A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory

Pseudocode 2

Input: Objective function 𝑓(𝑥),𝑥=[𝑥₁,𝑥₂,…,𝑥_𝑑]^𝑇; algorithm’s parameters 𝑛,𝑓_min,𝑓_max,𝛼,𝑛_𝑡;

BEGIN

 For 𝑖=1 To 𝑛 do

  Initialize 𝑥^𝑡_𝑖, 𝑟⁰_𝑖, 𝐴⁰_𝑖;

  Calculating the initial fitness;

 End For

 While (𝑡<iter_max)

  Update position use formula (8)~(12);

  Evaluate fitness 𝑓𝑥_𝑖 to find 𝑥_best;

  For 𝑖=1 To 𝑛 do

   If (rand >𝑟_𝑖)

    Generate a 𝑥_new around the selected best solution use formula (2);

   End If

  End For

  Evaluate fitness 𝑓(𝑥_new);

  For 𝑖=1 To 𝑛 do

   If (rand <𝐴_𝑖)

    Generate a 𝑥_new around the selected best solution use formula (13);

   End If

  End For

  Evaluate fitness 𝑓(𝑥_new);

  If (𝑓(𝑥^𝑡+1_best)<𝑓(𝑥^𝑡_best))

    Update 𝑟^𝑡_𝑖, 𝐴^𝑡_𝑖 use formula (3), (14);

  End If

  𝑡 = 𝑡+1;

 End While

END

Output: 𝑥_best,fitness_min;