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

Pseudocode 1

Objective function 𝑓(𝑥),𝑥=[𝑥₁,𝑥₂,…,𝑥_𝑑]^𝑇

Initialize the bat population 𝑥_𝑖(𝑖=1,2,…,𝑛) and 𝑣_𝑖

Define pulse frequency 𝑓_𝑖 at 𝑥_𝑖 initialize pulse rates 𝑟_𝑖 and the loudness 𝐴_𝑖

While (𝑡< Max number of iterations)

 Generate new solutions by adjusting frequency,

 and updating velocities and locations/solutions (1)

 if (rand >𝑟_𝑖)

  Select a solution among the best solutions

  Generate a local solution around the selected best solution

 end if

 Generate a new solution by flying randomly

 if (rand <𝐴_𝑖 & 𝑓(𝑥_𝑖)<𝑓(𝑥_∗))

  Accept the new solutions

  Increase 𝑟_𝑖 and reduce 𝐴_𝑖

 end if

 Rank the bats and find the current best 𝑥_∗

end while

Postprocess results and visualization