K-cut Crossover Using Graph Theory in Genetic Network Programming

Abstract. In this study, we focus on Genetic Network Programming (GNP) which is the graph-based evolutionary algorithm. Similar to Genetic Algorithm (GA) and Genetic Programming (GP), GNP applies genetic operators to an individual, which is represented by a directed graph, in order to solve a given problem. GNP is usually applied to automatic generation of programs which control a mobile robot. Since the crossover exchanges a sub-graph of parent individuals, a selection of a sub-graph is an important factor. Some selection methods are proposed in previous work. However, the selection method based on the graph theory is not proposed even though the individual is represented by a graph. In this study, we propose a k-cut crossover based on the graph theory. The proposed k-cut crossover selects a sub-graph by using a minimum k-cut algorithm which finds a minimum graph partition on weighted graph. We applied the GNP with the k-cut crossover to the automatic generation of programs in the tileworld, and the experimental result shows the advantage of the k-cut crossover.