Understanding flow of non-Newtonian fluids in porous media is critical to successful operation of several important processes, including polymer flooding, filtration, and food processing. In some cases, such as when a non-Newtonian fluid can be represented by the power-law model, simulation of its flow in a porous medium is a straightforward extension of that of Newtonian fluids. In other cases, such as flow of Bingham fluids, there is a minimum external threshold pressure below which there would be no macroscopic flow in the porous medium. Computing the threshold pressure is a difficult problem, however. We present a new algorithm for determining the threshold pressure for flow of a Bingham fluid through a porous medium, modeled by a pore-network (PN) model. The algorithm, the ant colony optimization (ACO), is described in detail and together with the PN model is used to determine the minimum pressure for flow of Bingham fluids in a heterogeneous porous medium, the Mt. Simon sandstone, whose PN and morphological properties were extracted from the sandstone's image. To assess the accuracy and computational efficiency of the ACO algorithm, we also carry out the same computations with two previous methods, namely invasion percolation with memory (IPM) and the path of minimum pressure (PMP) algorithms. The IPM does not guarantee identification of the optimal flow path with the minimum threshold pressure, while the PMP algorithm provides an approximate, albeit accurate, solution of the problem. We also compare the computational complexity of the three methods. For large PNs, both the IPM and PMP are much less efficient than the ACO algorithm. Finally, we study the effect of the morphology of the pore space on the minimum threshold pressure.