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Running time analysis of the Pareto archived evolution strategy on pseudo-Boolean functions

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Abstract

Evolutionary algorithms have long been quite successfully applied to solve multi-objective optimization problems. However, theoretical analysis of multi-objective evolutionary algorithms (MOEAs) is mainly restricted to the simple evolutionary multi-objective optimizer (SEMO). The Pareto archived evolution strategy (PAES) is a simple but important multi-objective evolutionary algorithm which is come from the study of telecommunication problems, and it has been successfully applied to many optimization problems, such as image processing and signal processing. In this paper, we make a first step toward studying the rigorous running time analysis for PAES. We show that the PAES outperforms the SEMO on function PATH when the PAES uses a simple mutation operator. However, it can not find the whole Pareto front with overwhelming probability on the well-studied function LOTZ. Additional experiments show that the experimental results are in agreement with the theoretical results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61773410, 61703183), the Natural Science Foundation of Jiangxi Province of China (20151BAB217008) and the Foundation for Distinguished Young Talents in Higher Education of Guangdong (2015KQNCX086).

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, Guangdong, 510665, People’s Republic of China

    Xue Peng

  2. College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang, 314001, People’s Republic of China

    Xiaoyun Xia & Weizhi Liao

  3. Huashang College, Guangdong University of Finance and Economics, Guangzhou, Guangdong, 511300, People’s Republic of China

    Zhanwei Guo

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  1. Xue Peng
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  2. Xiaoyun Xia
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  3. Weizhi Liao
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  4. Zhanwei Guo
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Correspondence to Xiaoyun Xia.

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Peng, X., Xia, X., Liao, W. et al. Running time analysis of the Pareto archived evolution strategy on pseudo-Boolean functions. Multimed Tools Appl 77, 11203–11217 (2018). https://doi.org/10.1007/s11042-017-5466-3

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  • DOI: https://doi.org/10.1007/s11042-017-5466-3

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