Bistability in a Gene Pool GA with Mutation

It is possible for a GA to have two stable fixed points on a single-peak fitness landscape. These can correspond to meta-stable finite populations. This phenomenon is called bistability, and is only known to happen in the presence of recombination, selection, and mutation. This paper models the bistability phenomenon using an infinite population model of a GA based on gene pool recombination. Fixed points and their stability are explicitly calculated. This is possible since the infinite population model of the gene pool GA is much more tractable than the infinite population model for the standard simple GA. For the needle-in-the-haystack fitness function, the fixed point equations reduce to a single variable polynomial equation, and stability of fixed points can be determined from the derivative of the single variable equation. We also show empirically that bistability can occur on a single-peak landscape where there is selective pressure toward the optimum at every point of the search space. ∗ This paper was written while Alden Wright was visiting the School of Computer Science, University of Birmingham, UK.