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Inputs:
  Population size (N)
  Maximum number of iterations (max_iter)
  Inertia weight (w)
  Cognitive influence factor (c1)
  Social influence factor (c2)

Initialization:
  Initialize the population of particles randomly within the search space
  Initialize particle velocities randomly
  Initialize personal best (Pbest) positions for each particle
  Initialize global best (Gbest) position

Main Loop:
  Repeat for each iteration until max_iter is reached:
    For eachparticle i in the population:
      Calculate the fitness value of particle i's current position

      Update Pbest for particle i:
        If the fitness of particle i's current position is better than its previous Pbest fitness:
          Update particle i's Pbest position

      Update Gbest:
        If the fitness of particle i's current position is better than the fitness of Gbest:
          Update Gbest position to particle i's current position

      Update particle velocity and position:
        For each dimension d in the particle's position and velocity:
          Generate random values r1 and r2

          Update particle velocity:
            New velocity = (w * old velocity) + (c1 * r1 * (Pbest - current position)) + (c2 * r2 * (Gbest - current position))

          Update particle position:
            New position = current position + new velocity

          Ensure particle position is within the boundaries of the search space

End of Main Loop

Output:
  Return the Gbest position as the optimal solution
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