Atomistic simulations such as density functional theory and embedded-atom method calculations are essential for predicting many materials properties in the integrated computational materials engineering framework. For many thermodynamic properties, searching the convex hull is necessary to obtain phase stability information for materials selection, synthesis, and characterization in simulations/experiments. With increasingly complicated structures and compositions of materials, the computational cost of the expensive density functional theory calculations has become a barrier to materials design. Thus, there is a need to maximize information gained from each calculation while simultaneously identifying subsequent high-value calculations. In this work, we show that new data acquisition strategies can consider the geometry of the convex hull to maximize the yield of batch experiments done with limited computational resources. Based on Bayesian-Gaussian optimization, we developed uncertainty-based acquisition functions for weighing the configurations of multi-component alloys to learn the ground-state line. The proposed acquisition methods were validated by learning the formation energy convex hulls of the Co-Ni metallic system, the Zr-O ionic compound system, the Ni-Al-Cr ternary alloys, and the intermetallic (Ni 1−x ,Co x ) 3 Al planar defect system. By comparing to the conventional acquisition scheme using the genetic algorithm models, we demonstrated that the proposed strategies have the advantages of reducing training parameters and user interactions for selecting candidate batch experiments. We show that new acquisition functions can reduce the number of experiments required to obtain the ground-state line error by more than 30%. The new strategies can be extended to multicomponent systems and coupled with cost functions.