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.

We describe a framework for modeling optimization problems for solution on a grid computer. The framework is easy to adapt to multiple grid engines and can seamlessly integrate evolving mechanisms from particular computing platforms. It facilitates the widely used master-worker model of computing and is shown to be flexible and powerful enough for a large variety of optimization applications. In particular, we summarize a number of new features of the GAMS modeling system that provide a lightweight, portable, and powerful framework for optimization on a grid. We provide downloadable examples of its use for embarrasingly parallel financial applications, decomposition of complementarity problems, and for solving very difficult mixed-integer programs to optimality. Computational results are provided for a number of different grid engines, including multicore machines, a pool of machines controlled by the Condor resource manager, and the grid engine from Sun Microsystems.

The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation server that can transform the models from their basic GAMS format into other formats, including AMPL, BARON, LGO, LINGO, and MINOPT. The translation server can also be used to transform industrial models that contain confidential information. Such transformations allow many of these models to be distributed to the research community as highly relevant algorithmic test models.