Conventional gradient-based techniques are prone to getting trapped into local optimum and convergence is slow. To overcome these drawbacks, this study attempts to combine genetic algorithm, avoiding local minima and achieving global convergence quickly and correctly by searching in several regions simultaneously. The authors' methodology utilizes a hybrid genetic algorithm-back propagation strategy. The proposed algorithm combines the local searching ability of the gradient-based back-propagation strategy with the global searching capability of the genetic algorithm. The genetic algorithm is used to decide the initial weights of the gradient decent methods so that all of the initial weights can be searched intelligently. The genetic operators and parameters are carefully designed to avoid premature convergence and permutation problems. For an evaluation purpose, the performance and generalization capabilities of genetic algorithm-back propagation are compared with those of models developed with the commonly used technique of back propagation (back propagation-artificial neural network). This strategy is applied to a highly nonlinear system of distillation column. The results demonstrate that a carefully designed hybrid genetic algorithm-back propagation neural network outperforms the gradient descent-based neural network in identification and, consequently, approximate model predictive control of the distillation column. Since the derived genetic algorithm-back propagation model is more accurate than a back propagation-artificial neural network model, an approximate model predictive control controller reveals a better performance.