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

Algorithm 1

HS method.

Begin

  Step  1. Initialize the HM.

  Step  2. Evaluate the fitness.

  Step  3.  while the halting criteria is not satisfied do

       for  𝑑=1 : D  do

         if  rand < HMCR then  // memory consideration

           𝑥_new(𝑑)=𝑥_𝑎(𝑑)  where  𝑎∈(1,2,…,HMS)

           if rand < PAR then   // pitch adjustment

             𝑥_new(𝑑)=𝑥_old(𝑑)+𝑏𝑤×(2×rand−1)

           endif

         else           // random selection

           𝑥_new(𝑑)=𝑥_min,𝑑+rand×(𝑥_max,𝑑−𝑥_min−𝑑)

         endif

       endfor d

       Update the HM as  𝑥_𝑤=𝑥_new,  if  𝑓(𝑥_new)<𝑓(𝑥_𝑤)  (minimization objective)

       Update the best harmony vector

  Step  4. end  while

  Step  5.  Output results.

End.