  We regard the Casimir energy of the universe as the main contribution to the
cosmological constant. Using 5 dimensional models of the universe, the flat
model and the warped one, we calculate Casimir energy. Introducing the new
regularization, called {\it sphere lattice regularization}, we solve the
divergence problem. The regularization utilizes the closed-string
configuration. We consider 4 different approaches: 1) restriction of the
integral region (Randall-Schwartz), 2) method of 1) using the minimal area
surfaces, 3) introducing the weight function, 4) {\it generalized
path-integral}. We claim the 5 dimensional field theories are quantized
properly and all divergences are renormalized. At present, it is explicitly
demonstrated in the numerical way, not in the analytical way. The
renormalization-group function ($\be$-function) is explicitly obtained. The
renormalization-group flow of the cosmological constant is concretely obtained.
