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Design and analysis of migration in parallel evolutionary algorithms

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Abstract

Parallelization is becoming a more important issue for solving difficult optimization problems. Island models combine phases of independent evolution with migration where genetic information is spread out to neighbored islands. This can lead to an increased diversity within the population. Despite many successful applications, the reasons behind the success of island models are not well understood. We perform a first rigorous runtime analysis for island models and construct a function where phases of independent evolution as well as communication among the islands are essential. A simple island model with migration finds a global optimum in polynomial time, while panmictic populations as well as island models without migration need exponential time, with very high probability. Our results lead to new insights into the usefulness of migration, how information is propagated in island models, and how to set parameters such as the migration interval. This is a novel contribution to the theoretical foundation of parallel EAs. Further, we provide empirical results that complement the theoretical results, investigate the robustness with respect to the choice of the migration interval and compare various migration topologies using statistical tests.

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Notes

  1. Recall that this is a provably good value for \(\tau =50{,}000\) by Theorem 3. For other migration intervals, there generally is no provably good value, so for \(\tau \ne 50{,}000\) the choice of 25,000 is somewhat arbitrary.

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Acknowledgments

We thank Thomas Jansen, Nicola Beume, Mike Preuß, Günter Rudolph, and Thomas Sauerwald for fruitful discussions on preliminary results. The authors were partially supported by postdoctoral fellowships from the German Academic Exchange Service. Dirk Sudholt was partially supported by EPSRC grant EP/D052785/1.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Applied Sciences Zittau/Görlitz, Görlitz, Germany

    Jörg Lässig

  2. Department of Computer Science, University of Sheffield, Sheffield, UK

    Dirk Sudholt

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  1. Jörg Lässig
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  2. Dirk Sudholt
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Correspondence to Dirk Sudholt.

Additional information

Communicated by E. Alba.

This manuscript is partly based on preliminary results from Lässig and Sudholt (2010a, b).

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Lässig, J., Sudholt, D. Design and analysis of migration in parallel evolutionary algorithms. Soft Comput 17, 1121–1144 (2013). https://doi.org/10.1007/s00500-013-0991-0

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