The progress rate of the (1 +λ)-ES (Evolution Strategy) is analyzed on the parabolic ridge test function. A differentprogress behavior is observed for the (1, λ)-ES than for the sphere model test function. The characteristics of the progress rate picture for the plus strategy differs little from the one obtained for the sphere model, but this strategy has drastically worse progress rate values than those obtained for the comma strategy. The dynamics of the distance to the progress axis is also investigated. A theoretical formula is derived to estimate the change in this distance over generations. This formula is used to derive the expected value of the problem-specific distance to the ridge axis. The correctness of the formulae is supported by simulation results.

Three main streams of evolutionary algorithms (EAs), probabilistic optimization algorithms based on the model of natural evolution, are compared in this article: evolution strategies (ESs), evolutionary programming (EP), and genetic algorithms (GAs). The comparison is performed with respect to certain characteristic components of EAs: the representation scheme of object variables, mutation, recombination, and the selection operator. Furthermore, each algorithm is formulated in a high-level notation as an instance of the general, unifying basic algorithm, and the fundamental theoretical results on the algorithms are presented. Finally, after presenting experimental results for three test functions representing a unimodal and a multimodal case as well as a step function with discontinuities, similarities and differences of the algorithms are elaborated, and some hints to open research questions are sketched.