Computer Science and Operations Research continue to have a synergistic relationship and this book - as a part of the Operations Research and Computer Science Interface Series - sits squarely in the center of the confluence of these two technical research communities. The research presented in the volume is evidence of the expanding frontiers of these two intersecting disciplines and provides researchers and practitioners with new work in the areas of logic programming, stochastic optimization, heuristic search and post-solution analysis for integer programs. The chapter topics span the spectrum of application level. Some of the chapters are highly applied and others represent work in which the application potential is only beginning. In addition, each chapter contains expository material and reviews of the literature designed to enhance the participation of the reader in this expanding interface.

Special tools are required for examining and solving optimization problems. The main tools in the study of local optimization are classical calculus and its modern generalizions which form nonsmooth analysis. The gradient and various kinds of generalized derivatives allow us to ac complish a local approximation of a given function in a neighbourhood of a given point. This kind of approximation is very useful in the study of local extrema. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for solving these problems. The simplest and most well-known area of global and simultaneously local optimization is convex programming. The fundamental tool in the study of convex optimization problems is the subgradient, which actu ally plays both a local and global role. First, a subgradient of a convex function f at a point x carries out a local approximation of f in a neigh bourhood of x. Second, the subgradient permits the construction of an affine function, which does not exceed f over the entire space and coincides with f at x. This affine function h is called a support func tion. Since f(y) ~ h(y) for ally, the second role is global. In contrast to a local approximation, the function h will be called a global affine support.

Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.

This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V. The introductory sec tion of each chapter should further guide the individual reader toward material that is of interest to him. A reader who has had a good course in advanced calculus should be able to understand the defini tions and statements of the theorems and should be able to follow a substantial portion of the mathematical development. The entire book can be read by someone familiar with the basic aspects of Lebesque integration and functional analysis. For the reader who wishes to find out more about applications we recommend references [2], [13], [33], [35], and [50], of the Bibliography at the end of the book.

This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: * It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; * It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; * It accounts for the risk averse nature of decision makers; and * It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making.

Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t, heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration

The electric power industry is currently undergoing an unprecedented reform. The deregulation of electricity supply industry has introduced new opportunity for competition to reduce the cost and cut the price. It is a tremendous challenge for utilities to maintain an economical and reliable supply of electricity in such an environment. Faced by an increasingly complicated existence, power utilities need efficient tools and aids to ensure that electrical energy of the desired quality can be provided at the lowest cost. The overall objective, both for short-term and long-term operations, is then to find the best compromise between the requirements of security and economy. That is, effective tools are urgently required to solve highly constrained optimisation problems. In recent years, several major modem optimisation techniques have been applied to power systems. A large number of papers and reports have been published. In this respect, it is timely to edit a book on this topic with an aim to report the state of the art development internationally in this area.

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.

Econometrics as an applied discipline attempts to use information in a most efficient manner, yet the information theory and entropy approach developed by Shannon and others has not played much of a role in applied econometrics. Econometrics of Information and Efficiency bridges the gap. Broadly viewed, information theory analyzes the uncertainty of a given set of data and its probabilistic characteristics. Whereas the economic theory of information emphasizes the value of information to agents in a market, the entropy theory stresses the various aspects of imprecision of data and their interactions with the subjective decision processes. The tools of information theory, such as the maximum entropy principle, mutual information and the minimum discrepancy are useful in several areas of statistical inference, e.g., Bayesian estimation, expected maximum likelihood principle, the fuzzy statistical regression. This volume analyzes the applications of these tools of information theory to the most commonly used models in econometrics. The outstanding features of Econometrics of Information and Efficiency are: A critical survey of the uses of information theory in economics and econometrics; An integration of applied information theory and economic efficiency analysis; The development of a new economic hypothesis relating information theory to economic growth models; New lines of research are emphasized.

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

In February 2002, the Industrial and Systems Engineering (ISE) De partment at the University of Florida hosted a National Science Founda tion Workshop on Collaboration and Negotiation in Supply Chain Man agement and E Commerce. This workshop focused on characterizing the challenges facing leading edge firms in supply chain management and electronic commerce, and identifying research opportunities for de veloping new technological and decision support capabilities sought by industry. The audience included practitioners in the areas of supply chain management and E Commerce, as well as academic researchers working in these areas. The workshop provided a unique setting that has facilitated ongoing dialog between academic researchers and industry practitioners. This book codifies many of the important themes and issues around which the workshop discussions centered. The editors of this book, all faculty members in the ISE Department at the University of Florida, also served as the workshop's coordinators. In addition to workshop participants, we also invited contributions from leading academics and practitioners who were not able to attend. As a result, the chapters herein represent a collection of research contributions, monographs, and case studies from a variety of disciplines and viewpoints. On the aca demic side alone, chapter authors include faculty members in supply chain and operations management, marketing, industrial engineering, economics, computer science, civil and environmental engineering, and building construction departments.

In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.

The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.

This book integrates the key concepts of mathematical programming (MP) and constraint programming (CP) into a unified framework that allows them to be generalized and combined. The unification of MP and CP creates optimization methods that have much greater modeling power, increased computational speed, and a sizeable reduction computational coding. This integration along with constraint programming being incorporated into a number of programming languages, brings the field a step closer to being able to simply state a problem and having the computer solve it.

This book presents new optimization algorithms designed to improve the efficiency of tool paths for five-axis NC machining of sculptured surfaces. The book covers both the structure of the SLAM problem in general and proposes a new extremely efficient approach. It can be used by undergraduate and graduate students and researchers in the field of NC machining and CAD/CAM as well as by corporate research groups for advanced optimization of cutting operations.

In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods).

The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems.

This volume contains the edited versions of papers presented at the IUTAM-Symposium Topological design optimization of structures, machines and materials - status and perspectives, held at Rungstedgaard, near Copenhagen, Denmark, in October 2005. The Symposium was attended by scientists in mechanics, optics, and applied mathematics from 19 countries.

It is now more than 15 years ago that the so-called homogenization method was proposed as a basis for computational means to optimize the topology and shape of continuum structures. From initially being capable mainly of treating minimum compliance design we now see the basic material distribution idea of the methodology applied to a wide range of structural and mechanical problems as well as to problems that couple structural response to other physical responses. Also, the method has provided insight for micro-mechanical studies, meaning that the method has given feedback to the area which provided impetus to the field of topological design optimization in its creation. Finally, topological design is now an integral part of most FEM software systems and it has become a standard industrial tool in some fields.

The IUTAM Symposium provided a forum for the exchange of ideas for future developments in the area of topological design optimization. This encompassed the application to fluid-solid interaction problems, acoustics problems, and to problems in biomechanics, as well as to other multiphysics problems. New basic modelling paradigms, covering new geometry modelling such as level-set methods and topological derivatives, as well as developments in computational approaches were also focus areas.

This book introduces the new experimentalism in evolutionary computation, providing tools to understand algorithms and programs and their interaction with optimization problems. It develops and applies statistical techniques to analyze and compare modern search heuristics such as evolutionary algorithms and particle swarm optimization. The book bridges the gap between theory and experiment by providing a self-contained experimental methodology and many examples.

This book addresses issues associated with the interface of computing, optimisation, econometrics and financial modeling, emphasizing computational optimisation methods and techniques. The first part addresses optimisation problems and decision modeling, plus applications of supply chain and worst-case modeling and advances in methodological aspects of optimisation techniques. The second part covers optimisation heuristics, filtering, signal extraction and time series models. The final part discusses optimisation in portfolio selection and real option modeling.

This book provides a complete overview of production systems and describes the best approaches to analyze their performance. Written by experts in the field, this work also presents numerous techniques that can be used to describe, model, and optimize the performance of various types of production lines. The book is intended for researchers, production managers, and graduate students in industrial, mechanical, and systems engineering.

The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book 's features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.

This book is a tutorial survey of the methodologies that are at the confluence of several fields: Computer Science, Mathematics and Operations Research. It provides a carefully structured and integrated treatment of the major technologies in optimization and search methodology. The chapter authors are drawn from across Computer Science and Operations Research and include some of the world 's leading authorities in their field. It can be used as a textbook or a reference book to learn and apply these methodologies to a wide range of today 's problems.

This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. The book will appeal to those working in operations research and management science, and mathematicians interested in optimization theory and its applications.