The Hefei Advanced Light Facility (HALF) proposed by the National Synchrotron Radiation Laboratory is a green-field vacuum ultraviolet and soft X-ray diffraction-limited storage ring light source with a beam energy of 2.2 GeV and emittance goal of less than 100 pm rad. Inspired by the ESRF-EBS hybrid multi-bend achromat (HMBA), SLS-2, and Diamond-II lattices, we propose and design a modified H6BA lattice as the baseline lattice of the HALF storage ring with 20 identical cells and a natural emittance of approximately 86 pm rad. In this study, three other types of HMBA lattices comprising two H7BA lattices and a H6BA lattice are designed for HALF with the same number of cells. The main storage ring properties of these four HMBA lattices are compared. Because the intra-beam scattering (IBS) effect is significant in the HALF storage ring, we calculate and compare the equilibrium emittances of the four lattices with IBS included. These comparisons show that the present modified H6BA lattice, which has a relatively low equilibrium emittance and more straight sections, is preferred for the HALF storage ring after a comprehensive consideration.