An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Algorithm 4

Modified ABC 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

(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 (29)

(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 source and the probability values 𝑝_𝑖 by using (27)

     // 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

(16)    if  𝑓(𝑉_𝑖)>𝑓(𝑋_𝑖)  then  𝑡𝑟𝑖𝑎𝑙(𝑖)=0

(17)    else  𝑡𝑟𝑖𝑎𝑙(𝑖)=𝑡𝑟𝑖𝑎𝑙(𝑖)+1

(18)    end if

(19)  Set 𝑖=𝑖+1

(20)   if  𝑖 > SN  then  Set 𝑖=1

(21)   end if

(22)  end while

     // The scout bees phase  

(23)  for  𝑖=1 to SN  do

(24)   if  𝑡𝑟𝑖𝑎𝑙(𝑖) ≥ SN  then

(25)   Perform Algorithm 3 to implement chaotic search

(26)   end if

(27)  end for

(28) Set 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛=𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛+1

(29) end while