Massachusetts Institute of Technology Press
This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh transform. The mixing scheme (comprised of crossover and mutation) is essentially “triangularized” when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.
Random heuristic search, Geiringer’s theorem, Walsh transform, Fourier transform
Vose, Michael D. and Wright, Alden H., "The Simple Genetic Algorithm and the Walsh Transform: Part II, The Inverse" (1998). Computer Science Faculty Publications. 6.