A Fixed Point Analysis Of A Gene Pool GA With Mutation

This paper analyzes a recombination/mutation/selection genetic algorithm that uses gene pool recombination. For linear fitness functions, the infinite population model can be described by ` equations where ` is the string length. For linear fitness functions, we show that there is a single fixed point and that this fixed point is stable. For the ONEMAX fitness function, the model reduces to a linear recurrence in a single variable which can be explicitly solved. The time-to-convergence for ONEMAX is given.