The value of representing a complex petroleum mixture in terms of a small (similar to 10-100) number of molecules motivated the development of a novel algorithm for building a representative set of molecular structures. This hybrid Monte Carlo-quadrature method represents a molecule as a collection of molecular attribute building blocks (e.g. number of aromatic rings, number of naphthenic rings, number and length of sidechains, etc.). Each attribute is represented by a probability distribution function which can be sampled via Monte Carlo simulation to yield a large ensemble of representative molecules, the properties of the ensemble being constrained to match experimentally measured analytical data. In order to represent the information contained within these probability distribution functions in a reduced form, a quadrature method has been developed for the selection of an optimal small set (similar to 10-20) of molecules. The mole fractions of this small set are further optimized to match experimental data. Both the small and large ensembles are capable of matching a large number of key analytical properties for a complex petroleum feedstock.