Improving Grammatical Evolution in Santa Fe Trail using Novelty Search

Abstract

Grammatical Evolution is an evolutionary algorithm that can evolve complete programs using a Backus Naur form grammar as a plug-in component to describe the output language. An important issue of Grammatical Evolution, and evolutionary computation in general, is the difficulty in dealing with deceptive problems and avoid premature convergence to local optima. Novelty search is a recent technique, which does not use the standard fitness function of evolutionary algorithms but follows the gradient of behavioral diversity. It has been successfully used for solving deceptive problems mainly in neuro-evolutionary robotics where it was originated. This work presents the first application of Novelty Search in Grammatical Evolution (as the search component of the later) and benchmarks this novel approach in a wellknown deceptive problem, the Santa Fe Trail. For the experiments, two grammars are used: one that defines a search space semantically equivalent to the original Santa Fe Trail problem as defined by Koza and a second one which were widely used in the Grammatical Evolution literature, but which defines a biased search space. The application of novelty search requires to characterize behavior, using behavior descriptors and compare descriptions using behavior similarity metrics. The conducted experiments compare the performance of standard Grammatical Evolution and its Novelty Search variation using four intuitive behavior descriptors. The experimental results demonstrate that Grammatical Evolution with Novelty Search outperforms the traditional fitness based Grammatical Evolution algorithm in the Santa Fe Trail problem demonstrating a higher success rates and better solutions in terms of the required steps.