Convergence Time Analysis of Particle Swarm Optimization Based on Particle Interaction

Algorithm 2

Statistical model of social-only PSO. Distribution 𝜃 is represented by 𝜇=(𝜇₁,𝜇₂,…,𝜇_𝑛) and 𝜎=(𝜎₁,𝜎₂,…,𝜎_𝑛). Acceleration coefficient 𝐶∼𝑈(0,𝑐).

procedure STATISTICAL INTERPRETATION OF SOCIAL-ONLY PSO (Objective

Function ℱ∶ℝ^𝑛→ℝ)

   Initialize: 𝜎←𝜎₀,𝜇←𝜇₀

   while the stopping criterion is not satisfied do

    for  𝑖=1,2,…,𝑚  do

     for  𝑗=1,2,…,𝑛  do

       𝐏_𝐢𝑗∼𝑁(𝜇_𝑗,𝜎²_𝑗)

     end for

    end for

     𝐏_𝐚=min_𝐏𝐢{ℱ(𝐏_𝐢)}

     for  𝑖=1,2,…,𝑚  do

     for  𝑗=1,2,…,𝑚  do

       𝐏^′_𝐢𝑗←𝐏_𝐢𝑗+𝐶(𝐏_𝐚𝑗−𝐏_𝐢𝑗)

     end for

     end for

   𝜇←(∑^𝑚_𝑖=1𝐏^′_𝐢)/𝑚

   𝜎²←MLE(𝐏^′_𝟏,𝐏^′_𝟐,…,𝐏^′_𝐦)

  end while

end procedure