Application of Artificial Bee Colony Algorithm to Portfolio Adjustment Problem with Transaction Costs

Algorithm 3

Chaotic search for scout bees.

(1) Set the maximum number of chaotic iteration max𝐾=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_min𝑥^𝑗_max−𝑥^𝑗_min

(4) end for

  // The iterative process of chaotic search

(5) while   𝑘<max𝐾   do

(6)    for   𝑗=1 to 𝐷   do

(7)    𝑐𝑥_𝑘+1,𝑗=4𝑐𝑥_𝑘,𝑗1−𝑐𝑥_𝑘,𝑗

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

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

(9)    end for

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

(10)   if   𝑓(𝑉)>𝑓𝑥_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