Genetic programming: profiling reasonable parameter value windows with varying problem difficulty

Abstract

Genetic Programming (GP) algorithms benefit from careful consideration of parameter values, especially for complex problems. We submit that determining the optimal parameter value is not as important as finding a window of reasonable parameter values. We test seven problems to determine if windows of reasonable parameter values for mutation rates and population size exist. The results show narrowing, expanding and static windows of effective mutation rates dependent upon the problem type. The results for varying population sizes show that less complex problems use more resources per solution with increasing population size. Conversely as the problem difficulty increases we see either no significant change in solution effort as population size increases, indicating constant efficiency or in some cases we discover decreasing solution effort with larger population sizes. This suggests that in general as the instances of a problem increase in difficulty increasing the population size will either have no effect on efficiency or, for some problems, will lead to relatively small increases in efficiency.