Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint

Algorithm 3

Modified firefly algorithm.

Generate initial population of fireflies 𝑥_𝑖 and 𝑧_𝑖 (𝑖=1,2,3,…,𝑆𝑁) by using (33) and (35)

Apply arrangement algorithm

Light intensity 𝐼_𝑖 at point 𝑥_𝑖 is defined by 𝑓(𝑥)

Define light absorption coefficient 𝛾

Define number of iterations IN

Calculate fitness and CV for all fireflies using (26) and (36)

Set initial values for 𝛼

Set 𝑡 value to 0

while  𝑡<𝐼𝑁  do

 for  𝑖=1 to SN  do

  for  𝑗=1 to 𝑖  do

   if  𝐼_𝑖<𝐼_𝑗  then

    Move firefly 𝑖 towards firefly 𝑗 in 𝑑 dimension using (37) and (38)

    Attractiveness varies with distance 𝑟 via exp[−𝛾𝑟]

    Evaluate new solution, replace worse with better solution

    using Deb’s method and update light intensity

    if  solution 𝑖 is not improved and 𝑡_𝑖<𝐸𝐵𝑃  then

     𝑈𝐼𝐶_𝑖 increment by 1

    else

     𝑈𝐼𝐶_𝑖 set to 0

    end if

   end if

  end for

 end for

 if  𝑡<𝐸𝐵𝑃  then

  replace all agents whose UIC > AT with random agents using (33)

 end if

 Apply arrangement algorithm

 Rank all fireflies and find the current best

 Recalculate values for 𝛼 using (39)

end while