Searching the Best (Formulation, Solver, Configuration) for Structured Problems

Complex, hierarchical, multi-scale industrial and natural systems generate increasingly large mathematical models. I-DARE is a structure-aware modeling-reformulating-solving environment based on Declarative Programming, that allows the construction of complex structured models. The main aim of the system is to produce 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. This requires exploration of a high-dimensional space comprising all (structured) reformulations of a given instance, all available solvers for (each part of) the formulation, and all possible configurations of the relevant algorithmic parameters for each solver. A fundamental pre-requisite for this exploration is the ability to predict the efficiency of a given (set of) algorithm(s), considering their configuration(s), for a given instance; this is, however, a vastly nontrivial task. This article describes how the I-DARE system organizes the information on the instance at hand in order to make the search in the (formulation, solver, configuration) space possible with several different exploration techniques. In particular, we propose a way to combine general machine learning mechanisms and ad-hoc methods, where available, in order to effectively compute the "objective function" of the search, i.e., the prediction of the effectiveness of a point in the space. We also discuss how this mechanism can take upon itself part of the exploration, the one in the sub-space of configurations, thus simplifying the task to the rest of the system by reducing the dimensionality of the search space it has to traverse