A Study of the Role of Single Node Mutation in Genetic Programming

Abstract. In this paper we examine the effects of single node mutations on trees evolved via genetic programming. The results show that neutral mutations are less likely for nodes nearer the root and that as evolution proceeds neutral mutations of nodes near the root are progressively less likely. Studies of crossover in tree based GP have shown that when smaller and/or deeper branches are selected for crossover the resulting change in fitness is smaller and the probability of fitness neutral crossover is larger [3,1,4,2]. In this paper we continue this research for mutations by studying the relationship between the depth of single node mutations and the probability of fitness neutral mutations. Our GP is steady-state, population size 100, 0.7 crossover rate, 90/10 crossover, 4 member tournament selection. Results are the average of 100 trials. The initial population is generated with full tree with depth of 4. The test prob-lem is symbolic regression; the target function is f(x) = x3 +2x2 − 5x+3 in the range [0, 2π] or [−π, π]. Fitness is the square root of the sum of the squared er