Genetic Algorithms and the O(n Ln N) Complexity on Selected Test Functions

Genetic algorithms (GAs) are useful in the eld of continuous parameter optimization. Many results indicate that, due to their robust-ness and their ability of escaping from local optima, GAs are especially suitable for optimizing multimodal functions that contain millions of misleading local optima. The existing theory is based on spherical symmetric functions and suggest an O(n ln n) complexity for particular GAs. However, the widely-used test functions are not spherical symmetric but decomposable and recent results indicate that GAs fail under a a simple rotation of the coordinate system. This paper shows that, when applied to a decomposable function with n independent parameters, any GA that features an elitist selection scheme, a broad mutation operator, and uses a mutation probability m p = 1=n, converges with an O(n ln n) complexity; it is not necessary to use a highly optimized genetic algorithms.