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Hierarchical multi-strategy firefly algorithm based on Hammersley initialization
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DOI：10.1007/s00500-025-10837-z.png)
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Abstract
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To tackle the problems related to slow convergence speed, decreased diversity in the later iterations, and susceptibility to getting trapped in local optima in the firefly algorithm. This paper proposes a hierarchical multi-strategy firefly algorithm based on Hammersley initialization (MOFA-HWG). First, the population is initialized using the Hammersley sequence, which generates points with small differences and a uniformly distributed point set, thus improving the initial population quality. Secondly, the population dynamics is split into two levels based on the dominance relationship, the upper-level fireflies introduce the golden sine strategy to improve the information sharing among fireflies and the optimal solution, narrowing the search range for high-quality fireflies, and accelerating population convergence; the lower-level fireflies introduce the logarithmic increment weight strategy, which allows expansion the search range during the early iterations to explore potential high-quality solutions, while also avoiding stagnation in the later iterations. Lastly, a non-uniform centroid reverse mutation is proposed to perturb the optimal solution, enhancing the algorithm’s ability for local escape. By conducting simulation experiments on benchmark functions with MOFA-HWG in comparison to 5 classical and 11 recent multi-objective optimization algorithms, and performing ablation studies to validate the effectiveness of multi-strategy harmonization, the results show that MOFA-HWG achieves the best performance in terms of GD, SP, MS, and IGD metrics. The algorithm significantly enhances both the optimization speed and accuracy, while also demonstrating the ability to escape local optima.
Keywords:
Multi-objective firefly algorithm
Hammersley sequence
Hierarchical learning
Centroid reverse learning
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