A fixed point analysis of a gene pool GA with mutation
Alden H. Wright, Jonathan E. Rowe, Riccardo Poli, Christopher Rhodes Stephens · 2002
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 ℓ equations where ℓ 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. 1