This study presents the normative knowledge source for the belief space of cultural algorithm(CA) based on an adaptive Radial Basis Function Neural Network (RBFNN). The use of the RBFNN makes it possible to use the previous upper and lower bounds of the normative knowledge to update them and to extract a logical relationship between the previous parameters of the normative knowledge and their new values. The proposed algorithm(NKCA) is similar to what the human brain does, i.e. to predict the new values of the bounds of normative knowledge based on the previous ones and some knowledge, which it has gained from the previous successive updates. Finally, the proposed cultural algorithm is evaluated on 10 unimodal and multimodal benchmark functions. The algorithm is compared with several other optimization algorithms including previous version of cultural algorithm. In order to have a fair comparison, the number of cost function evaluation is kept the same for all optimization algorithms. The obtained results show that the proposed modification enhances the performance of the CA in terms of convergence speed and global optimality.