An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Algorithm 3

Chaotic search for scout bees.

(1) Set the maximum number of chaotic iteration 𝐾=100 and iterative variable 𝑘=1

  // The variable 𝑐𝑥_𝑘,𝑗 denotes the 𝑗th chaotic variable in the 𝑘th iteration

(2) for  𝑗=1 to 𝐷  do

(3) 𝑐𝑥_𝑘,𝑗=(𝑥_𝑖,𝑗−𝑥^𝑗_min)/(𝑥^𝑗_max−𝑥^𝑗_min)

(4) end for

(5) while  𝑘<𝐾  do

(6)  for  𝑗=1 to 𝐷  do

(7)  𝑐𝑥_𝑘+1,𝑗=4𝑐𝑥_𝑘,𝑗(1−𝑐𝑥_𝑘,𝑗)

   // 𝑉=[𝑣₁,…,𝑣_𝐷] represents a candidate solution

(8)  𝑣_𝑗=𝑥^𝑗_min+𝑐𝑥_𝑘+1,𝑗(𝑥^𝑗_max−𝑥^𝑗_min)

(9)  end for

   // Greedy selection is applied between {𝑉,𝑋_𝑖}

(10) if  𝑓(𝑉)>𝑓(𝑥_𝑖)

(11)   Replace solution 𝑋_𝑖 with candidate solution 𝑉

(12)   Set 𝑡𝑟𝑖𝑎𝑙=0

(13)   Break

(14) else

(15)   Set 𝑡𝑟𝑖𝑎𝑙(𝑖)=𝑡𝑟𝑖𝑎𝑙(𝑖)+1

(16) end if

(17) Set 𝑘=𝑘+1

(18) end while