The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities of particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In the designed ANN-PSOIP scheme, a merit function is proposed by using the mean square error sense along with continuous mapping of ANNs for the NSO-LE-MPDD model. The training of these nets is capable of using the integrated competence of PSO and IP scheme. The inspiration of the ANN-PSOIP approach instigates to present a reliable, steadfast, and consistent arrangement relates the ANNs strength for the soft computing optimization to handle with such inspiring classifications. Furthermore, the statistical soundings using the different operators certify the convergence, accurateness, and precision of the ANN-PSOIP scheme.

当前的研究与通过应用人工神经网络（ANNs）的近似熟练度和针对非线性二阶Lane-Emden多受电弓延迟微分（NSO-LE-MPDD）模型提出的一种新型的神经群智能启发式算法有关粒子群优化（PSO）的全局搜索功能以及有效/快速内点（IP）方法，即ANN-PSOIP方案。在设计的ANN-PSOIP方案中，针对NSO-LE-MPDD模型，通过使用均方误差感知以及ANN的连续映射，提出了一项价值函数。这些网络的训练能够利用PSO和IP方案的综合能力。ANN-PSOIP方法的灵感激发了人们提出可靠，坚定，一致的安排关系到ANN的实力，以进行软计算优化以应对此类启发性分类。此外，使用不同算子的统计测深证明了ANN-PSOIP方案的收敛性，准确性和精确性。