Artificial Intelligence Techniques for Automatic Reformulation of Complex Problems: the I-DARE Project

Complex, hierarchical, multi-scale industrial and natural systems generate increasingly large mathematical models. Practitioners are usually able to formulate such models in their ``natural'' form; however, solving them often requires finding an appropriate reformulation to reveal structures in the model which make it possible to apply efficient, specialized approaches. I-DARE is a structure-aware modeling-reformulation-solving environment based on Declarative Programming. It allows the construction of complex structured models, that can be automatically and algorithmically reformulated to search for the best formulation, intended as the one for which the most efficient solution approach is available. In order to accommodate (potentially) all possible specialized solution methods, it defines a general software framework for solvers, that are ``registered'' to specific problem structures. This article describes in details the application of Artificial Intelligence in the modeling and reformulation modules of I-DARE, showing how Declarative Programming can be used to design a structure-aware modeling environment that allows for a new automatic reformulation methodology.