In this paper, a fast migration method is proposed. Our method executes local relocation on a model placement where an additional module is added to it for modification with a minimum number of displacements. This method is based on mean-field annealing (MFA), which produces a solution as reliable as a previously used method called simulated annealing. The proposed method requires substantially less time and hardware, and it is less sensitive to the initial and final temperatures. In addition, the solution runtime is mostly independent of the size and complexity of the input model placement. Our proposed MFA algorithm is optimized by enabling module rotation inside an energy function called permissible distances preservation energy. This, in turn, allows more options in moving the engaged modules. Finally, a three-phase cooling process governs the convergence of problem variables called neurons or spins.