The present study is related to solve the nonlinear dynamics of a smoke model using artificial neural networks (ANNs) under the optimization procedures of global heuristic and local search scheme. The genetic algorithm (GA) and sequential quadratic programming (SQP), i.e., GA-SQP used as global–local search approaches. The smoke nonlinear medical model depends upon four categories named as potential smokers, temporary smokers, smokers and permanent smokers. For solving these categories of the smoke system, an error based objective function is designed using these nonlinear equations and the initial conditions of the model. The performance through optimization of the objective function is testified using the ANNs and the hybrid combination of the GA-SQP for solving the nonlinear dynamics of the smoke system. To check the perfection of the proposed stochastic approach, the obtained results through the hybrid of GA-SQP are compared with the Adams scheme. Moreover, the designed scheme through statistical performances using different operators authenticates the reliability and stability to solve the nonlinear smoke model.