Genetic Programming: Analysis of Optimal Mutation Rates in a Problem with Varying Difficulty

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In this paper we test whether a correlation exists between the optimal mutation rate and problem difficulty. We find that the range of optimal mutation rates is inversely proportional to problem difficulty. We use numerical sweeps of the mutation rate parameter to probe a problem with tunable difficulty. The tests include 3 different types of individual selection methods. We show that when problem difficulty increases, the range of mutation rates improving performance over crossover alone narrowed; e.g. as the problem difficulty increases the genetic program becomes more sensitive to the optimal mutation rate. In general, we found that the optimal mutation rate across a range of mutation types and level of difficulty is close to 1/C, where C is the maximum size of the individual.