Simulated annealing: in mathematical global optimization computation, hybrid with local or global search, and practical applications in crystallography and molecular modelling

Simulated annealing (SA) was inspired from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects, both are attributes of the material that depend on its thermodynamic free energy. In this Paper, firstly we will study SA in details on its initial feasible solution choosing, initial temperature selecting, neighborhood solution searching, efficient way of calculating for the difference of objective function values of two neighborhood solutions, acceptance function (Metropolis function), temperature cooling, and the criteria of inner and outer loops’ stopping, etc. Then, hybrid pure SA with local (or global) search optimization methods allows us to be able to design several effective and efficient global search optimization methods. In order to keep the original sense of SA, we clarify our understandings of SA in crystallography and molecular modeling field through the studies of prion amyloid fibrils.