Non Local Thermal Equilibrium (Non-LTE) stellar atmosphere models are the way forward to obtain accurate abundances, which is crucial for understanding of the history of stars, galaxies and the Universe as a whole. The fastest and most common methods to determine stellar abundances are based on the measurement of equivalent widths (EWs) or the computation of synthetic spectra of absorption lines of the chemical element in LTE calculation. However, due to the computational expense of Non-LTE computation of line formation, it is always difficult and intractable to apply such calculation towards a lot of stars without pre-calculated grids. Therefore, abundance inference based on EW data is very promising for Non-LTE chemical abundance determination. We present a robust multivariate interpolation tool to quantify the effect of dependencies between stellar parameters and constrain the errors of inferred abundance using Non-LTE correction. We also construct a Non-LTE EW-library for a larger grid for cool FGK stars. We utilized several global optimizers, including differential evolution and simplicial homology global optimization algorithms to obtain optimized stellar parameters. We also implemented a Bayesian framework to determine the uncertainties of optimized stellar parameters. Our preliminary results towards several metal-poor benchmark stars indicate consistent and well-constrained uncertainties. Finally we intend to make our set of tools publicly available for the community. This can make Non-LTE spectroscopic analysis to be easily implemented in large spectroscopic surveys.