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

Algorithm 4

Modified artificial bee colony algorithm.

(1) Set population size SN, the number of maximum cycles MCN and the control parameter 𝑙𝑖𝑚𝑖𝑡

(2) Perform Algorithm 2 to fulfill the chaotic initialization of population 𝑥_𝑖(𝑖=1,2,…,SN), and calculate

  their objective function values and fitness value values. Set 𝑡𝑟𝑖𝑎𝑙(𝑖)=0(𝑖=1,2,…,SN) and 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛=1

(3) while  iteration ≤MCN   do

  // The employed bees phase

(4)   for   𝑖=1 to SN  do

(5)    Produce a new candidate food source 𝑉_𝑖 corresponding to food source 𝑋_𝑖 using (24)

(6)    if   (𝑓(𝑉_𝑖)>𝑓(𝑋_𝑖))   Then   𝑡𝑟𝑖𝑎𝑙(𝑖)=0

(7)    else   𝑡𝑟𝑖𝑎𝑙(𝑖)=𝑡𝑟𝑖𝑎𝑙(𝑖)+1

(8)    end if

(9)   end for

(10)  Calculate the fitness values of all food sources and the probability values 𝑝_𝑖 by using (15)

  // The onlooker bees phase

(11)  Set 𝑡=0,𝑖=1

(12)   while   𝑡<SN   do

(13)    if   𝑟𝑎𝑛𝑑𝑜𝑚()<𝑝_𝑖   then

(14)   Set 𝑡=𝑡+1

(15)   Produce a new candidate food source 𝑉_𝑖 for the onlooker bee corresponding to food source 𝑋_𝑖 using (24)

(16)   if   𝑓(𝑉_𝑖)>𝑓(𝑋_𝑖)   then

(17)    𝑡𝑟𝑖𝑎𝑙(𝑖)=0

(18)   else   𝑡𝑟𝑖𝑎𝑙(𝑖)=𝑡𝑟𝑖𝑎𝑙(𝑖)+1

(19)   end if

(20)    end if

(21)   Set 𝑖=𝑖+1

(22)      if   𝑖>SN   then   𝑖=1

(23)      end if

(24)   end while

  //The scout bees phase

(25)   for   𝑖=1 to SN  do

(26)    if   𝑡𝑟𝑖𝑎𝑙(𝑖)>𝑙𝑖𝑚𝑖𝑡   then

(27)     Perform Algorithm 3 to implement chaotic search

(28)    end if

(29)   end for

(30)  Set 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛=𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛+1

(31) end while