This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas and techniques into both optimization theory, and into some numerical algorithms for large-scale optimization problems. The presentation is based on the recent understanding that rigorous mathematical analysis of algorithms, parallel computing techniques, and "hands-on" experimental work on real-world problems must go hand in hand in order to achieve the greatest advantage from novel parallel computing architectures. The three parts of the book thus bring together relevant theory, careful study of algorithms, and modelling of significant real world problems. The problem domains include: image reconstruction, radiation therapy treatment planning, transportation problems, portfolilo management, and matrix estimation. This text can be used both as a reference for researchers and as a text for advanced graduate courses.
Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math- ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air- line crew scheduling, corporate planning, computer-aided design and man- ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca- tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover- ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo- rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi- tion, linear programming relaxations are often the basis for many approxi- mation algorithms for solving NP-hard problems (e.g. dual heuristics).
This book shows how the Bayesian Approach (BA) improves wellÂ known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some imporÂ tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lanÂ guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization probÂ lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of disÂ crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribuÂ tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. DifÂ ferent examples illustrate different points of the general subject. HowÂ ever, one can consider each example separately, too.
Ethnographic Research: A Guide to General Conduct is the first in the ASA Research Methods series. This volume is about ethnographic research, the production of data, and the practical aspects of research practice. It is general and introductory in scope. Designed as a handbook, it is suitable for rapid reference. It provides basic outlines on general practical matters of concern to all those engaged in ethnographic research, introduces the series as a whole, and serves as a guide to existing literature on issues not specifically covered by the more specialized volumes which follow.
This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]
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