Herein we present the R package rFSA, which implements an algorithm for improved variable selection. The algorithm searches a data space for models of a user-specified form that are statistically optimal under a measure of model quality. Many iterations afford a set of feasible solutions (or candidate models) that the researcher can evaluate for relevance to his or her questions of interest. The algorithm can be used to formulate new or to improve upon existing models in bioinformatics, health care, and myriad other fields in which the volume of available data has outstripped researchers' practical and computational ability to explore larger subsets or higher-order interaction terms. The package accommodates linear and generalized linear models, as well as a variety of criterion functions such as Allen's PRESS and AIC. New modeling strategies and criterion functions can be adapted easily to work with rFSA.