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Adaptation of operators and continuous control parameters in differential evolution for constrained optimization

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Abstract

A large number of differential evolution algorithms has been proposed in recent years, many of which have been used to solve mainly unconstrained problems. However, similar to other evolutionary algorithms, their performances are highly dependent on their search operators and control parameters. Although many investigations have been conducted to ensure appropriate choices of these operators and parameters, the task is recognized as tedious. In this research, a differential evolution algorithm, which includes a new mechanism for automatically selecting the best combinations of parameters (amplification factor, crossover rate, and population size) as well as search operators, is developed. Instead of choosing discrete values for the amplification factor and crossover rate from a given set of values, this study adaptively selects them from some given continuous ranges and, furthermore, proposes a new methodology for handling constraints. The performance of the algorithm is assessed using a well-known set of constrained problems, with the experimental results demonstrating that it is superior to state-of-the-art algorithms.

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Notes

  1. This was a condition in the CEC2010 competition, which is used in this paper to assess the performance of DE-AOPS.

  2. The source code is available upon request .

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Author information

Authors and Affiliations

  1. School of Engineering and IT (SEIT), University of New South Wales at Canberra, Canberra, ACT, 2600, Australia

    Saber Elsayed, Ruhul Sarker & Tapabrata Ray

  2. Depto. de Computación, CINVESTAV-IPN, Mexico City, Mexico

    Carlos Coello Coello

  3. Zagazig University, Zagazig, Egypt

    Saber Elsayed

Authors
  1. Saber Elsayed
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  2. Ruhul Sarker
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  3. Carlos Coello Coello
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  4. Tapabrata Ray
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Corresponding author

Correspondence to Saber Elsayed.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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The authors declare that they have no conflict of interest.

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Informed consent was obtained from all individual participants included in the study.

Additional information

Communicated by V. Loia.

Appendices

Appendix A

See Table 10.

Table 10 Best and average fitness values (FV) achieved by DE-AOPS and 8 state-of-the-art algorithms, where “*” and “–” refer infeasible solutions, while “n/a” refers to not available results
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Appendix B

See Fig. 4.

Fig. 4
figure 4

The best combination of F (green squares) and Cr (blue circles) at every combinations reduction level for the 10D and 30D test problems, respectively. Each integer value of each parameter represents its corresponding range as described in Sect. 4. Each subplot is for the best solution obtained (color figure online)

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Elsayed, S., Sarker, R., Coello, C.C. et al. Adaptation of operators and continuous control parameters in differential evolution for constrained optimization. Soft Comput 22, 6595–6616 (2018). https://doi.org/10.1007/s00500-017-2712-6

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