improved Gaussian processes and the area minimization statistic. Two prevalent cosmologies and the fitting results on the relevant cosmological parameters are presented in Sect. 4. Finally, we summarize our conclusions in Sect. 5.

Simulated strong lensing systems
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For a specific strong lensing system with the intervening galaxy acting as a lens (at redshift $z_l$), the multiple image separation of the source (at redshift $z_s$) depends only on angular diameter distances to the lens and to the source, as long as one has a reliable model for the mass distribution within the lens. Moreover, compared with late-type and unknown-type counterparts, early-type galaxies are more likely to serve as intervening lenses for the background sources (quasars or galaxies). This is because such galaxies contain most of the cosmic stellar mass of the Universe. The recently released large sample include 118 galaxy-scale strong gravitational lensing systems discovered and observed in SLACS, BELLS, LSD, and SL2S surveys [@Cao15Ap], which can be used to place stringent constrains on cosmological parameters in alternative cosmological models [@Li16], and to study the mass density distribution in early-type galaxies [@Cao16]. Recent analytical work has forecast the number of galactic-scale lenses to be discovered in the forthcoming photometric surveys 