Probabilistic Model-Based Multistep Crossover Considering Dependency Between Nodes in Tree Optimization

Abstract

Deterministic Multistep crossover fusion (dMSXF) is one of promising crossover methods of a tree-based genetic programming. dMSXF performs a multistep local search from a parent in the direction approaching the other parent. In the local search, neighborhood solutions are generated by operators based on a replacement, an insertion and a deletion of nodes to combine both parents’ small traits step by step. In our previous work, we improved the search efficiency of dMSXF by introducing a probabilistic model constructed by the search information to the generation of neighborhood solutions. In the method, the probabilistic model considers nodes individually and a node dependency is ignored. The method has a room to further improve if a probabilistic model that can treat information about a dependency relationship between nodes. In this paper, we introduce a probabilistic model which considers the dependency between a parent node and a child node. The search performance of the proposed method is evaluated on symbolic regression problems.