In this paper, the effective parameters on the ductility demand of the seismically base isolated structure are investigated, and then a relation between the strength reduction factor and the target ductility is presented. The investigation has been conducted by modelling the base isolated structure as a two degree of freedom model in the OpenSees software, and the possibility of yielding in the superstructure has been considered in the model. Results show that the period of isolator and superstructure have the most effect on the ductility demand, therefore these two parameters beside the strength reduction factor and the target ductility have been used as variables of  relation. A nonlinear regression model has been developed for forecasting the relation and the constant parameters of the proposed scheme has been obtained based on an optimization model solved by modified artificial bee colony (ABC) algorithm. A database including 224 models under 20 earthquake records with 2% probability of exceedance in 50 years have been generated for this purpose. Since there is not any explicit closed form formula to calculate the strength reduction factor for a specific target ductility; another optimization model has been developed to calculate the data used as input of the nonlinear regression model. The proposed relation includes two nonlinear functions and it is able to quantify the inelastic performance of base isolated structures for a wide range of earthquake records accurately.