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Analysis of the (1, )-ES on the Parabolic Ridge

The progress rate of the (1 )-ES (Evolution Strategy) is analyzed on the parabolic ridge test function. A differentprogress behavior is observed for the (1, )-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.