Table 1 Pseudo code of the Monte-Carlo algorithm with simulated annealing

σ =σ ₀

While T > T _low

   Repeat t time

choose random $\tilde{\sigma }\in N\left(\sigma \right)$

If $\eta \left(\tilde{\sigma }\right)\le \eta \left(\sigma \right)$

$\sigma =\tilde{\sigma }$

Else

x = random(0, 1)

If $x<e\frac{-\eta (\tilde{\sigma })+(\sigma )}{T}$

$\sigma =\tilde{\sigma }$

   T = T * 0.9

Return σ and η(σ)