The Geometric Buchberger algorithm is a specialization of the classical Buchberger algorithm to the case of toric ideals, with applications in the solution of families of integer programming problems. In this paper, we investigate the performance of the Geometric Buchberger algorithm in a variety of combinatorial optimization problems with both integer and binary variables, introducing algorithmic improvements for the latter case in the form of an efficient criterion for detecting S-binomials that can be truncated away. Our experiments show that our implementation, available in the package IPGBs.jl, computes Gröbner bases for toric ideals of combinatorial optimization problems more efficiently than the previous state-of-the-art.