This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs) by leveraging the complementary strengths of multiple optimisation strategies. Traditional learning methods, such as gradient-based approaches, often struggle to optimise high-dimensional and uncertain environments, while single-method metaheuristics may fail to exploit the solution space fully. To address these challenges, we propose the constrained Hybrid Metaheuristic (cHM) algorithm, a novel approach that combines multiple population-based optimisation techniques into a unified framework. The proposed procedure operates in two phases: an initial probing phase evaluates multiple metaheuristics to identify the best-performing one based on the error rate, followed by a fitting phase where the selected metaheuristic refines the PNN to achieve optimal smoothing parameters. This iterative process ensures efficient exploration and convergence, enhancing the network's generalisation and classification accuracy. cHM integrates several popular metaheuristics, such as BAT, Simulated Annealing, Flower Pollination Algorithm, Bacterial Foraging Optimization, and Particle Swarm Optimisation as internal optimisers. To evaluate cHM performance, experiments were conducted on 16 datasets with varying characteristics, including binary and multiclass classification tasks, balanced and imbalanced class distributions, and diverse feature dimensions. The results demonstrate that cHM effectively combines the strengths of individual metaheuristics, leading to faster convergence and more robust learning. By optimising the smoothing parameters of PNNs, the proposed method enhances classification performance across diverse datasets, proving its application flexibility and efficiency.

翻译：本研究探讨了混合元启发式算法通过整合多种优化策略的互补优势来增强概率神经网络（PNNs）训练效果的潜力。传统学习方法（如基于梯度的方法）往往难以优化高维和不确定环境，而单一元启发式方法可能无法充分利用解空间。为应对这些挑战，我们提出了约束混合元启发式（cHM）算法，这是一种将多种基于种群的优化技术整合到统一框架中的新方法。该流程分为两个阶段运行：初始探测阶段评估多种元启发式算法，根据错误率确定性能最佳者；随后在拟合阶段，选定的元启发式算法对PNN进行精细调整以获得最优平滑参数。这一迭代过程确保了高效的探索与收敛，从而提升了网络的泛化能力和分类精度。cHM整合了多种主流元启发式算法作为内部优化器，例如BAT算法、模拟退火算法、花朵授粉算法、细菌觅食优化算法和粒子群优化算法。为评估cHM的性能，我们在16个具有不同特征的数据集上进行了实验，包括二分类与多分类任务、平衡与非平衡类别分布以及多样化的特征维度。结果表明，cHM能有效融合各元启发式算法的优势，实现更快的收敛速度和更稳健的学习性能。通过优化PNN的平滑参数，所提方法在多种数据集上均提升了分类性能，证明了其应用灵活性与高效性。