Result: Convergence behavior of the (1^+,Lambda) evolution strategy on the ridge functions

The convergence behavior of $\onel$--ES is investigated at parabolic ridge, sharp ridge, and at the general case of the ridge functions. % (for larger values of the parameter $\alpha$). The progress rate, the distance to the ridge axis, the success rate, and the success probability are used in the analysis. The strong dependency of the $(1 \! + \! \lambda)$--ES to the initial conditions is shown using parabolic ridge test function when low distances to the ridge axis are chosen as the start value. The progress rate curve and the success probability curve of the sharp ridge is explained quite exactly using a simple local model. Two members of the corridor model family are compared to %the some members of the ridge function family, % (with large $\alpha$), and they do not seem to be the limit case of the ridge function family according to our measures for convergence behavior.