The problem of sample size determination (SSD) for any black box model is addressed in this work. Four novel SSD algorithms namely HC, SOOP, HC+SOOP and V-SOOP, based on hypercube sampling, space filling and optimization study are proposed to tackle the issues of over-fitting, accuracy and computational speed of surrogate models. In this version, the novel algorithms are shown to run simultaneously with an ANN surrogate building algorithm proposed recently by our group. As a case study, a highly nonlinear industrially validated Induration model with 22 inputs and 5 outputs, is considered and parsimonious ANNs are built using the proposed SSD techniques. The surrogate assisted optimization is found to be 10 times faster than the conventional optimization using NSGA II, thus enabling its online implementation. © 2017 IEEE.