Novel Response Surface Designs and LASSO‐Regularized Neural Network Models for Robust Optimization With Limited Data

Traditional experimental design approaches have long been used to optimize response variables and process parameters in laboratory studies. However, these classical structures often lack flexibility and efficiency when dealing with limited experimental data. This research introduces innovative response surface designs that integrate diverse experimental regions and include an optimal balance of unique and replicated trials to enable precise estimation of model, lack‐of‐fit, and pure error terms. The proposed designs are constructed using structured combinations of factorial, fractional factorial, intermediate, axial, and center‐point subsets to improve region coverage, estimation efficiency, and diagnostic capability. The performance of the proposed designs was assessed using a range of numerical and graphical optimality criteria to ensure robustness and efficiency. To further examine the predictive capability of the proposed designs, artificial neural network modeling enhanced with least absolute shrinkage and selection operator regularization was employed as a complementary analytical tool. The predictive capabilities of response surface methodology and neural networks were systematically computed considering polynomial approximation orders. Results reveal that some of the proposed subset designs demonstrated superior efficiency compared with conventional experimental plans, offering a cost‐effective and reliable alternative for process optimization under data‐limited conditions.