We present a technique for the structural optimization of atom models to study long time relaxation processes involving different time scales. The method takes advantage of the benefits of both the kinetic Monte Carlo ͑KMC͒ and the molecular dynamics simulation techniques. In contrast to ordinary KMC, our method allows for an estimation of a true lower limit for the time scale of a relaxation process. The scheme is fairly general in that neither the typical pathways nor the typical metastable states need to be known prior to the simulation. It is independent of the lattice type and the potential which describes the atomic interactions. It is adopted to study systems with structural and/or chemical inhomogeneity which makes it particularly useful for studying growth and diffusion processes in a variety of physical systems, including crystalline bulk, amorphous systems, surfaces with adsorbates, fluids, and interfaces. As a simple illustration we apply the locally activated Monte Carlo to study hydrogen diffusion in diamond.