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Cooperative coevolutionary algorithms for dynamic optimization: an experimental study

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Abstract

In this paper, we study the cooperative coevolutionary algorithms (CCEAs) for dynamic optimization. We introduce the CCEAs with two popular types of individuals: (1) random immigrants (RIs) that increase the diversity for changing environments, and (2) elitist individuals that increase the local convergence to the optima. The CCEAs are evaluated on a standard suite of benchmark problems and are compared with evolution strategies (ES). Our experimental results show that the CCEAs are efficient in locating and tracking optima in dynamic environments. They are superior to the ES when the RI individuals and the elitist individuals are used. In addition, we empirically investigate how the CCEAs perform with different parameter settings. These settings include collaboration methods, the use of plus–comma selections, and the number of RI individuals and elitist individuals. We also investigate the CCEAs that use a mutative σ-self adaptation. The CCEAs perform the best when they use the best collaboration method and the plus selection. The use of the mutative σ-self adaptation is insignificant. Our results also show that the CCEAs are more scalable than the ES in dynamic environments.

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Notes

  1. In [2], the original individuals are the parents and the offspring in an EA.

  2. In the literature, elites are generally the individuals that have the highest fitness and are unmutated from generations to generations.

  3. The term “best response curves” was originally used in a two-populations CCEA [38, 41]. The authors also mentioned that when more than two populations are used, the best-response curves become the best-response surfaces or the best-response subspaces in higher dimensions.

  4. We can also define a CCEA individual such that the dimensions of a component is greater than 1, i.e. \({\mathbf {x}}_b \in {\mathbb {R}}^d\,{\text{ for }}\,d > 1\).

  5. The settings were based the results of the sensitivity analysis in the final set of experiments, where the optimal performance was achieved when \(\kappa =10,\iota =10\). For fair comparisons with the second settings, we also maintain a total number of individuals to 40, and therefore λ is 20.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Chun-Kit Au & Ho-Fung Leung

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  1. Chun-Kit Au
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Correspondence to Chun-Kit Au.

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Au, CK., Leung, HF. Cooperative coevolutionary algorithms for dynamic optimization: an experimental study. Evol. Intel. 7, 201–218 (2014). https://doi.org/10.1007/s12065-014-0117-3

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