Software Testing Effort (STE), which contributes about 25-40% of the total development effort, plays a significant role in software development. In addressing the issues faced by companies in finding relevant datasets for STE estimation modeling prior to development, cross-company modeling could be leveraged. The study aims at assessing the effectiveness of cross-company (CC) and within-company (WC) projects in STE estimation. A robust multi-objective Mixed-Integer Linear Programming (MILP) optimization framework for the selection of CC and WC projects was constructed and estimation of STE was done using Deep Neural Networks. Results from our study indicate that the application of the MILP framework yielded similar results for both WC and CC modeling. The modeling framework will serve as a foundation to assist in STE estimation prior to the development of new a software project.