•The architecture and learning parameters of an ANN are optimized using Robust Design.•The proposed methodology reduces the number of simulations.•MAPE, MSE, and Rall metrics are used for the proposed ANN validation.•The optimized ANN used to predict the surface roughness of cutting edges in different depths during laser processing. The Feed-Forward and Backpropagation Artificial Neural Networks (FFBP-ANN) are generally employed for cut surfaces quality characteristics predictions. However, the determination of the neurons on the hidden layer and the training parameters’ values are tasks requiring many trials according to the Full-Factorial Approach (FFA). Therefore, in this work, a methodology is presented for the optimization of an FFBP-NN and the application of the Taguchi Design of Experiments (TDE). Nine combinations of four variables were examined, having three levels each, according to the L9 (34) orthogonal array. The number of neurons in the hidden layer (N), the learning rate (mu), the increment factor (mu+) and the decrement factor (mu-) are employed as variables. In addition, Mean Squared Error (MSE) and overall regression index (Rall) was decided as the objective functions. Thus, TDE diminishes the FFBP-ANN arrangements to nine from eighty-one of FFA. The optimized FFBP-ANN predicts the surface roughness in various cut depths during laser cutting of thin thermoplastic plates.