Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and both perturbation analysis of the system and numerical simulations of the corresponding nonlinear dynamic equation governing the film morphological profile. Three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of island array stabilization, which corresponds to the formation of steady but nonordered arrays of strained quantum dots, occurs at later time for smaller misfit strain. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical studies on quantum dot coarsening and stabilization.