FINITE-TIME SCALING OF ENERGY IN SIMULATED ANNEALING

The energy of a local minimum obtained by the simulated annealing generally depends on a time-tau in which a complex system has been immersed in a heat bath. How the resultant energy E(tau) scales with a time-tau is an interesting question. The diffusion process of a point in a wiggly parabola is analysed to discuss the scaling. The model is exactly solvable and the energy is found to scale as E(tau) = epsilon + c(ln-tau)-1. This scaling is considered rather common to general complex systems. However, the limit epsilon obtained from practical data is not necessarily the ground state energy of a system.