This article presents an algorithm developed to determine the appropriate sample size for constructing accurate artificial neural networks as surrogate models in optimization problems. In the algorithm, two model evaluation methods-cross-validation and/or bootstrapping-are used to estimate the performance of various networks constructed with different sample sizes. The optimization of a CO2 capture process with aqueous amines is used as the case study to illustrate the application of the algorithm. The output of the algorithm-the network constructed using the appropriate sample size-is used in a process synthesis optimization problem to test its accuracy. The results show that the model evaluation methods are successful in identifying the general trends of the underlying model and that objective function value of the optimum solution calculated using the surrogate model is within 1% of the actual value. (C) 2012 American Institute of Chemical Engineers AIChE J, 59: 805-812, 2013