Self-adaptation and global convergence: a counter-example

The self-adaptation of the mutation distribution is a distinguishing feature of evolutionary algorithms that optimize over continuous variables. It is widely recognized that self-adaptation accelerates the search for optima and enhances the ability to locate optima accurately, but it is generally unclear whether these optima are global ones or not. Here, it is proven that the probability of convergence to the global optimum is less than one in general, even if the objective function is continuous.