Parallel model representations

Most mathematical programming models and knowledge-based systems in optimization from exist in various representations; however, the user is frequently not aware of this. For example, a model which is developed with a knowledge-based system such as the PM system of Krishnan (1988) will have several representations in Prolog and then will be translated into another representation in Structured Modeling before it is solved. Also, a model which is developed in the GAMS language will be translated into an MPS input form internally before the problem is passed to a solver such as MINOS. The results from MINOS are then passed back to GAMS and the user sees the results in the style of the GAMS representation of the model. This could be called a vertical set of model representations since the user can modify only one representation and the models are passed down directly to the solver.

This paper argues that in considering knowledge-based systems with optimization we should begin to employ a set of parallel model representations, any one of which the user can see and modify. These can be called horizontal model representations. For example, a given model might be represented in graphical, knowledge base, modeling language, and mathematical forms. The user would be able to modify any of these versions and have the other representations altered automatically to reflect the changes.