Local performance of the \((\mu/\mu_I,\lambda)\)-ES in a noisy environment.

*(English)*Zbl 1001.68199
Martin, Worthy N. (ed.) et al., Foundations of genetic algorithms - 6. 6th biennial meeting, FOGA-6, Charlottesville, VA, USA, 2000. Orlando, FL: Morgan Kaufmann Publishers/ Academic Press/ Harcourt. 127-141 (2002).

Summary: While noise is a phenomenon present in many real-world optimization problems, the understanding of its potential effects on the performance of evolutionary algorithms is still incomplete. In the realm of evolution strategies in particular, it can frequently be observed that one-parent strategies are outperformed by multi-parent strategies in noisy environments. However, mathematical analyses of the performance of evolution strategies in noisy environments have so far been restricted to the simpler one-parent strategies.

This paper investigates the local performance of a multi-parent evolution strategy employing intermediate multi-recombination on a noisy sphere in the limit of infinite parameter space dimension. The performance law that is derived neatly generalizes a number of previously obtained results. Genetic repair is shown to be present and unaffected by the noise. In contrast to previous findings in a noise-free environment, the efficiency of the simple \((1+1)\)-ES can be exceeded by multi-parent strategies in the presence of noise. It is demonstrated that a much improved performance as compared to one-parent strategies can be achieved. For large population sizes the effects of noise all but vanish.

For the entire collection see [Zbl 0976.00032].

This paper investigates the local performance of a multi-parent evolution strategy employing intermediate multi-recombination on a noisy sphere in the limit of infinite parameter space dimension. The performance law that is derived neatly generalizes a number of previously obtained results. Genetic repair is shown to be present and unaffected by the noise. In contrast to previous findings in a noise-free environment, the efficiency of the simple \((1+1)\)-ES can be exceeded by multi-parent strategies in the presence of noise. It is demonstrated that a much improved performance as compared to one-parent strategies can be achieved. For large population sizes the effects of noise all but vanish.

For the entire collection see [Zbl 0976.00032].

##### MSC:

68W05 | Nonnumerical algorithms |

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\textit{D. V. Arnold} and \textit{H.-G. Beyer}, in: Foundations of genetic algorithms (FOGA-6). 6th biennial meeting on Foundations of Genetic Algorithms, Charlottesville, VA, USA, July 21-23, 2000. Orlando, FL: Morgan Kaufmann Publishers/ Academic Press/ Harcourt. 127--141 (2002; Zbl 1001.68199)