As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results.
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This work was supported by National Natural Science Foundation of China (Nos. 61872153 and 61972288), Natural Science Foundation of Guangdong Province (No.2018A030313318), and Key-Area Research and Development Program of Guangdong Province (No. 2020B0101090004).
Key-Area Research and Development Program of Guangdong Province (CN),2020B0101090004, Guo-Qiang Zeng, National Natural Science Foundation of China (CN),61872153, Min-Rong Chen, 61972288,Guo-Qiang Zeng, Natural Science Foundation of Guangdong Province (CN), 2018A030313318, Min-Rong Chen.
Conflict of interest
Min-Rong Chen declares that she has no conflict of interest. Liu-Qing Yang declares that she has no conflict of interest. Guo-Qiang Zeng declares that he has no conflict of interest. Kang-Di Lu declares that he has no conflict of interest. Yi-Yuan Huang declares that she has no conflict of interest.
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Chen, MR., Yang, LQ., Zeng, GQ. et al. IFA-EO: An improved firefly algorithm hybridized with extremal optimization for continuous unconstrained optimization problems. Soft Comput 27, 2943–2964 (2023). https://doi.org/10.1007/s00500-022-07607-6
- Firefly algorithm
- extremal optimization
- Probability choice strategy
- Adaptive step size
- Continuous optimization problems