Gams General Algebraic Modeling System

[Dashonn Moulton]

Thegeneral algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations. The system is available for use on various computer platforms. Models are portable from one platform to another.

GAMS was the first algebraic modeling language (AML)[2] and is formally similar to commonly used fourth-generation programming languages. GAMS contains an integrated development environment (IDE) and is connected to a group of third-party optimization solvers. Among these solvers are BARON, COIN-OR solvers, CONOPT, COPT Cardinal Optimizer, CPLEX, DICOPT, IPOPT, MOSEK, SNOPT, and XPRESS.

GAMS allows the users to implement a sort of hybrid algorithm combining different solvers. Models are described in concise, human-readable algebraic statements. GAMS is among the most popular input formats for the NEOS Server.[citation needed] Although initially designed for applications related to economics and management science, it has a community of users from various backgrounds of engineering and science.

The driving force behind the development of GAMS were the users of mathematical programming who believed in optimization as a powerful and elegant framework for solving real life problems in science and engineering. At the same time, these users were frustrated by high costs, skill requirements, and an overall low reliability of applying optimization tools. Most of the system's initiatives and support for new development arose in response to problems in the fields of economics, finance, and chemical engineering, since these disciplines view and understand the world as a mathematical program.

The idea of an algebraic approach to represent, manipulate, and solve large-scale mathematical models fused old and new paradigms into a consistent and computationally tractable system. Using generator matrices for linear programs revealed the importance of naming rows and columns in a consistent manner. The connection to the emerging relational data model became evident. Experience using traditional programming languages to manage those name spaces naturally lead one to think in terms of sets and tuples, and this led to the relational data model.

Combining multi-dimensional algebraic notation with the relational data model was the obvious answer. Compiler writing techniques were by now widespread, and languages like GAMS could be implemented relatively quickly. However, translating this rigorous mathematical representation into the algorithm-specific format required the computation of partial derivatives on very large systems. In the 1970s, TRW developed a system called PROSE that took the ideas of chemical engineers to compute point derivatives that were exact derivatives at a given point, and to embed them in a consistent, Fortran-style calculus modeling language. The resulting system allowed the user to use automatically generated exact first and second order derivatives. This was a pioneering system and an important demonstration of a concept. However, PROSE had a number of shortcomings: it could not handle large systems, problem representation was tied to an array-type data structure that required address calculations, and the system did not provide access to state-of-the art solution methods. From linear programming, GAMS learned that exploitation of sparsity was key to solving large problems. Thus, the final piece of the puzzle was the use of sparse data structures.

A transportation problem from George Dantzig is used to provide a sample GAMS model.[6] This model is part of the model library which contains many more complete GAMS models. This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories.

The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming and optimization. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large scale modeling applications, and allows you to build large maintainable models that can be adapted quickly to new situations.

The GAMS user guide is essential to understanding the application and making the most of it. The guide and this page should help you to get started with your simulations. Please refer to the Documentation section for a link to the guide.

The GAMS IDE is not available on Linux, only command line execution is possible. If the IDE is needed for model development, run the gamside on Windows (as described above) to generate the model, then submit to the Linux cluster (as described above) to run the model.

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Stable isotope-assisted metabolic flux analysis (MFA) is a powerful method to estimate carbon flow and partitioning in metabolic networks. At its core, MFA is a parameter estimation problem wherein the fluxes and metabolite pool sizes are model parameters that are estimated, via optimization, to account for measurements of steady-state or isotopically-nonstationary isotope labeling patterns. As MFA problems advance in scale, they require efficient computational methods for fast and robust convergence. The structure of the MFA problem enables it to be cast as an equality-constrained nonlinear program (NLP), where the equality constraints are constructed from the MFA model equations, and the objective function is defined as the sum of squared residuals (SSR) between the model predictions and a set of labeling measurements. This NLP can be solved by using an algebraic modeling language (AML) that offers state-of-the-art optimization solvers for robust parameter estimation and superior scalability to large networks. When implemented in this manner, the optimization is performed with no distinction between state variables and model parameters. During each iteration of such an optimization, the system state is updated instead of being calculated explicitly from scratch, and this occurs concurrently with improvement in the model parameter estimates. This optimization approach starkly contrasts with traditional "shooting" methods where the state variables and model parameters are kept distinct and the system state is computed afresh during each iteration of a stepwise optimization. Our NLP formulation uses the MFA modeling framework of Wiechert et al. [1], which is amenable to incorporation of the model equations into an NLP. The NLP constraints consist of balances on either elementary metabolite units (EMUs) or cumomers. In this formulation, both the steady-state and isotopically-nonstationary MFA (inst-MFA) problems may be solved as an NLP. For the inst-MFA case, the ordinary differential equation (ODE) system describing the labeling dynamics is transcribed into a system of algebraic constraints for the NLP using collocation. This large-scale NLP may be solved efficiently using an NLP solver implemented on an AML. In our implementation, we used the reduced gradient solver CONOPT, implemented in the General Algebraic Modeling System (GAMS). The NLP framework is particularly advantageous for inst-MFA, scaling well to large networks with many free parameters, and having more robust convergence properties compared to the shooting methods that compute the system state and sensitivities at each iteration. Additionally, this NLP approach supports the use of tandem-MS data for both steady-state and inst-MFA when the cumomer framework is used. We assembled a software, eiFlux, written in Python and GAMS that uses the NLP approach and supports both steady-state and inst-MFA. We demonstrate the effectiveness of the NLP formulation on several examples, including a genome-scale inst-MFA model, to highlight the scalability and robustness of this approach. In addition to typical inst-MFA applications, we expect that this framework and our associated software, eiFlux, will be particularly useful for applying inst-MFA to complex MFA models, such as those developed for eukaryotes (e.g. algae) and co-cultures with multiple cell types.

Alexander Meeraus is an engineer and businessman who made significant contributions to the development of optimization software. In particular, he created the GAMS (General Algebraic Modeling System) software system for modeling complicated systems. He was born in Vienna, Austria, and studied mechanical engineering at the Technology University of Vienna, where he received his engineering degree in 1968. Meeraus went on to work in software programming for computer-aided design at General Electric and time-sharing systems prior to joining the World Bank in Washington, D.C., in 1972.

As an economist and chief analyst at the World Bank, Meeraus developed large-scale optimization methods for application areas in economic planning. To help with this work, he created the GAMS system for algebraic modeling. In 1976, he introduced GAMS to researchers and academics at the International Symposium on Mathematical Programming in Budapest, Hungary. Meeraus spent over a decade at the World Bank, continuing his research work on investment planning and managing the research and development group that developed GAMS. There, he co-wrote several books, including his 1988 guide, which emphasized OR applications to the planning of investment programs, agriculture, oil refineries, and macroeconomics. In 1987, he started GAMS Development Corporation in Washington, D.C., where he led a team of engineers responsible for developing optimization software for operations research methodologies.

Meeraus spent the majority of the 1980s and 1990s developing the optimization system and software for GAMS. He worked on a variety of projects, including the long-term development and application of optimization software, and consulted with clients in the agricultural, chemical, energy, finance, and government sectors. Meeraus expanded GAMS in Europe with GAMS Software GmbH in 1996, where, as co-founder, he oversaw the development of the GAMS branch in Germany. He was also instrumental in establishing extensive libraries of optimization problem for testing optimization software.

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