  A new generation of storage ring-based light source, called
diffraction-limited storage ring (DLSR), with the emittance approaching the
diffraction limit for multi-keV photons by using the multi-bend achromat
lattice, has attracted worldwide and extensive studies of several laboratories,
and been seriously considered as a goal of upgrading the existing facilities in
the imminent future. Among various DLSR proposals, the PEPX design based on the
third-order achromat concept and with the special design of a high-beta
injection straight section demonstrated that, it is feasible to achieve
sufficient ring acceptance for off-axis injection in a DLSR. For the High
Energy Photon Source planned to be built in Beijing, PEPX-type lattice has been
designed and continuously improved. In this paper, we report the evolution of
the PEPX-type design, and discuss the main issues relevant to the linear optics
design and nonlinear optimization.
