Modeling languages
Provides a general introduction to modeling languages.
Modeling languages were created to simplify the solving of mathematical programming problems. The fundamental insight underlying traditional modeling languages is the recognition that many mathematical programming problems can be expressed in a computer language whose syntax is close to the standard presentation of these problems in textbooks and scientific papers. These languages typically provide a number of data types such as arrays and sets, as well as computer-language equivalents to traditional algebraic notations.
For instance, in AMPL, an expression such as
can be written as
sum {i in 1..n} a[i] * x[i]
In addition, some of these languages provide a clean separation between the model and the instance data.
Finally, they are sometimes extended by a command language that makes it possible to solve sequences of related models and to make modifications to the models and solve the modified models. Traditional modeling languages have many benefits that make them appealing for stating and solving mathematical programming problems. Perhaps their most significant contribution is to provide a language that directly supports the natural statement of these problems. This language abstracts away the implementation details of the underlying solver and users are then relieved of mundane, low-level, considerations and can focus on the modeling of their applications. Also important is the clear separation between the model and the instance data, which ensures that the same model can be applied to many instances without inducing additional work. Note that, in these languages, the solver is a black box that can only be accessed through a set of well-defined parameters.
Traditional modeling languages are particularly strong in mathematical programming applications, e.g., linear and integer programming. This is not surprising since this is the area from where they emerged. In addition, these problems are naturally expressed using traditional algebraic notations and effective solvers are available to solve the resulting models.