In this paper, we first briefly survey the main surrogate model building approaches discussed in the literature considering also design of experiments strategies and dimensionality reduction procedures: we mainly focus on sub-set approaches and sampling strategies for constrained regression problems. We delineate a systematic methodology for surrogate modelling in presence of model constraints, such as non-negativity of the model responses. The main contribution of this paper is twofold: from one side we extend the principal component analysis framework to the case of constrained regression problem, from the other we propose a novel methodology which integrates the subset selection and the previous principal component regression procedure. Finally, we apply the two novel algorithms to two fundamental chemical processes in petroleum refinery, namely catalytic reforming and light naphtha isomerization. The numerical results show the comparisons between the two algorithms in terms of computational and accuracy trade-offs.