Simulated Annealing

Simulated Annealing - Solutions

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Describe the concept of an annealing schedule.

Answer: An annealing schedule is a scheme for lowering the simulated temperature from time to time, after allowing the system to reach equilibrium at each new temperature.
Describe the essence of the Metropolis algorithm.

Answer: In the Metropolis algorithm, a unit is chosen at random and subjected to a small displacement, and the resulting change in energy ΔE of the system is computed. If ΔE ≤ 0, the displacement is unconditionally accepted, while if ΔE > 0, the displacement is accepted with probability pexp(–ΔE/T, where p is a constant and T is the pseudo-temperature. This process is repeated until the system reaches equilibrium.
What is the purpose of allowing displacements that increase the energy E in an algorithm that aims to minimise E?

Answer: This is to allow the system to escape from local minima of the energy landscape.