Model Regularization in Cevolutionary Architectures Evolving Straight Line Code

摘要

Frequently, when an evolutionary algorithm is applied to a population of symbolic expressions, the shapes of these symbolic expressions are very different at the first generations whereas they become more similar during the evolving process. In fact, when the evolutionary algorithm finishes most of the best symbolic expressions only differ in some of its coefficients. In this paper we present several coevolutionary strategies of a genetic program that evolves symbolic expressions represented by straight line programs and an evolution strategy that searches for good coefficients. The presented methods have been applied to solve instances of symbolic regression problem, corrupted by additive noise. A main contribution of the work is the introduction of a fitness function with a penalty term, besides the well known fitness function based on the empirical error over the sample set. The results show that in the presence of noise, the coevolutionary architecture with penalized fitness function outperforms the strategies where only the empirical error is considered in order to evaluate the symbolic expressions of the population.