Simulated annealing for symbolic regression

Symbolic regression aims to hypothesize a functional relationship involving explanatory variables and one or more dependent variables, based on examples of the desired input-output behavior. Genetic programming is a meta-heuristic commonly used in the literature to achieve this goal. Even though Symbolic Regression is sometimes associated with the potential of generating interpretable expressions, there is no guarantee that the returned function will not contain complicated constructs or even bloat. The Interaction-Transformation (IT) representation was recently proposed to alleviate this issue by constraining the search space to expressions following a simple and comprehensive pattern. In this paper, we resort to Simulated Annealing to search for a symbolic expression using the IT representation. Simulated Annealing exhibits an intrinsic ability to escape from poor local minima, which is demonstrated here to yield competitive results, particularly in terms of generalization, when compared with state-of-the-art Symbolic Regression techniques, that depend on population-based meta-heuristics, and committees of learning machines.