Algorithm 1: Particle swarm optimization

Input: POP, Dim, T, [lb, ub], [vmin, vmax].

Output: Best_fitness, Best_pos.

1: Initialize population with random positions and velocities within the search space [lb, ub].

2: Evaluate fitness for each particle

3: Update personal best position (pBest_Pos) and personal best fitness (pBest_fitness) if necessary.

4: Determine if the maximum T has been reached.

5: Update (pBest_Pos) and pBest_fitness based on the best particle’s position and the fitness. Update based on the position and fitness of the best particles (pBest_Pos) and pBest_fitness.

6: Record the best fitness value in the iteration.

7: Update the inertia weight $\omega$ if necessary.

8: Reached cycle count T, ending cycle.

9: Return pBest_Pos and pBest_fitness.