Knowledge based aids for model construction

Abstract

Recent years have seen the emergence of improved computer-based support for mathematical modeling. However, these systems do not support the transition from the requirements specifications to the model construction phase of the modeling life cycle and require skills that most users of decision support systems do not possess. This research proposes a knowledge-based architecture for constructing models in a dynamic and flexible manner and implements this architecture to support the construction of linear programming models of production, distribution and inventory planning problems. This has involved the design of a declarative problem specification language based on first-order logic, formulation and representation of transformations based on domain-independent modeling principles and the introduction of an object-oriented scheme to represent knowledge used to construct and generate executable specifications of algebraic equations. The proposed architecture applies concepts hitherto unused in dynamic model construction. The specification of the problem in the first-order language yields a logic model which, in addition to serving as input to the model construction process, is used to support structural revision of the problem description and to infer qualitative problem details. Supplementing model construction through features to support model evolution and the deduction of problem details adds an important dimension in light of the increased need for integrated decision support. The representation of knowledge used to construct algebraic equations via an object-oriented scheme provides the capacity to apply domain-independent model building rules instead of instantiating stored equational forms. The significance of this research is its addition of an "intelligent" component to the model management system in a decision support system which facilitates the use of mathematical models by users unfamiliar with mathematical modeling.