标题： 带约束的混合元启发式算法用于概率神经网络学习 显示英文标题

标题： Constrained Hybrid Metaheuristic Algorithm for Probabilistic Neural Networks Learning

摘要： 本研究探讨了混合元启发式算法在利用多种优化策略的互补优势来增强概率神经网络（PNNs）训练方面的潜力。 传统的学习方法，如基于梯度的方法，在优化高维和不确定环境时常常遇到困难，而单一方法的元启发式算法可能无法充分探索解空间。 为了解决这些挑战，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。 所提出的程序分为两个阶段：初始探测阶段根据误差率评估多种元启发式算法，以确定表现最佳的一个，随后进入拟合阶段，其中选定的元启发式算法优化PNN以获得最佳平滑参数。 这种迭代过程确保了高效的探索和收敛，提高了网络的泛化能力和分类准确性。 cHM集成了几种流行的元启发式算法，如BAT、模拟退火、花授粉算法、细菌觅食优化和粒子群优化作为内部优化器。 为了评估cHM的性能，实验在16个具有不同特征的数据集上进行，包括二分类和多类分类任务、平衡和不平衡类别分布以及不同的特征维度。 结果表明，cHM有效地结合了各个元启发式的优点，从而实现了更快的收敛和更稳健的学习。 通过优化PNN的平滑参数，所提出的方法在各种数据集上提高了分类性能，证明了其应用的灵活性和效率。 显示英文摘要

摘要： 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.