus designs systematically improved. These possibilities have stimulated an interest in the mathematical foundations of structural optimization. The challenge of this book is to bridge a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in a sufficiently simple form to make them available for practical use and to allow their critical appraisal for improving and adapting these results to specific models. Special attention is to pay to the description of optimal structures of composites; to deal with this problem, novel mathematical methods of nonconvex calculus of variation are developed. The exposition is accompanied by examples.
At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization."
Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. In online optimization the main issue is incomplete data, and the scientific challenge: How well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In real-time optimization there is an additional requirement, decisions have to be computed very fast in relation to the time frame of the instance we consider. Online and real-time optimization problems occur in all branches of optimization. These areas have developed their own techniques but they are addressing the same issues: quality, stability, and robustness of the solutions. To fertilize this emerging topic of optimization theory and to foster cooperation between the different branches of optimization, the Deutsche Forschungsgemeinschaft (DFG) has supported a Priority Programme "Online Optimization of Large Systems".
This book highlights recent developments in multidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various applications of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), environmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine). The book provides recent research results in optimization-based visualization. Evolutionary algorithms and a two-level optimization method, based on combinatorial optimization and quadratic programming, are analyzed in detail. The performance of these algorithms and the development of parallel versions is discussed. The encorporation of new visualization techniques to improve the capabilies of artificial neural networks (self-organizing maps, feed-forward networks) is also discussed. The book includes over 100 detailed images presenting examples of the different visualization techniques that are presented. This book is intended for scientists and researchers in any field of study where complex and multidimensional data must be represented visually.
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.
V-INVEX FUNCTIONS AND VECTOR OPTIMIZATION summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past several decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990?s. V-invex functions are areas in which there has been much interest because it allows researchers and practitioners to address and provide better solutions to problems that are nonlinear, multi-objective, fractional, and continuous in nature. Hence, V-invex functions have permitted work on a whole new class of vector optimization applications. There has been considerable work on vector optimization by some highly distinguished researchers including Kuhn, Tucker, Geoffrion, Mangasarian, Von Neuman, Schaiible, Ziemba, etc. The authors have integrated this related research into their book and demonstrate the wide context from which the area has grown and continues to grow. The result is a well-synthesized, accessible, and usable treatment for students, researchers, and practitioners in the areas of OR, optimization, applied mathematics, engineering, and their work relating to a wide range of problems which include financial institutions, logistics, transportation, traffic management, etc.
With the ever increasing growth of services and the corresponding demand for Quality of Service requirements that are placed on IP-based networks, the essential aspects of network planning will be critical in the coming years. A wide number of problems must be faced in order for the next generation of IP networks to meet their expected performance. With Performance Evaluation and Planning Methods for the Next Generation Internet, the editors have prepared a volume that outlines and illustrates these developing trends. A number of the problems examined and analyzed in the book are: -The design of IP networks and guaranteed performance -Performances of virtual private networks -Network design and reliability -The issues of pricing, routing and the management of QoS -Design problems arising from wireless networks -Controlling network congestion -New applications spawned from Internet use -Several new models are introduced that will lead to better Internet performance These are a few of the problem areas addressed in the book and only a selective example of some of the coming key areas in networks requiring performance evaluation and network planning.
This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. Of particular interest are the applications of nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management and lot sizing, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.
These proceedings consist of 30 selected research papers based on results presented at the 10th Balkan Conference & 1st International Symposium on Operational Research (BALCOR 2011) held in Thessaloniki, Greece, September 22-24, 2011. BALCOR is an established biennial conference attended by a large number of faculty, researchers and students from the Balkan countries but also from other European and Mediterranean countries as well. Over the past decade, the BALCOR conference has facilitated the exchange of scientific and technical information on the subject of Operations Research and related fields such as Mathematical Programming, Game Theory, Multiple Criteria Decision Analysis, Information Systems, Data Mining and more, in order to promote international scientific cooperation. The carefully selected and refereed papers present important recent developments and modern applications and will serve as excellent reference for students, researchers and practitioners in these disciplines. "
This book aims to present, in a unified approach, a series of mathematical results con cerning triangular norm-based measures and a class of cooperative games with Juzzy coalitions. Our approach intends to emphasize that triangular norm-based measures are powerful tools in exploring the coalitional behaviour in 'such games. They not and simplify some technical aspects of the already classical axiomatic the only unify ory of Aumann-Shapley values, but also provide new perspectives and insights into these results. Moreover, this machinery allows us to obtain, in the game theoretical context, new and heuristically meaningful information, which has a significant impact on balancedness and equilibria analysis in a cooperative environment. From a formal point of view, triangular norm-based measures are valuations on subsets of a unit cube [0, 1]X which preserve dual binary operations induced by trian gular norms on the unit interval [0, 1]. Triangular norms (and their dual conorms) are algebraic operations on [0,1] which were suggested by MENGER [1942] and which proved to be useful in the theory of probabilistic metric spaces (see also [WALD 1943]). The idea of a triangular norm-based measure was implicitly used under various names: vector integrals [DVORETZKY, WALD & WOLFOWITZ 1951], prob abilities oj Juzzy events [ZADEH 1968], and measures on ideal sets [AUMANN & SHAPLEY 1974, p. 152].
This book collects the latest theoretical and technological concepts in the design and control of various linear machines and drive systems. Discussing advances in the new linear machine topologies, integrated modeling, multi-objective optimization techniques, and high-performance control strategies, it focuses on emerging applications of linear machines in transportation and energy systems. The book presents both theoretical and practical/experimental results, providing a consistent compilation of fundamental theories, a compendium of current research and development activities as well as new directions to overcome critical limitations.
In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received new impetus. The growing interest in multiobjective problems, both from the theoretical point of view and as it concerns applications to real problems, asks for a general scheme which embraces several existing developments and stimulates new ones. In this book the authors provide the newest results and applications of this quickly growing field. This book will be of interest to graduate students in mathematics, economics, and engineering, as well as researchers in pure and applied mathematics, economics, engineering, geography, and town planning. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book.
Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to classical facility location and to problems in computational geometry are pointed out. Audience: The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.
Evolutionary computation techniques have attracted increasing att- tions in recent years for solving complex optimization problems. They are more robust than traditional methods based on formal logics or mathematical programming for many real world OR/MS problems. E- lutionary computation techniques can deal with complex optimization problems better than traditional optimization techniques. However, most papers on the application of evolutionary computation techniques to Operations Research /Management Science (OR/MS) problems have scattered around in different journals and conference proceedings. They also tend to focus on a very special and narrow topic. It is the right time that an archival book series publishes a special volume which - cludes critical reviews of the state-of-art of those evolutionary com- tation techniques which have been found particularly useful for OR/MS problems, and a collection of papers which represent the latest devel- ment in tackling various OR/MS problems by evolutionary computation techniques. This special volume of the book series on Evolutionary - timization aims at filling in this gap in the current literature. The special volume consists of invited papers written by leading - searchers in the field. All papers were peer reviewed by at least two recognised reviewers. The book covers the foundation as well as the practical side of evolutionary optimization.
In operations research and computer science it is common practice to evaluate the performance of optimization algorithms on the basis of computational results, and the experimental approach should follow accepted principles that guarantee the reliability and reproducibility of results. However, computational experiments differ from those in other sciences, and the last decade has seen considerable methodological research devoted to understanding the particular features of such experiments and assessing the related statistical methods. This book consists of methodological contributions on different scenarios of experimental analysis. The first part overviews the main issues in the experimental analysis of algorithms, and discusses the experimental cycle of algorithm development; the second part treats the characterization by means of statistical distributions of algorithm performance in terms of solution quality, runtime and other measures; and the third part collects advanced methods from experimental design for configuring and tuning algorithms on a specific class of instances with the goal of using the least amount of experimentation. The contributor list includes leading scientists in algorithm design, statistical design, optimization and heuristics, and most chapters provide theoretical background and are enriched with case studies. This book is written for researchers and practitioners in operations research and computer science who wish to improve the experimental assessment of optimization algorithms and, consequently, their design.
This book presents select peer-reviewed papers presented at the International Conference on Numerical Optimization in Engineering and Sciences (NOIEAS) 2019. The book covers a wide variety of numerical optimization techniques across all major engineering disciplines like mechanical, manufacturing, civil, electrical, chemical, computer, and electronics engineering. The major focus is on innovative ideas, current methods and latest results involving advanced optimization techniques. The contents provide a good balance between numerical models and analytical results obtained for different engineering problems and challenges. This book will be useful for students, researchers, and professionals interested in engineering optimization techniques.
The aim of stochastic programming is to find optimal decisions
in problems which involve uncertain data. This field is currently
developing rapidly with contributions from many disciplines
including operations research, mathematics, and probability. At the
same time, it is now being applied in a wide variety of subjects
ranging from agriculture to financial planning and from industrial
engineering to computer networks. This textbook provides a first
course in stochastic programming suitable for students with a basic
knowledge of linear programming, elementary analysis, and
probability. The authors aim to present a broad overview of the
main themes and methods of the subject. Its prime goal is to help
students develop an intuition on how to model uncertainty into
mathematical problems, what uncertainty changes bring to the
decision process, and what techniques help to manage uncertainty in
solving the problems. The book is highly illustrated with chapter summaries and many
examples and exercises. Students, researchers and practitioners in
operations research and the optimization area will find it
particularly of interest. Review of First Edition: "The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998) "
This book considers problems of optimization arising in the design of electromagnetic radiators and receivers. The authors develop a systematic general theory that can be applied to a wide class of structures. The theory is illustrated with familiar, simple examples and indications of how the results can be applied to more complicated structures. The final chapter introduces techniques from multicriteria optimization in antenna design. The material is intended for a dual audience of mathematicians and mathematically-sophisticated engineers. References to both the mathematics and engineering literature help guide the reader through the necessary mathematical background.
This handbook gathers state-of-the-art research on optimization problems in power distribution systems, covering classical problems as well as the challenges introduced by distributed power generation and smart grid resources. It also presents recent models, solution techniques and computational tools to solve planning problems for power distribution systems and explains how to apply them in distributed and variable energy generation resources. As such, the book therefore is a valuable tool to leverage the expansion and operation planning of electricity distribution networks.
The aim of this volume is to show how Fuzzy Sets and Systems can help to provide robust and adaptive heuristic optimization algorithms in a variety of situations. The book presents the state of the art and gives a broad overview on the real practical applications that Fuzzy Sets, based on heuristic algorithms, have. |
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