A parallel algorithm for understanding design spaces and performing convex hull computations

Abstract

A novel algorithm to compute the convex hull of any given hyperdimensional data set is presented. This algorithm has lower memory requirements than state of the art software, and runtimes which are typically much faster than conventional programs and algorithms which do the same. A discussion is presented which examines the large importance that convex hull computations serve in creating general surrogate models from data sets, and their importance to machine learning algorithms. In addition to the deep reaching applications in many fields, this algorithm can be used to help solve design problems, specifically those in preliminary design when surrogate models are used to perform rapid design trades. The algorithm is presented, in addition to algorithms which compute volumes and facilitate understanding of hyperdimensional spaces which cannot be easily visualized. This paper concludes with the presentation of a representative design problem containing similar dimensionality and numbers of points as a standard engineering preliminary design problem. The minimum number of points needed for the interpolation of a general surrogate model during design and analysis is then discussed, including the proposal of a new metric.