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The Benefit of Recombination in Noisy Evolutionary Search

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Algorithms and Computation (ISAAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9472))

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Abstract

Practical optimization problems frequently include uncertainty about the quality measure, for example due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings meta-heuristics are a popular choice for deriving good optimization algorithms, most notably evolutionary algorithms which mimic evolution in nature. Empirical evidence suggests that genetic recombination is useful in uncertain environments because it can stabilize a noisy fitness signal. With this paper we want to support this claim with mathematical rigor.

The setting we consider is that of noisy optimization. We study a simple noisy fitness function that is derived by adding Gaussian noise to a monotone function. First, we show that a classical evolutionary algorithm that does not employ sexual recombination (the \(( \mu +1) \)-EA) cannot handle the noise efficiently, regardless of the population size. Then we show that an evolutionary algorithm which does employ sexual recombination (the Compact Genetic Algorithm, short: cGA) can handle the noise using a graceful scaling of the population.

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Acknowledgements

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 618091 (SAGE).

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Authors and Affiliations

  1. Hasso Plattner Institute, Potsdam, Germany

    Tobias Friedrich, Timo Kötzing, Martin S. Krejca & Andrew M. Sutton

Authors
  1. Tobias Friedrich
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  2. Timo Kötzing
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  3. Martin S. Krejca
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  4. Andrew M. Sutton
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Corresponding author

Correspondence to Timo Kötzing .

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Editors and Affiliations

  1. Masdar Institute, Abu Dhabi, United Arab Emirates

    Khaled Elbassioni

  2. Kyoto University, Kyoto, Japan

    Kazuhisa Makino

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Friedrich, T., Kötzing, T., Krejca, M.S., Sutton, A.M. (2015). The Benefit of Recombination in Noisy Evolutionary Search. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_13

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  • DOI: https://doi.org/10.1007/978-3-662-48971-0_13

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  • Print ISBN: 978-3-662-48970-3

  • Online ISBN: 978-3-662-48971-0

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