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Gas Network Optimization by MINLP
This thesis is about mathematical optimization for an efficient operation of gas transmission networks. The challenging question is how to expand and operate the network in order to facilitate the transportation of specified gas quantities at minimum cost. This problem is a major challenge for gas network operators. It is extremely hard to solve due to the combinatorial complexity of the active network elements such as compressors, the nonlinear physical characteristic of pipelines, and the immense sizes of the problem instances. Mathematical models and optimization techniques can result in huge gains for the network operators in terms of cost reductions and automated computations. We tackle this challenge by developing novel mathematical theory and associated innovative optimization algorithms for large scale instances. This allows us to produce solutions for a real-world instance, i.e., the largest gas network in Germany.
Evaluating Gas Network Capacities
This book addresses a seemingly simple question: Can a certain amount of gas be transported through a pipeline network? The question is difficult, however, when asked in relation to a meshed nationwide gas transportation network and when taking into account the technical details and discrete decisions, as well as regulations, contracts, and varying demands, involved. This book provides an introduction to the field of gas transportation planning and discusses in detail the advantages and disadvantages of several mathematical models that address gas transport within the context of its technical and regulatory framework, shows how to solve the models using sophisticated mathematical optimization algorithms, and includes examples of large-scale applications of mathematical optimization to this real-world industrial problem. Readers will also find a glossary of gas transport terms, tables listing the physical and technical quantities and constants used throughout the book, and a reference list of regulation and gas business literature.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
This book constitutes the refereed proceedings of the 8th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2011, held in Berlin, Germany, in May 2011. The 13 revised full papers and 7 revised short papers presented together with 3 invited lectures were carefully reviewed and selected from 35 submissions. The papers are focused on both theoretical and practical, application-oriented issues and present current research with a special focus on the integration and hybridization of the approaches of constraint programming, artificial intelligence, and operations research technologies for solving large scale and complex real life combinatorial optimization problems.
Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty
The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, Jonas Schweiger addresses applications, where nonconvexity in the model and uncertainty in the data pose principal difficulties. In the first part, he contributes strong relaxations for non-convex problems such as the non-convex quadratic programming and the Pooling Problem. In the second part, he contributes a robust model for gas transport network extension and a custom decomposition approach. All results are backed by extensive computational studies.
Evaluating Gas Network Capacities
"This book deals with a simple sounding question whether a certain amount of gas can be transported by a given pipeline network. While well studied for a single pipeline, this question gets extremely difficult if we consider a meshed nation wide gas transportation network, taking into account all the technical details and discrete decisions, as well as regulations, contracts, and varying demand. This book describes several mathematical models to answer these questions, discusses their merits and disadvantages, explains the necessary technical and regulatory background, and shows how to solve this question using sophisticated mathematical optimization algorithms."--
Network Optimization
Network optimization is important in the modeling of problems and processes from such fields as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. Recent advances in data structures, computer technology, and algorithm development have made it possible to solve classes of network optimization problems that until recently were intractable. The refereed papers in this volume reflect the interdisciplinary efforts of a large group of scientists from academia and industry to model and solve complicated large-scale network optimization problems.
Proofs from THE BOOK
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Hydraulics of Pipeline Systems
The first of its kind, this modern, comprehensive text covers both analysis and design of piping systems. The authors begin with a review of basic hydraulic principles, with emphasis on their use in pumped pipelines, manifolds, and the analysis and design of large pipe networks. After the reader obtains an understanding of how these principles are implemented in computer solutions for steady state problems, the focus then turns to unsteady hydraulics. These are covered at three levels:
Mixed Integer Nonlinear Programming
Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
Nonlinear Optimization
This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.
