Hierarchical knowledge in self-improving Grammar-Based Genetic Programming

Structure of a grammar can influence how well a Grammar-Based Genetic Programming system solves a given problem but it is not obvious to design the structure of a grammar, especially when the problem is large. In this paper, our proposed Bayesian Grammar-Based Genetic Programming with Hierarchical Learning (BGBGP-HL) examines the grammar and builds new rules on the existing grammar structure during evolution. Once our system successfully finds the good solution(s), the adapted grammar will provide a grammar-based probabilistic model to the generation process of optimal solution(s). Moreover, our system can automatically discover new hierarchical knowledge (i.e. how the rules are structurally combined) which composes of multiple production rules in the original grammar. In the case study using deceptive royal tree problem, our evaluation shows that BGBGP-HL achieves the best performance among the competitors while it is capable of composing hierarchical knowledge. Compared to other algorithms, search performance of BGBGP-HL is shown to be more robust against deceptiveness and complexity of the problem.