Model Development and Optimization for Space Engineering: Concepts, Tools, Applications, and Perspectives
The theory and methodology of finding the best possible solution to a broad range of optimization problems has been of interest since the beginnings of modern operations research. The key theoretical results regarding important model types and algorithmic
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Model Development and Optimization for Space Engineering: Concepts, Tools, Applications, and Perspectives Giorgio Fasano and Ja´nos D. Pinte´r
Abstract The theory and methodology of finding the best possible solution to a broad range of optimization problems has been of interest since the beginnings of modern operations research. The key theoretical results regarding important model types and algorithmic frameworks have been followed by optimization software implementations that are used to handle a large and still growing variety of applications. Our discussion is focused on the practice of nonlinear—specifically including also global and mixed integer optimization, in the context of space engineering applications. We review some of the prominent solution approaches, model development tools, and software implementations of optimization (solver) engines and then relate our discussion to selected applications in space engineering. The review portion of this work cites contributions by our coauthors to the present volume (Fasano and Pinte´r, Modeling and Optimization in Space Engineering, Springer Science + Business Media, New York, 2012) while also drawing on an extensive list of other sources. Keywords Optimization models and methods • Continuous nonlinear (global and local) optimization • Mixed-integer linear and nonlinear models • Modeling languages and systems • Solution strategies and optimization software • LGO solver suite for nonlinear optimization • Current and prospective optimization applications in space engineering
MSC Classification (2000) 68 T20, 90 C11, 90 C30, 90 C59, 90 C90, 90-02, 90-08 G. Fasano Thales Alenia Space Italia S.p.A., Str. Antica di Collegno 253, Turin 10146, Italy e-mail: [email protected] J.D. Pinte´r (*) Pinte´r Consulting Services Inc., Halifax, NS, Canada e-mail: [email protected] G. Fasano and J.D. Pinte´r (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and Its Applications 73, DOI 10.1007/978-1-4614-4469-5_1, # Springer Science+Business Media New York 2013
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G. Fasano and J.D. Pinte´r
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Introduction Modeling and Optimization: An Operations Research Framework
Operations research (OR) provides a scientifically established objective framework and methodology to assist analysts and decision makers in finding feasible or optimized decisions across a vast range of decision-making issues. Decision problems can be frequently modeled by constrained optimization models: we want to find the best possible decision that satisfies a given set of constraints. In the present discussion, we shall consider the continuous optimization model defined by the following ingredients: • • • •
x: decision vector, an element of the real Euclidean n-space Rn l, u: explicit, finite n-vector bounds of x that define an interval (“box”) in Rn f(x): continuous objective function, f:Rn!R g(x): m-vector of continuous constraint functions, g:Rn!Rm
Applying these notations, a very general class of optimization models can be concisely formu
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