A Search for Counterexamples to Two Conjectures on the Simple Genetic Algorithm.
Alden H. Wright, G. Bidwell · 1996
We empirically searched for cycling and chaotic behavior in the infinite population Simple Genetic Algorithm. We found examples of period 2 cycling (which we expected) and long period cycling (which we didn't expect). These examples had mutation and crossover distributions which do not correspond to the way that mutation and crossover are normally used in practice. We also searched unsuccessfully for stable polymorphic fixed points in the zero mutation case. 1 Introduction Vose (1990) introduced a rigorous dynamical system model for the binary-representation genetic algorithm with proportional selection, with the simplifying assumption of an infinite population size. This model has been further extended in Vose & Liepins (1991), Vose & Wright (1994), and Vose (1996). If the string length is `, the model is defined in terms of a differentiable mapping G from R n into itself, where n = 2 ` . The mapping G describes how a population changes from one generation to the next. Conjectur...