Psychology has to deal with many interacting variables. The analyses usually used to uncover such relationships have many constraints that limit their utility. We briefly discuss these and describe recent work that uses genetic programming to evolve equations to combine variables in nonlinear ways in a number of different domains. We focus on four studies of interactions from lexical access experiments and psychometric problems. In all cases, genetic programming described nonlinear combinations of items in a manner that was subsequently independently verified. We discuss the general implications of genetic programming and related computational methods for multivariate problems in psychology.