An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization

Algorithm 3

HS/FA method.

Begin

  Step  1. Initialization. Set 𝑡=1; define 𝛾; set 𝛼, 𝛽₀ at 𝑟=0; set HMCR and PAR; set the

     number of top fireflies KEEP.

  Step  2. Evaluate the light intensity I.

  Step  3. While  t < MaxGeneration do

      Sort the fireflies by light intensity I;

      for  𝑖=1 : KEEP (all Top fireflies) do

         for  𝑗=1 : NP (all fireflies) do

           if  (𝐼_𝑗<𝐼_𝑖)  then

             Move firefly i towards j;

           else

               for  𝑘=1 : D (all elements) do  // Mutate

              if  (rand < HMCR) then

                𝑟₁=⌈NP∗rand⌉

                𝑥_𝜈(𝑘)=𝑥_𝑟1(𝑘)

                if (rand < PAR) then

                  𝑥_𝜈(𝑘)=𝑥_𝜈(𝑘)+𝑏𝑤×(2×rand−1)

                end if

              else

                𝑥_𝜈(𝑘)=𝑥_min,𝑘+rand×(𝑥_max,𝑘−𝑥_min,𝑘)

              end if

               end for  k

           end if

          Update attractiveness;

          Update light intensity;

         end for  j

      end for  i

      Evaluate the light intensity I.

      Sort the population by light intensity I;

       𝑡=𝑡+1;

  Step  4. end while

End.