A Memetic Algorithm for Symbolic Regression

Abstract

This research aims to address the practical difficulties of computational heuristics for symbolic regression, which models data with algebraic expressions. In particular we are motivated by cases in which the target unknown function may be best represented as the ratio of functions. We propose an alternative general approach based on a different representation of mathematical models with an analytic continued fraction representation, from which rational function models can be extracted. A memetic algorithm, which is a paradigm of meta-heuristic optimization based on the evolution of solutions by a set of computational agents, is implemented to generate solutions in this representation. A population of computational agents with problem domain knowledge improves feasible solutions using local search heuristics and produces models that fit the data better. In addition, the agents compete in searching for function models with fewer number of variables. Agent interactions are constrained by a population structure which has been previously used in several successful MAs for other combinatorial optimization problems. We utilize a tree-based population structure to improve the algorithm’s consistency and performance. Data from real-world applications are used to measure the potential of our approach and benchmark its performance against other approaches in symbolic regression.