Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

Algorithm 2

OHS Algorithm.

Step 1. Set the parameters, 𝐻𝑀𝑆,𝐻𝑀𝐶𝑅,𝑝𝑎𝑟𝑎^min,𝑝𝑎𝑟𝑎^max,𝐵𝑊^min,𝐵𝑊^max, and 𝑁𝐼.

Step 2. Initialize the HM with 𝑋_0𝑖,𝑗.

Step 3. Opposition based HM initialization.

     for (𝑖=0;𝑖<𝐻𝑀𝑆;𝑖++)

     for (𝑗=0;𝑗<𝑛;𝑗++)

      𝑂𝑋_0𝑖,𝑗=𝑝𝑎𝑟𝑎_𝑗^min+𝑝𝑎𝑟𝑎_𝑗^max−𝑋_0𝑖,𝑗    // 𝑂𝑋₀: Opposite of initial X ₀

     end for

     end for

     // End of Opposition-based HM initialization.

     Select HMS fittest individuals from set of 𝑋_0𝑖,𝑗,𝑂𝑋_0𝑖,𝑗 as initial HM; HM being

     the matrix of fittest X vectors

Step 4. Improvise a new harmony 𝑋^new as follows:

     Update 𝑃𝐴𝑅(𝑔𝑛) by (14) and 𝐵𝑊(𝑔𝑛) using (15).

     for (𝑖=0;𝑖<𝐻𝑀𝑆;𝑖++)

     for 𝑗=0;𝑗<𝑛;𝑗++

        if (𝑟₁<𝐻𝑀𝐶𝑅) then

         𝑋^new_𝑖,𝑗=𝑋^𝑎_𝑖,𝑗             // 𝑎∈(1,2,…,𝐻𝑀𝑆)

          if 𝑟₂<𝑃𝐴𝑅𝑔𝑛 then

           𝑋^new_𝑖,𝑗=𝑋^new_𝑖,𝑗±𝑟₃×𝐵𝑊(𝑔𝑛)         // 𝑟₁,𝑟₂,𝑟₃∈[0,1]

          end if

        else

          𝑋^new_𝑖,𝑗=𝑝𝑎𝑟𝑎^min_𝑖,𝑗+𝑟×𝑝𝑎𝑟𝑎^max_𝑖,𝑗−𝑝𝑎𝑟𝑎^min_𝑖,𝑗        // 𝑟∈[0,1]

        end if

     end for

   end for

Step 5. Update the HM as 𝑋^worst=𝑋^new if 𝑓𝑋^new<𝑓𝑋^worst

Step 6. Opposition based generation jumping

     if 𝑟𝑎𝑛𝑑₂<𝐽_𝑟                     // 𝑟𝑎𝑛𝑑₂∈[0,1], 𝐽_𝑟:

     Jumping rate

      for (𝑖=0;𝑖<𝐻𝑀𝑆;𝑖++)

       for (𝑗=0;𝑗<𝑛;𝑗++)

        𝑂𝑋_𝑖,𝑗=min_𝑗^𝑔𝑛+max_𝑗^𝑔𝑛−𝑋_𝑖,𝑗

        // min_𝑗^𝑔𝑛: minimum value of the jth variable in the current generation (gn)

        // max_𝑗^𝑔𝑛: maximum value of the jth variable in the current generation (gn)

         Select 𝐻𝑀𝑆 fittest HM from the set of 𝑋_𝑖,𝑗,𝑂𝑋_𝑖,𝑗 as current HM.

        end for

       end for

      end if

      // End of opposition-based generation jumping.

Step 7. If 𝑁𝐼 is completed, return the best harmony vector 𝑋^best in the HM; otherwise go back to Step 4.