Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems

Algorithm 1

The basic steps of the cuckoo search.

(1)  Basic  parameters'  setting  Objective function 𝑓(𝑥),𝑥=𝑥₁,…,𝑥_𝑑,

  initial population of 𝑛 host nests 𝑥_𝑖(𝑖=1,2,…,𝑛), boundaries for each

  dimension 𝑥_𝑖=𝑥_𝑖,1,…,𝑥_𝑖,𝑑 and so forth.

(2)  While  Termination condition is not satisfied  do

(3)   Get a cuckoo (𝑖,𝑖=1,2,…,𝑛) randomly by Lévy flights (28).

(4)    Evaluate its fitness 𝐹_𝑖;

(5)    If  𝐹_𝑖>𝐹_𝑗

(6)    Replace 𝑗 by the new solution

(7)    End

(8)    Abandon a fraction 𝑝_𝑎 of worse nests.

(9)    Build new ones at new locations via Lévy flights (28) (𝑖,𝑖=1,2,…,𝑛).

(10)    Keep the best solutions (or nests with quality solutions).

(11)     Rank the solutions and find the current best.

(12)  end  while

(13)  Output  Global optimum 𝑄_𝑔