Catenary metasurface has been widely used in fields such as wild-angle imaging, spectral detection, and broadband absorbers, due to its advantages of high efficiency and broadband. In our previous studies, perfect wavefront control of catenary metasurface is achieved via field-driven optimization (FDO). However, the proposed method focuses solely on the performance of catenary metasurfaces at a specific wavelength. Here, considering the broadband and multifunctional of the catenary and catenary-like metasurfaces, multi-objectives FDO is proposed. With 30 iterations, the average diffraction efficiency of the catenary metasurface increases to ~96% at the wavelength of 9-13 μm. In addition, considering the functionality, the catenary and catenary-like metasurfaces are optimized with a pair of orthogonal polarized light incidences. The optimization process preserves the chiral nature of the catenary metasurface. After 30 iterations, the diffraction efficiency of the catenary metasurface is improved from 96.4% to 99.2%. For catenary-like metasurfaces, the diffraction efficiencies exceed 90% for both left-handed and right-handed elliptically polarized light incidences. Our work provides a methodology for designing multifunctional complex continuous metasurfaces, which may further promote catenary optics.