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.