Bistability of the Needle Function in the Presence of Truncation Selection

Alden Wright¹ and Greg Cripe²

¹University of Montana, Missoula MT USA

²Spokane Falls Community College, Spokane WA USA

Abstract. 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.

LNCS 3103, p. 330 ff.

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