Thin sheets of titanium alloys are widely used in aerospace and automotive industries for specific applications. The creation of micro holes with requisite hole quality in thin sheets of these alloys using energy of electric discharge is a challenging task for manufacturing engineers. Hole sinking electrical discharge micromachining (HS-EDMM) is one of the most promising micromachining processes to create symmetrical and non-symmetrical micro holes. The present paper is related to selection of optimum parameter settings for obtaining maximum material removal, minimum tool wear and minimum hole taper in HS-EDMM. In this paper an attempt has been made to develop an integrated model (ANN-GRA-PCA) of single hidden layer back propagation neural network (BPNN) for prediction and grey relational analysis (GRA) coupled with principal component analysis (PCA) hybrid optimization strategy with multiple responses of HS-EDMM of Ti-6Al-4V. Experiments have been conducted to generate dataset for training and testing of the network where input parameters consist of gap voltage, capacitance of capacitor and the resulting performance parameters are represented by material removal rate (MRR), tool wear rate (TWR), and hole taper ($T_a$). The results indicate that the integrated model is capable to predict and optimize process performance with reasonable accuracy under varied operating conditions of HS-EDMM. The proposed approach would be extendable to other configurations of EDMM processes for different materials.