We searched for the minimum energy state of a three-atom dipolar cluster at a wide range of atomic dipole moment by simulated annealing and nongradient optimization. At the intermediate dipole moment (mu) range in which both the close pack and the linear states are of similar energy, the search for the lower energy close pack minimum requires a careful choice of initial guess. The isomerization pathway was followed along an assumed minimum energy path and the minimum energy cluster at a given isomerization coordinate was optimized with constraint imposed on the movement of atoms. The transition state was generally not located halfway along the assumed minimum energy path. The activation barrier was found to be lower than the inversion barrier of LJ(3) (mu=0). The origin of the difficulty of searching for the close pack structure at intermediate mu appears to be its narrow range of phase space on the asymmetric potential surface. The contribution of the dipole energy to the total (%E) reveals the mu dependence for both isomers such that both isomers are dipole dominated structures at high mu.