There are several types of neural networks (NNs) that are widely used for data classification tasks. The supervised learning NN is an advanced network with a training algorithm for setting the weights and biases of the network in its training phase. However, traditional training algorithms such as backpropagation have some drawbacks, such as slow convergence speed and falling into local minima, which reduces the performance of the classifier. Therefore, different nature-inspired metaheuristic algorithms are integrated with the NN training algorithms to provide derivative-free solutions for complex classification problems. Consequently, this paper proposes the integration of a particle swarm optimization (PSO) algorithm with an improved Elman recurrent neural network (ERNN) to form a PSO-ERNN metaheuristic model. The key contribution of this study is the development of a new dimensional equation for ERNN architecture and the integration of PSO in ERNN learning to produce the PSO-ERNN model. The PSO is constructed to train the NN and ERNN models to achieve a fast convergence rate and avoid local minima problems. The PSO-ERNN model is validated by comparing it against the standard PSO-NN metaheuristic model and similar models from the literature. The PSO-NN and PSO-ERNN models are tested and evaluated using ten benchmark classification problems of breast cancer, heart, hepatitis, liver, wine, iris, lung cancer, yeast, Pima Indians diabetes, and ionosphere datasets. In the training phase, the results show that the PSO-ERNN model performs better than the PSO-NN model when the training set has a bigger size of samples. In the testing phase, the PSO-ERNN model outperforms the PSO-NN model for all the tested datasets except the lung cancer and yeast datasets, in which the accuracy percentage slightly decreases. In the validation phase, the PSO-ERNN model shows better performance quality in terms of accuracy percentage in six of the tested datasets. The average percentage of the training, testing, and validation accumulation show that the PSO-NN performs better than the PSO-ERNN in the lung cancer (87.27, 83.32), and heart (73.56, 70.64) datasets. On the other hand, the PSO-ERNN performs better than the PSO-NN in the iris (88.18, 86.74), hepatitis (88.60, 87.93), wine (89.16, 86.08), liver (73.56, 70.64), ionosphere (83.98, 78.94), and breast cancer (94.84, 91.17). PSO-NN and PSO-ERNN produce the same average results in the Pima Indians diabetes (84.00, 84.00) and yeast (91.31, 91.30) dataset. These results show clearly that the PSO-ERNN generally outperforms the PSO-NN when considering the overall results of the ten datasets. Nevertheless, the combinations of the PSO-NN and PSO-ERNN are proven to represent consistent and robust classification methods. The computational efficiencies of the training processes in both the PSO-NN and PSO-ERNN models are highly improved when coupled with the PSO.

有多种类型的神经网络 (NN) 被广泛用于数据分类任务。监督学习 NN 是一种高级网络，带有训练算法，用于在训练阶段设置网络的权重和偏差。然而，传统的反向传播等训练算法存在收敛速度慢、陷入局部最小值等缺点，从而降低了分类器的性能。因此，不同的受自然启发的元启发式算法与 NN 训练算法相结合，为复杂的分类问题提供无导数的解决方案。因此，本文提出将粒子群优化 (PSO) 算法与改进的 Elman 递归神经网络 (ERNN) 相结合，形成 PSO-ERNN 元启发式模型。本研究的主要贡献是为 ERNN 架构开发了新的维度方程，并将 PSO 集成到 ERNN 学习中以生成 PSO-ERNN 模型。构造 PSO 以训练 NN 和 ERNN 模型以实现快速收敛速度并避免局部最小值问题。通过将 PSO-ERNN 模型与标准 PSO-NN 元启发式模型和文献中的类似模型进行比较来验证 PSO-ERNN 模型。PSO-NN 和 PSO-ERNN 模型使用乳腺癌、心脏、肝炎、肝脏、葡萄酒、虹膜、肺癌、酵母、皮马印第安人糖尿病和电离层数据集的十个基准分类问题进行测试和评估。在训练阶段，结果表明，当训练集具有更大的样本量时，PSO-ERNN 模型的性能优于 PSO-NN 模型。在测试阶段，对于除肺癌和酵母数据集以外的所有测试数据集，PSO-ERNN 模型均优于 PSO-NN 模型，其中准确率略有下降。在验证阶段，PSO-ERNN 模型在六个测试数据集的准确率百分比方面显示出更好的性能质量。训练、测试和验证累积的平均百分比表明，PSO-NN 在肺癌 (87.27, 83.32) 和心脏 (73.56, 70.64) 数据集上的表现优于 PSO-ERNN。另一方面，PSO-ERNN 在虹膜 (88.18, 86.74)、肝炎 (88.60, 87.93)、酒 (89.16, 86.08)、肝脏 (73.56, 70.64)、电离层 (83.98) 方面的表现优于 PSO-NN 78.94) 和乳腺癌 (94.84, 91.17)。PSO-NN 和 PSO-ERNN 在皮马印第安人糖尿病 (84.00, 84.00) 和酵母菌 (91.31, 91. 30) 数据集。这些结果清楚地表明，在考虑十个数据集的整体结果时，PSO-ERNN 通常优于 PSO-NN。尽管如此，PSO-NN 和 PSO-ERNN 的组合已被证明代表了一致且稳健的分类方法。当与 PSO 结合使用时，PSO-NN 和 PSO-ERNN 模型中训练过程的计算效率得到了极大的提高。