Optimal mutation probability for genetic algorithms

We derive the value of the mutation probability which maximizes the probability that the genetic algorithm finds the optimum value of the objective function under simple assumptions. This value is compared with the optimum mutation probability derived in other studies. An empirical study shows that this value, when used with a larger scaling factor in linear scaling, improves the performance of the genetic algorithm. This feature is then added to a model developed by Hinton and Nowlan which allows certain bits to be guessed in an effort to increase the probability of finding the optimum solution.