Gams Algebraic Modelling

[Ara Kistner]

TheGAMS modeling language allows modelers to quickly translate real world optimization problems into computer code. The gams language compiler then translates this code into a format the solvers can understand and solve. This architecture provides great flexibility, by allowing changing the solvers used without changing the model formulation.

The above can easiliy be formulated using the GAMS language. The use of concise algebraic descriptions makes the model highly compact, with a logical structure. Internal documentation, such as explanation of parameters and units of measurement, makes the model easy to read.

When data values are to be calculated, you first declare the parameter (i.e. give it a symbol and, optionally, index it), then give its algebraic formulation. GAMS will automatically make the calculations.

Decision variables are expressed algebraically, with their indices specified. From this general form, GAMS generates each instance of the variable in the domain.Variables are specified as to type: FREE, POSITIVE, NEGATIVE, BINARY, or INTEGER. The default is FREE.The objective variable (z, here) is simply declared without an index.

Objective function and constraint equations are first declared by giving them names. Then their general algebraic formulae are described. GAMS now has enough information (from data entered above and from the algebraic relationships specified in the equations) to automatically generate each individual constraint statement - as you can see in the output report below. An extensive set of tools enables you to model any expression that can be stated algebraically: arithmetic, indexing, functions and exception-handling log (e.g. if-then-else and such-that constructs).

The model is given a unique name (here, TRANSPORT), and the modeler specifies which equations should be included in this particular formulation. In this case we specified ALL which indicates that all equations are part of the model. This would be equivalent to MODEL TRANSPORT /COST, SUPPLY, DEMAND/ . This equation selection enables you to formulate different models within a single GAMS input file, based on the same or different given data.

This paper aims to illustrate the use of the augmented epsilon-constraint method implemented in general algebraic modelling system (GAMS), aimed at optimizing the geometry of a thermoacoustic regenerator. Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be produced. However, the most inhibiting characteristic of thermoacoustic cooling is their current lack of efficiencies.

Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight.

A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters. This study highlights the fact that the geometrical parameters are interdependent, which support the use of a multi-objective approach for optimization in thermoacoustic.

The research output from this paper can be a valuable resource to support designers in building efficient thermoacoustic device. The research illustrates the use of a lexicographic optimization to provide more meaningful results describing the geometry of thermoacoustic regenerator. It applies the epsilon-constraint method (AUGMENCON) to solve a five-criteria mixed integer non-linear problem implemented in GAMS (GAM software).

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