The curse of high-dimensional search spaces: observing premature convergence in unimodal functions

It might come to a surprise, if some properly designed evolutionary algorithms might not be able to sufficiently optimize simple, continuous, unimodal objective functions. Keeping in mind the evolutionary algorithms´ high performance especially in the field of global function optimization, getting stuck (also known as premature convergence) at suboptimal function values is attributed mostly to the presence of distracting local optima. This paper describes some examples in which such a behavior occurs. It also gives some explanations of the underlying reasons. These explanations indicate, as a conclusion, that premature convergence might happen very well at continuous, unimodal functions (and consequently in real-world applications).