A Local and Global Search Combined Particle Swarm Optimization Algorithm and Its Convergence Analysis

Pseudocode 1

Step  1: Let parameters; including swarm size PS, maximum of generation endgen and others

    parameters will be used in LGSCPSO algorithm.

Step  2: Iteration process

  (i) Generate stochastically initialization population and velocity;

  (ii) Evaluate each particle’s fitness;

  (iii) Initialize 𝑔𝐵𝑒𝑠𝑡 position with the lowest fitness particle in the whole swarm;

  (iv) Initialize 𝑝𝐵𝑒𝑠𝑡 position with a copy of particle itself;

  (v) Initialize 𝑙𝐵𝑒𝑠𝑡 position with the best particle of initializing population;

  (vi) k ≔ 0;

While (the maximum endgen of generation is not met)

{

  (i) k ≔𝑘+1;

  (ii) Generate next swarm by (3), (4);

  (iii) Evaluate swarm;

   { (a) Compute each particle’s fitness in the swarm;

      (b) Find new 𝑃_𝑔, 𝑃_𝑙 of the swarm and 𝑃_𝑖 of each particle by comparison, and update 𝑃_𝑖 and 𝑃_𝑔;

      (c) Update 𝑃_𝑙 using the best particle of 𝑘 generation colony;}

}

Step  3: Output optimization results.