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This text provides an excellent balance of theory and application that enables you to deploy powerful algorithms, frameworks, and methodologies to solve complex optimization problems in a diverse range of industries. Each chapter is written by leading experts in the fields of parallel and distributed optimization. Collectively, the contributions serve as a complete reference to the field of combinatorial optimization, including details and findings of recent and ongoing investigations.
Solving combinatorial optimization problems can often lead to runtime growing exponentially as a function of the input size. But important real-world problems, industrial applications, and academic research challenges, may demand exact optimal solutions. In such situations, parallel processing can reduce the runtime from days or months, typical when one workstation is used, to a few minutes or even seconds. Partners of the CEC-sponsored SCOOP Project (Solving Combinatorial Optimization Problems in Parallel) contributed, on invitation, to this book; much attention was paid to competent coverage of the topic and the style of writing. Readers will include students, scientists, engineers, and professionals interested in the design and implementation of parallel algorithms for solving combinatorial optimization problems.
In the past two decades, breakthroughs in computer technology have made a tremendous impact on optimization. In particular, availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete and global optimization problems. The chapters in this volume cover a broad spectrum of recent research in parallel processing of discrete and related problems. The topics discussed include distributed branch-and-bound algorithms, parallel genetic algorithms for large scale discrete problems, simulated annealing, parallel branch-and-bound search under limited-memory constraints, parallelization of greedy randomized adaptive search procedures, parallel optical models of computing, randomized parallel algorithms, general techniques for the design of parallel discrete algorithms, parallel algorithms for the solution of quadratic assignment and satisfiability problems. The book will be a valuable source of information to faculty, students and researchers in combinatorial optimization and related areas.
Real world problems addressed in various fields (operations management, logistics, production scheduling, distribution problems, military) are becoming more complex due to the globalization of firm activities. The need to provide solutions in real time is essential, and advances in computer technology have helped. In addition, developments in methods and software have played a significant role in addressing large complex problems. The goal of this edited book is to teach the reader how to develop, design, implement parallel branch and bound algorithms and technology to solve combinatorial optimization problems, while increasing productivity and quality. The field is new but has sufficiantly matured for a group of experts in the field to present state of the art design and implementation techniques of parallel branch and bound algorithms.
This book contains papers presented at the Workshop on Parallel Processing of Discrete Optimization Problems held at DIMACS in April 1994. The contents cover a wide spectrum of the most recent algorithms and applications in parallel processing of discrete optimization and related problems. Topics include parallel branch and bound algorithms, scalability, load balancing, parallelism and irregular data structures and scheduling task graphs on parallel machines. Applications include parallel algorithms for solving satisfiability problems, location problems, linear programming, quadratic and linear assignment problems. This book would be suitable as a textbook in advanced courses on parallel algorithms and combinatorial optimization.
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).
Efficient parallel solutions have been found to many problems. Some of them can be obtained automatically from sequential programs, using compilers. However, there is a large class of problems - irregular problems - that lack efficient solutions. IRREGULAR 94 - a workshop and summer school organized in Geneva - addressed the problems associated with the derivation of efficient solutions to irregular problems. This book, which is based on the workshop, draws on the contributions of outstanding scientists to present the state of the art in irregular problems, covering aspects ranging from scientific computing, discrete optimization, and automatic extraction of parallelism. Audience: This first book on parallel algorithms for irregular problems is of interest to advanced graduate students and researchers in parallel computer science.
This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.
This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.