Interval Linear Programming And Extensions
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Interval Linear Programming and Extensions
This book delves into the intricate world of interval programming, offering a comprehensive exploration of mathematical programming problems characterized by interval data. Interval data, often arising from uncertainties like measurement errors or estimations, are also pivotal in analyzing stability, sensitivity, and managing numerical issues. At the heart of this book is the principle of interval analysis, ensuring that all possible realizations of interval data are accounted for. Readers will uncover a wealth of knowledge as the author meticulously examines how variations in input coefficients affect optimal solutions and values in linear programming. The chapters are organized into three parts: foundational concepts of interval analysis, linear programming with interval data, and advanced extensions into multiobjective and nonlinear problems. This book invites readers to explore critical questions about stability, duality, and practical applications across diverse fields. With contributions from eminent scholars, it provides a unique blend of theoretical insights and practical case studies. Designed for both researchers and students with a basic understanding of mathematics, this book serves as an essential resource for anyone interested in mathematical programming. Whether used as a monograph or a lecture textbook, it offers clear explanations and comprehensive proofs to make complex concepts accessible. Scholars in operations research, applied mathematics, and related disciplines will find this volume invaluable for advancing their understanding of interval programming.
Constraint Programming and Decision Making
In many application areas, it is necessary to make effective decisions under constraints. Several area-specific techniques are known for such decision problems; however, because these techniques are area-specific, it is not easy to apply each technique to other applications areas. Cross-fertilization between different application areas is one of the main objectives of the annual International Workshops on Constraint Programming and Decision Making. Those workshops, held in the US (El Paso, Texas), in Europe (Lyon, France) and in Asia (Novosibirsk, Russia), from 2008 to 2012, have attracted researchers and practitioners from all over the world. This volume presents extended versions of selected papers from those workshops. These papers deal with all stages of decision making under constraints: (1) formulating the problem of multi-criteria decision making in precise terms, (2) determining when the corresponding decision problem is algorithmically solvable; (3) finding the corresponding algorithms and making these algorithms as efficient as possible and (4) taking into account interval, probabilistic and fuzzy uncertainty inherent in the corresponding decision making problems. The resulting application areas include environmental studies (selecting the best location for a meteorological tower), biology (selecting the most probable evolution history of a species), and engineering (designing the best control for a magnetic levitation train).