Efficient interleaved sampling of training data in genetic programming

The ability to generalize beyond the training set is important for Genetic Programming (GP). Interleaved Sampling is a recently proposed approach to improve generalization in GP. In this technique, GP alternates between using the entire data set and only a single data point. Initial results showed that the technique not only produces solutions that generalize well, but that it so happens at a reduced computational expense as half the number of generations only evaluate a single data point. This paper further investigates the merit of interleaving the use of training set with two alternatives approaches. These are: the use of random search instead of a single data point, and simply minimising the tree size. Both of these alternatives are computationally even cheaper than the original setup as they simply do not invoke the fitness function half the time. We test the utility of these new methods on four, well cited, and high dimensional problems from the symbolic regression domain. The results show that the new approaches continue to produce general solutions despite taking only half the fitness evaluations. Size minimisation also prevents bloat while producing competitive results on both training and test data sets. The tree sizes with size minisation are substantially smaller than the rest of the setups, which further brings down the training costs.