Fitness functions based on test cases are very common in Genetic Programming (GP). This process can be assimilated to a learning task, with the inference of models from a limited number of samples. This paper is an investigation on two methods to improve generalization in GP-based learning: 1) the selection of the best-of-run individuals using a three data sets methodology, and 2) the application of parsimony pressure in order to reduce the complexity of the solutions. Results using GP in a binary classification setup show that while the accuracy on the test sets is preserved, with less variances compared to baseline results, the mean tree size obtained with the tested methods is significantly reduced.
Some GP learning applications @cite_11 @cite_2 @cite_18 have made use of a three data sets methodology, but without making a thorough analysis of its effects. Panait and Luke @cite_25 conducted some experiments on different approaches to increase the robustness of the solutions generated by GP, using a three data sets methodology to evaluate the efficiency of each approach. Rowland @cite_21 and Kushchu @cite_4 conducted studies on generalization in EC and GP. Both of their argumentations converge toward the testing of solutions in previously unseen situations for improving robustness.
@cite_18 @cite_4 @cite_21 @cite_2 @cite_25 @cite_11
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In genetic programming (GP), learning problems can be classified broadly into two types: those using data sets, as in supervised learning, and those using an environment as a source of feedback. An increasing amount of research has concentrated on the robustness or generalization ability of the programs evolved using GP. While some of the researchers report on the brittleness of the solutions evolved, others proposed methods of promoting robustness generalization. It is important that these methods are not ad hoc and are applicable to other experimental setups. In this paper, learning concepts from traditional machine learning and a brief review of research on generalization in GP are presented. The paper also identifies problems with brittleness of solutions produced by GP and suggests a method for promoting robustness generalization of the solutions in simulating learning behaviors using GP. EC-based supervised learning has been demonstrated to be an effective approach to forming predictive models in genomics, spectral interpretation, and other problems in modern biology. Longer-established methods such as PLS and ANN are also often successful. In supervised learning, overtraining is always a potential problem. The literature reports numerous methods of validating predictive models in order to avoid overtraining. Some of these approaches can be applied to EC-based methods of supervised learning, though the characteristics of EC learning are different from those obtained with PLS and ANN and selecting a suitably general model can be more difficult. This paper reviews the issues and various approaches, illustrating salient points with examples taken from applications in bioinformatics. This paper applies the evolution of GP teams to different classification and regression problems and compares different methods for combining the outputs of the team programs. These include hybrid approaches where (1) a neural network is used to optimize the weights of programs in a team for a common decision and (2) a realnumbered vector (the representation of evolution strategies) of weights is evolved with each term in parallel. The cooperative team approach results in an improved training and generalization performance compared to the standard GP method. The higher computational overhead of team evolution is counteracted by using a fast variant of linear GP. Many evolutionary computation search spaces require fitness assessment through the sampling of and generalization over a large set of possible cases as input. Such spaces seem particularly apropos to Genetic Programming, which notionally searches for computer algorithms and functions. Most existing research in this area uses ad-hoc approaches to the sampling task, guided more by intuition than understanding. In this initial investigation, we compare six approaches to sampling large training case sets in the context of genetic programming representations. These approaches include fixed and random samples, and adaptive methods such as coevolution or fitness sharing. Our results suggest that certain domain features may lead to the preference of one approach to generalization over others. In particular, coevolution methods are strongly domain-dependent. We conclude the paper with suggestions for further investigations to shed more light onto how one might adjust fitness assessment to make various methods more effective.