A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization

Algorithm 3

The hybrid meta-heuristic algorithm of HS/BA.

Begin

 Step  1: Initialization. Set the generation counter 𝑡=1; initialize the population of NP

    bats 𝑃 randomly and each bat corresponding to a potential

    solution to the given problem; define loudness 𝐴; set frequency 𝑄,

    the initial velocities 𝑣, and pulse rate 𝑟; set the harmony memory consideration

    rate HMCR, the pitch adjustment rate PAR and bandwidth bw;

    set maximum of elite individuals retained KEEP.

 Step  2: Evaluate the quality 𝑓 for each bat in 𝑃 determined by the objective function 𝑓(𝑥).

 Step  3: While the termination criteria is not satisfied or 𝑡 < MaxGeneration do

     Sort the population of bats 𝑃 from best to worst by order of quality 𝑓 for each bat.

     Store the KEEP best bats as KEEPBAT.

     for  𝑖=1:NP (all bats) do

         𝑣^𝑡_𝑖=𝑣_𝑖^𝑡−1+(𝑣^𝑡_𝑖−𝑥_∗)×𝑄

         𝑥^𝑡_𝑖=𝑥_𝑖^𝑡−1+𝑣^𝑡_𝑖

         if (rand > 𝑟) then

           𝑥^𝑡_𝑢=𝑥_∗+𝛼𝜀^𝑡

         end if

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

           if  (rand<HMCR)  then

            𝑟₁=⌈NP∗rand⌉

            𝑥_𝑣𝑗=𝑥_𝑟1𝑗 where 𝑟₁∈(1,2,…,HMS)

            if (rand < PAR)  then

               𝑥_𝑣𝑗=𝑥_𝑣𝑗+bw×(2×rand−1)

            endif

           else

             𝑥_𝑣(𝑗)=𝑥_min,𝑗+rand×(𝑥_max,𝑗−𝑥_min−𝑗)

           endif

         endfor  𝑗

         Evaluate the fitness for the offsprings 𝑥^𝑡_𝑢, 𝑥^𝑡_𝑖, 𝑥^𝑡_𝑣

         Select the offspring 𝑥^𝑡_𝑘 with the best fitness among the offsprings 𝑥^𝑡_𝑢, 𝑥^𝑡_𝑖, 𝑥^𝑡_𝑣.

         if (rand < 𝐴) then

          𝑥^𝑡_𝑟1=𝑥^𝑡_𝑘;

         end if

         Replace the KEEP worst bats with the KEEP best bats KEEPBAT stored.

     end for 𝑖

     𝑡=𝑡+1;

 Step  4: end while

 Step  5: Post-processing the results and visualization;

End.