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A novel hybrid dynamic fireworks algorithm with particle swarm optimization

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Abstract

In recent years, the fireworks algorithm (FWA) has attracted more and more attention due to its strong ability to solve optimization problems. However, the global performance of FWA is significantly affected by the explosion amplitude. In this paper, a dynamic fireworks algorithm with particle swarm optimization (DFWPSO) is developed to improve the global performance of FWA. In DFWPSO, a dynamic explosion amplitude mechanism based on the evolution speed of population, which is dynamically adjusted by evaluating the evolution speed of fitness in each iteration process, is designed to control the global and local searching information. Moreover, a new nonlinear minimal amplitude check strategy based on function decreasing is designed to obtain appropriate amplitude. Furthermore, a new firework updating mechanism based on particle swarm optimization (PSO) is implemented to accelerate the convergence of algorithm and cut down on computing resources. In addition, the selection operator of FWA is abandoned and all fireworks are updated by velocity and current location in each iteration process. To verify the performance of the proposed DFWPSO algorithm, three groups of the benchmark functions are used and tested for experiments. Compared with other variants of FWA and PSO variants, results show that the proposed algorithm performs competitively and effectively.

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Acknowledgements

This work was supported in part by the National Science Foundations of China (Grant Nos. 61976101, 61572224, 61304082 and 41475017) and the National Science Found for Distinguished Young Schools (Grant No. 61425009). This work is also partially supported by Anhui Provincial Natural Science Foundation (Grant No. 1708085MF140) and the Natural Science Foundation in colleges and universities of Anhui Province (Grant No. KJ2019B16).

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Authors and Affiliations

  1. School of Physics and Electrical Information, Huaibei Normal University, Huaibei, 235000, China

    Fang Zhu, Debao Chen & Feng Zou

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  1. Fang Zhu
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  2. Debao Chen
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  3. Feng Zou
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Correspondence to Fang Zhu.

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Appendix

Appendix

In Table 10, better mean error achieved in 21 functions, better standard deviation obtained in 12 functions, better median achieved in 15 functions, better best error achieved in 19 functions, better worst error achieved in 19 functions, out of total 30 CEC 2014 functions by FBBO. However, better mean error achieved in 14 functions, better standard deviation obtained in 18 functions, better median achieved in 20 functions, better best error achieved in 17 functions, better worst error achieved in 15 functions, out of total 30 CEC 2014 functions by DFWPSO. The two algorithms have their own advantages in CEC2014 test suites.

Table 10 Mean error, standard deviation, median, best, worst error value obtained by DFWPSO and FBBO for 30-dimensional CEC 2014 benchmark problems
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Zhu, F., Chen, D. & Zou, F. A novel hybrid dynamic fireworks algorithm with particle swarm optimization. Soft Comput 25, 2371–2398 (2021). https://doi.org/10.1007/s00500-020-05308-6

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