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

The progress behavior of evolution strategies (ES) using recombination is analyzed in this paper on the parabolic ridge. This test function represents landscapes far from the optimum. The ES algorithms with intermediate and dominant recombination are considered in the analysis. The derivations are presented for intermediate recombination. Thereafter, the formulae for dominant recombination are obtained using the so-called surrogate mutation model. In the analysis, the formulae are derived for the progress rate and for the stationary distance R() to the ridge axis. As a result, it will be shown that the progress rate can increase if recombination is applied. Simulations are used to show the appropriateness of the formulae derived.

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