Algebraic modeling languages for optimization

2011 ◽  
Keyword(s):  
Modeling Languages ◽  
Algebraic Modeling Languages

scholarly journals GEKKO Optimization Suite

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 106 ◽  
Author(s):  
Logan Beal ◽  
Daniel Hill ◽  
R. Martin ◽  
John Hedengren
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Object Oriented ◽  
Differential Algebraic Equations ◽  
Mixed Integer ◽  
Modeling Languages ◽  
Algebraic Equations ◽  
Simulation And Optimization ◽  
Algebraic Modeling Languages ◽  
Real Time Optimization

This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and integrated problem construction/solution/visualization. This paper introduces the GEKKO Optimization Suite, presents GEKKO’s approach and unique place among AMLs and optimal control packages, and cites several examples of problems that are enabled by the GEKKO library.

scholarly journals Web-Based Tool for Algebraic Modeling and Mathematical Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2751
Author(s):  
Vaidas Jusevičius ◽  
Remigijus Paulavičius
Keyword(s):  
State Of The Art ◽  
Mathematical Optimization ◽  
Modeling Languages ◽  
Problem Type ◽  
Web Based ◽  
Complex Syntax ◽  
Algebraic Modeling Languages ◽  
Cross Compatibility ◽  
Language Knowledge ◽  
Compatibility Complex

In this article, we present a new open-source tool for algebraic modeling and mathematical optimization. We begin by distilling the main gaps within the existing algebraic modeling languages and tools (varying performance, limited cross-compatibility, complex syntax, and different solver, feature, and problem type support). Later, we propose a state-of-the-art web-based tool (WebAML and Optimization System) for algebraic modeling languages and mathematical optimization. The tool does not require specific algebraic language knowledge, allows solving problems using different solvers, and utilizes the best characteristics of existing algebraic modeling languages. We also provide clear extension points and ideas on how we could further improve such a tool.

High-Performance Prototyping of Decomposition Methods in GAMS

2020 ◽  
Author(s):  
Timo Lohmann ◽  
Michael R. Bussieck ◽  
Lutz Westermann ◽  
Steffen Rebennack
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Application Programming Interface ◽  
Decomposition Methods ◽  
Planning Problem ◽  
Modeling Languages ◽  
Expansion Planning ◽  
Algebraic Modeling Languages ◽  
Algebraic Modeling Language

Prototyping algorithms in algebraic modeling languages has a long tradition. Despite the convenient prototyping platform that modeling languages offer, they are typically seen as rather inefficient with regard to repeatedly solving mathematical programming problems, a concept on which many algorithms are based. The most prominent examples of such algorithms are decomposition methods, such as the Benders decomposition, column generation, and the Dantzig–Wolfe decomposition. In this work, we discuss the underlying reasons for repeated solve deficiency with regard to speed in detail and provide an insider’s look into the algebraic modeling language GAMS. Further, we present recently added features in GAMS that mitigate some of the efficiency drawbacks inherent to the way modeling languages represent model data and ultimately solve a model. In particular, we demonstrate the grid-enabled gather-update-solve-scatter facility and the GAMS object-oriented application programming interface on a large-scale case study that involves a Benders decomposition–type algorithm for a power-expansion planning problem.

A Structure-Exploiting Tool in Algebraic Modeling Languages

2000 ◽  
Vol 46 (8) ◽  
pp. 1145-1158 ◽  
Author(s):  
Emmanuel Fragnière ◽  
Jacek Gondzio ◽  
Robert Sarkissian ◽  
Jean-Philippe Vial
Keyword(s):  
Modeling Languages ◽  
Algebraic Modeling Languages
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