Simulated Annealing

Simulated annealing is oriented in crystallization procedures in nature where the lowest energy state is achieved only when the temperature is lowered very slowly.

The temperature in nature is equivalent to fast the change in the system decreases. Parameters

  • Cost function


  • Easy to implement
  • Converges


  • expensive (takes forever)


Note that the original algorithm has an inner loop where is not changed. I do not see a reason for it.

  • while true
    • choose new state randomly
    • calculate difference in energy levels:
    • change state with probability:
    • Update occasionally

Mean-field Annealing

The idea of mean-field annealing is to estimate with . is updated with every temperature level .

The transition probabilities between to states are symmetric.

Is Markov Process.

Gibbs-Boltzmann-distribution (is symmetric)

Factorizing distribution


  • while true
    • calculate mean-fields
    • calculate moments
    • until