The bi-objective matroid optimization, an NP-hard problem, is addressed in this study. Three approaches—two heuristics and an explicit method—from the literature are compared. The two-phase method serves as the foundation for these techniques. During the first phase, The weighted sum approach is used to determine extreme efficient bases, while the recursive process and two heuristics, “neighborhood search” and “adjacent search,” are used during the second phase to determine non-extreme efficient bases. We assess how well the algorithms perform for various matroid kinds, such as partition matroids, graphic matroids, and uniform matroids. Our findings show how effective and useful the suggested method is for resolving bi-objective matroid problems.