Depth-control strategies for crossover in tree-based genetic programming

The standard subtree crossover operator in the tree-based genetic programming (GP) has been considered as problematic. In order to improve the standard subtree crossover, controlling depth of crossover points becomes a research topic. However, the existence of many different and inconsistent crossover depth-control schemes and the possibility of many other depth-control schemes make the identification of good depth-control schemes a challenging problem. This paper aims to investigate general heuristics for making good depth-control schemes for crossover in tree-based GP. It analyses the patterns of depth of crossover points in good predecessor programs of five GP systems that use the standard subtree crossover and four approximations of the optimal crossover operator on three problems in different domains. The analysis results show that an effective depth-control scheme is problem-dependent and evolutionary stage-dependent, and that good crossover events have a strong preference for roots and (less strongly) bottoms of parent program trees. The results also show that some ranges of depths between the roots and the bottoms are also preferred, suggesting that unequal-depth-selection-probability strategies are better than equal-depth-selection-probability strategies.

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