  Grammatical Evolution (GE) is one of the most popular Genetic Programming
(GP) variants, and it has been used with success in several problem domains.
Since the original proposal, many enhancements have been proposed to GE in
order to address some of its main issues and improve its performance.
  In this paper we propose Probabilistic Grammatical Evolution (PGE), which
introduces a new genotypic representation and new mapping mechanism for GE.
Specifically, we resort to a Probabilistic Context-Free Grammar (PCFG) where
its probabilities are adapted during the evolutionary process, taking into
account the productions chosen to construct the fittest individual. The
genotype is a list of real values, where each value represents the likelihood
of selecting a derivation rule. We evaluate the performance of PGE in two
regression problems and compare it with GE and Structured Grammatical Evolution
(SGE).
  The results show that PGE has a a better performance than GE, with
statistically significant differences, and achieved similar performance when
comparing with SGE.
