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

Algorithm 2

Chaotic initialization.

(1) Set population size SN and dimension of solution 𝐷

  //Randomly generate the initial value of chaotic variable 𝑐𝑥_𝑖,𝑗

(2) for   𝑗=1 to 𝐷   do

(3)    𝑐𝑥_1,𝑗=rand(0,1)

(4)    while   𝑐𝑥_1,𝑗∈{0,0.25,0.5,0.75,1}   do

(5)    𝑐𝑥_1,𝑗=rand(0,1)

(6)    end while

(7) end for

  // The iterative process of chaotic initialization

(8) for   𝑖=1 to SN  do

(9)    for   𝑗=1 to 𝐷   do

(10)    𝑥_𝑖,𝑗=𝑥^𝑗_min+𝑐𝑥_𝑖,𝑗𝑥^𝑗_max−𝑥^𝑗_min

(11)    𝑐𝑥_𝑖+1,𝑗=4𝑐𝑥_𝑖,𝑗1−𝑐𝑥_𝑖,𝑗

(12)   end for

(13) end for