Difference between revisions of "Category:AMPL"

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This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL does not support differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.
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This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL is a modeling language for mathematical programming, comparable to GAMS and ZIMBL. Its modeling syntax is very close to the mathematical one, and a wide range of linear and nonlinear (mixed-integer) solvers are interfaced. It comes with a commercial licence (free student version limited by 300 variables).
  
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MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bib id="Binder2001" />: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.  
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AMPL does not directly support control problems or differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.
  
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Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bib id="Bock1984" />,<bib id="Biegler1984" />, to (re)formulate the control problem by outer convexification <bib id="Sager2009" />, to use global optimization methods by under- and overestimators, e.g., <bib id="Esposito2000" />,<bib id="Papamichail2004" />,<bib id="Chachuat2006" />, to optimize the time-points for a given switching structure, e.g., <bib id="Kaya2003" />,<bib id="Gerdts2006" />,<bib id="Sager2009" />, to consider a static optimization problem instead of the transient behavior, e.g., <bib id="Grossmann2005" />, to approximate nonlinearities by piecewise-linear functions, e.g., <bib id="Martin2006" />, or by approximating the combinatorial decisions by continuous formulations, as in <bib id="Burgschweiger2009" /> for drinking water networks.
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They can be either obtained by hand, or by means of an automatized export. One example are the compilers available to process [[:Category:optimica | optimica]] models that automatically generate AMPL output, e.g., by applying a Radau collocation.
  
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We do not want to discuss these methods here, but rather refer to <bib id="Sager2009" />,<bib id="Sager2009b" /> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.
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Recently, the [[:Category:AMPL/TACO | TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. [[:Category:Muscod | MUSCOD-II]] is the first solver to support AMPL models using the TACO extension.
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Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''
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There are compilers available to process [[:Category:optimica | optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.
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Recently, the [[:Category:AMPL/TACO | TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II (Heidelberg) will be the first solver to support AMPL models using the TACO extensions.
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== References ==
 
== References ==
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<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
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[[Category: Implementation]]
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[[Category:Problem characterization]]
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Latest revision as of 09:56, 28 January 2016

This category lists all problems for which AMPL code is provided. AMPL is a modeling language for mathematical programming, comparable to GAMS and ZIMBL. Its modeling syntax is very close to the mathematical one, and a wide range of linear and nonlinear (mixed-integer) solvers are interfaced. It comes with a commercial licence (free student version limited by 300 variables).

AMPL does not directly support control problems or differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.

They can be either obtained by hand, or by means of an automatized export. One example are the compilers available to process optimica models that automatically generate AMPL output, e.g., by applying a Radau collocation.

Recently, the TACO Toolkit for AMPL Control Optimization is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II is the first solver to support AMPL models using the TACO extension.

References

[Biegler1984]Biegler, L.T. (1984): Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Computers \& Chemical Engineering, 8, 243--248Link to Google Scholar
[Binder2001]T. Binder; L. Blank; H.G. Bock; R. Bulirsch; W. Dahmen; M. Diehl; T. Kronseder; W. Marquardt; J.P. Schl\"oder; O.v. Stryk (2001): Introduction to Model Based Optimization of Chemical Processes on Moving Horizons. Online Optimization of Large Scale Systems: State of the ArtLink to Google Scholar
[Bock1984]H.G. Bock; K.J. Plitt (1984): A Multiple Shooting algorithm for direct solution of optimal control problems. Pergamon Press, Proceedings of the 9th IFAC World CongressLink to Google Scholar
[Burgschweiger2009]J. Burgschweiger; B. Gn\"adig; M.C. Steinbach (2009): Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks. The Open Applied Mathematics Journal, 3, 1--16Link to Google Scholar
[Chachuat2006]B. Chachuat; A.B. Singer; P.I. Barton (2006): Global methods for dynamic optimization and mixed-integer dynamic optimization. Industrial and Engineering Chemistry Research, 45, 8573--8392Link to Google Scholar
[Esposito2000]W.R. Esposito; C.A. Floudas (2000): Deterministic Global Optimization in Nonlinear Optimal Control Problems. Journal of Global Optimization, 17, 97--126Link to Google Scholar
[Gerdts2006]M. Gerdts (2006): A variable time transformation method for mixed-integer optimal control problems. Optimal Control Applications and Methods, 27, 169--182Link to Google Scholar
[Grossmann2005]I.E. Grossmann; P.A. Aguirre; M. Barttfeld (2005): Optimal synthesis of complex distillation columns using rigorous models. Computers \& Chemical Engineering, 29, 1203--1215Link to Google Scholar
[Kaya2003]C.Y. Kaya; J.L. Noakes (2003): A Computational Method for Time-Optimal Control. Journal of Optimization Theory and Applications, 117, 69--92Link to Google Scholar
[Martin2006]A. Martin; M. M\"oller; S. Moritz (2006): Mixed integer models for the stationary case of gas network optimization. Mathematical Programming, 105, 563--582Link to Google Scholar
[Papamichail2004]Papamichail, I.; Adjiman, C.S. (2004): Global optimization of dynamic systems. Computers \& Chemical Engineering, 28, 403--415Link to Google Scholar
[Sager2009]Sager, S.; Reinelt, G.; Bock, H.G. (2009): Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems. Mathematical Programming, 118, 109--149Link to Google Scholar
[Sager2009b]S. Sager (2009): Reformulations and Algorithms for the Optimization of Switching Decisions in Nonlinear Optimal Control. Journal of Process Control, 19, 1238--1247Link to Google Scholar
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