Ebook: Algebraic Modeling Systems: Modeling and Solving Real World Optimization Problems

This book Algebraic Modeling Systems – Modeling and Solving Real World Optimization Problems – deals with the aspects of modeling and solving real-world optimization problems in a unique combination. It treats systematically the major algebraic modeling languages (AMLs) and modeling systems (AMLs) used to solve mathematical optimization problems. AMLs helped significantly to increase the usage of mathematical optimization in industry. Therefore it is logical consequence that the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life had a second meeting devoted to AMLs, which, after 7 years, followed the original 71st Meeting of the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Optimization during April 23–25, 2003 in the German Physics Society Conference Building in Bad Honnef, Germany. While the first meeting resulted in the book Modeling Languages in Mathematical Optimization, this book is an offspring of the 86th Meeting of the GOR working group which was again held in Bad Honnef under the title Modeling Languages in Mathematical Optimization.

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This book presents a computational approach to the analysis of nonlinear and uncertain systems. The main focus is systems with piecewise linear dynamics. The class of piecewise linear systems examined has nonlinear, possibly discontinuous dynamics, and allows switching rules that incorporate memory and logic. These systems may exhibit astonishingly complex behaviors. Some aspects of the successful theory of linear systems and quadratic criteria are extended here to piecewise linear systems and piecewise quadratic criteria. The book also describes numerical procedures for assessing stability, computing induced gains, and solving optimal control problems for piecewise linear systems. These developments enable researchers to analyze a large and practically important class of control systems that are not easily dealt with when using other techniques Part 1. Introduction and Foundations -- Algebraic Modeling Languages: Introduction and Overview -- Towards a Self-Reflective, Context-Aware Semantic Representation of Mathematical Specifications -- Part 2. Selected Algebraic Modeling Systems -- GUSS: Solving Collections of Data Related Models Within GAMS -- Generalized Disjunctive Programming: Solution Strategies -- Xpress-Mosel -- Multi-Solver, Multi-Problem,Multi-Model, Multi-Node Modeling and Problem Solving -- Interval-Based Language for Modeling Scheduling Problems: An Extension to Constraint Programming -- Using Zimpl for Modeling Production Planning Problems -- Part 3. Aspects of Modeling and Solving Real World Problems -- Why Our Company Uses Programming Languages for Mathematical Modeling and Optimization -- Data Preparation for Optimization with R -- VisPlain®: Insight by Visualization -- Economic Simulation Models in Agricultural Economics: The Current and Possible Future Role of Algebraic Modeling Languages -- A Practioner's Wish List Towards Algebraic Modeling Systems