  We propose a new algorithm for computing the luminosity distance in the flat
universe with a cosmological constant based on Shchigolev's homotopy
perturbation method, where the optimization idea is applied to prevent the
arbitrariness of initial value choice in Shchigolev's homotopy. Compared with
the some existing numerical methods, the result of numerical simulation shows
that our algorithm is a very promising and powerful technique for computing the
luminosity distance, which has obvious advantages in computational
accuracy,computing efficiency and robustness for a given {\Omega_m}.
