This article aims to study the effect of membrane initial configuration and the membrane spontaneous curvature (local asymmetry of layers) on the shape transformation of lipid bilayer vesicles. Since the evolutionary models are considered as a generalization to the equilibrium methods, the used model is developed based on the dynamic equilibrium between the membrane bending potential and the environmental fluid friction in each domain of two-phase vesicle. The effect of membrane inertia on the dynamics of the system is ignored. Key parameters are the size of each phase and different combinations of protein distribution as the local spontaneous curvature. Assumed initial conditions are simple shapes such as dumbbell, biconcave and oblate that free vesicles are usually visible in these shapes. Previously published experimental observations are used to evaluate the numerical results. Some situations of homogeneous and multi-phase vesicles and red blood cells under the influence of the spontaneous curvature induction mechanisms (for example the composition of the membranes, membrane proteins such as albumin, environmental solution concentration changes) are simulated and the results presented in details. The possibility of the membrane deformation and the relation of membrane phenomena with the primary form and various curvature distributions are discussed.