Chaotic Multiquenching Annealing Applied to the Protein Folding Problem

Algorithm 1

MQP pseudocode.

(1)   Multi-quenching Phase Procedure( )

(2) Begin

(3)  //Setting section

(4)  𝑇₀ = Initial Temperature, 𝑇=𝑇₀

(5)  𝑇_Threshold = initial value

(6)  AlphaQuenching = initial value, tau = initial value

(7)  //Creation of initial solution

(8)  𝑆_𝑖 = Initial solution; E(𝑆_𝑖) = Energy(𝑆_𝑖);

(9)  𝑆_min = 𝑆_𝑖; E(𝑆_min) = E(𝑆_𝑖)

(10)  //Multi-quenching Cycles

(11)  Repeat //External Cycle (Temperature Cycle)

(12)    Repeat //Internal Cycle (Metropolis Cycle)

(13)      𝑆_𝑗 = Perturbation (𝑆_𝑖) //Uniform perturbation

(14)      DE = E(𝑆_𝑗) − E(𝑆_𝑖)

(15)      If DE ≤ 0 Then

(16)        𝑆_𝑖=𝑆_𝑗

(17)      else if e ^∧(−DE/T) > random [0,1] Then

(18)        𝑆_𝑖=𝑆_𝑗

(19)      end if

(20)      If 𝑆_𝑖 < 𝑆_min then //save 𝑆_min

(21)        𝑆_min = 𝑆_𝑖; E(𝑆_min) is saved

(22)      end if

(23)    Until Metropolis Cycle is Finish

(24)    tau = tau ^∧2

(25)    If (tau is very to close 0) Then

(26)      tau = initial value

(27)      Call Chaotic Search Procedure( )

(28)    end if

(29)    T = AlphaQuenching (1 − tau) T

(30)  Until T > 𝑇_Threshold //External Cycle

(31)  End procedure