A Cuckoo Search Algorithm for Multimodal Optimization

Procedure 1

(1) Define two new temporal vectors 𝐙 and 𝐘. The vector 𝐙 will hold the results of the iterative

   operations whereas 𝐘 will contain the final memory configuration. The vector 𝐙 is initialized with

   the elements of 𝐌 that have been sorted according to their fitness values, so that the first element

   represents the best one. On other hand, 𝐘 is initialized empty.

(2) Store the best element 𝐳₁ of the current 𝐙 in 𝐘.

(3) Calculate the Euclidian distances Δ_1,𝑗 between 𝐳₁ and the rest of elements from 𝐙  𝑗∈{2,…,|𝐙|},

   where |𝐙| represents the number of elements in 𝐙.

(4) Sort the distances Δ_1,𝑗 according to their magnitude. Therefore, a new index 𝑎 is incorporated to

   each distance Δ^𝑎_1,𝑗, where a indicate the place of Δ_1,𝑗 after the sorting operation. (𝑎=1 represents the shortest distance).

(5) Calculate the depuration ratio 𝐷_𝑅:

     for  𝑞=1  to  |𝐙|−1

    Obtain the element 𝐳_𝑗 corresponding to the distance Δ^𝑞_1,𝑗

    Compute 𝑓((𝐳₁+𝐳_𝑗)/2)

       if  (𝑓((𝐳₁+𝐳_𝑗)/2)>𝑓(𝐳₁) and 𝑓((𝐳₁+𝐳_𝑗)/2)>𝑓(𝐳_𝑗))

       𝐷_𝑅=0.85⋅𝐱₁−𝐱_𝑗

      break

      end  if

       if  𝑞=|𝐙|−1

       There is only one concentration

       end  if

     end  for

(6) Remove all elements inside 𝐷_𝑅 from 𝐙.

(7)  Sort the elements of 𝐙 according to their fitness values.

(8)  Stop, if there are more concentrations, otherwise return to Step 2.