The present research work is to put forth the numerical solutions of the nonlinear second-order Lane–Emden-pantograph (LEP) delay differential equation by using the approximation competency of the artificial neural networks (ANNs) trained with the combined strengths of global/local search exploitation of genetic algorithm (GA) and active-set (AS) method, i.e., ANNGAAS. In the proposed ANNGAAS, the objective function is designed by using the mean square error function with continuous mappings of ANNs for the LEP delay differential equation. The training of these constructed networks is conducted proficiently using the integrated capability of global search with GA and assisted local search along with AS approach. The performance of design computing paradigm ANNGAAS is evaluated effectively on variants of LEP delay differential models, while the statistical investigations based on different operators further validate the accuracy and convergence.

本研究工作是利用结合全局/局部强度训练的人工神经网络（ANN）的近似能力，提出非线性二阶Lane-Emden受电弓（LEP）延迟微分方程的数值解。遗传算法（GA）和活动集（AS）方法（即ANNGAAS）的搜索开发。在提出的ANNGAAS中，目标函数是使用均方误差函数与LEP延迟微分方程的ANN连续映射来设计的。通过使用具有GA的全局搜索和辅助的本地搜索以及AS方法的集成功能，可以熟练地对这些构建的网络进行训练。在LEP延迟差分模型的变体上，可以有效地评估设计计算范例ANNGAAS的性能，