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

Algorithm 2

Arrangement algorithm.

while  𝐾^∗_𝑖<𝐾  do

 select random asset 𝑗 such that 𝑗∉𝑄

 𝑧_𝑖,𝑗=1,𝑄=𝑄∪[𝑗],𝐾^∗_𝑖=𝐾^∗_𝑖+1

end while

while  𝐾^∗_𝑖>𝐾  do

 select random asset 𝑗 such that 𝑗∈𝑄

 𝑧_𝑖,𝑗=1,𝑄=𝑄−[𝑗],𝐾^∗_𝑖=𝐾^∗_𝑖−1

end while

while  true  do

 𝜃=∑_𝑗∈𝑄𝑥_𝑖,𝑗,𝑥_𝑖,𝑗=𝑥_𝑖,𝑗𝜓,𝜂=∑_𝑗∈𝑄max0,𝑥_𝑖,𝑗−𝛿_𝑖,𝜙=∑_𝑗∈𝑄max0,𝜂_𝑗−𝑥_𝑖,𝑗

 if  𝜂=0 and 𝜙=0  then

  exit algorithm

 end if

 for  𝑗=1 to 𝑁  do

  if  𝑧_𝑖,𝑗=1  then

   if  𝑥_𝑖,𝑗>𝛿_𝑗  then

    𝑥_𝑖,𝑗=𝛿_𝑗

   end if

   if  𝑥_𝑖,𝑗<𝜀_𝑗  then

    𝑥_𝑖,𝑗=𝜀_𝑗

   end if

  end if

 end for

end while