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<p>This paper presents Adaptive Fireworks Swarm Learning (AdaFSL), a novel hybrid algorithm that synergistically integrates swarm intelligence with first-order gradient optimization. AdaFSL introduces a gradient-guided explosion operator with an adaptive step size mechanism for efficient local search, and a cooperative learning strategy for dynamic hyperparameter tuning to ensure global diversity. To rigorously evaluate performance, we develop a new benchmark suite incorporating gradient information. Extensive experiments on functions up to 100,000 dimensions demonstrate that AdaFSL significantly outperforms representative metaheuristic, gradient-based, and hybrid algorithms in terms of convergence speed and solution precision. Furthermore, in training a convolutional neural network on the CIFAR-10 dataset, AdaFSL achieves a classification accuracy of 67%, markedly surpassing the 57–61% range of baseline optimizers. Additionally, it exhibits strong generalization on non-Euclidean data in a graph neural network node classification task. These results validate AdaFSL as a robust and scalable optimizer for complex, high-dimensional non-convex problems.</p>

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Adaptive fireworks swarm learning: a hybrid approach for non-convex optimization

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Yifan Liu,
  • Ying Tan

摘要

This paper presents Adaptive Fireworks Swarm Learning (AdaFSL), a novel hybrid algorithm that synergistically integrates swarm intelligence with first-order gradient optimization. AdaFSL introduces a gradient-guided explosion operator with an adaptive step size mechanism for efficient local search, and a cooperative learning strategy for dynamic hyperparameter tuning to ensure global diversity. To rigorously evaluate performance, we develop a new benchmark suite incorporating gradient information. Extensive experiments on functions up to 100,000 dimensions demonstrate that AdaFSL significantly outperforms representative metaheuristic, gradient-based, and hybrid algorithms in terms of convergence speed and solution precision. Furthermore, in training a convolutional neural network on the CIFAR-10 dataset, AdaFSL achieves a classification accuracy of 67%, markedly surpassing the 57–61% range of baseline optimizers. Additionally, it exhibits strong generalization on non-Euclidean data in a graph neural network node classification task. These results validate AdaFSL as a robust and scalable optimizer for complex, high-dimensional non-convex problems.