A baseline design for the High Energy Photon Source has been proposed, with a natural emittance of 60 pm.rad within a circumference of about 1.3 kilometers. Nevertheless, the nonlinear performance of the design needs further improvements to increase both the dynamic aperture and the momentum acceptance. In this study, genetic optimization of the linear optics is performed, so as to find all the possible solutions with weaker sextupoles and hence weaker nonlinearities, while keeping the emittance at the same level as the baseline design. The solutions obtained enable us to explore the dependence of nonlinear dynamics on the working point. The result indicates that with the same layout, it is feasible to obtain much better nonlinear performance with a delicate tuning of the magnetic field strengths and a wise choice of the working point.