With novel schemes using reverse bends and longitudinal gradient bends, the 4th generation low-emittance storage ring was designed for the Pohange Light Source-III: the upgrade of PLSII. A unit cell with one homogeneous bending magnet, designed by using a genetic algorithm, is commonly used in the design of multi-bend achromatic lattices to realize an extremely low natural emittance (100 pm) for a 3-GeV and 280-m ring. In order to obtain enough dynamic aperture for accumulating off-axis injected beam from the existing PLS-II linear accelerator, we optimized the nonlinear dynamics with a genetic algorithm after a tune scan along the dynamic aperture. As a result, enough dynamic aperture for off-axis injection and long lifetime for stable top-up operation were achieved.