Implementation of Particle Swarm Optimization

# python implementation of particle swarm optimization (PSO)
# minimizing rastrigin and sphere function

import random
import math    # cos() for Rastrigin
import copy    # array-copying convenience
import sys     # max float


#-------fitness functions---------

# rastrigin function
def fitness_rastrigin(position):
  fitnessVal = 0.0
  for i in range(len(position)):
    xi = position[i]
    fitnessVal += (xi * xi) - (10 * math.cos(2 * math.pi * xi)) + 10
  return fitnessVal

#sphere function
def fitness_sphere(position):
    fitnessVal = 0.0
    for i in range(len(position)):
        xi = position[i]
        fitnessVal += (xi*xi);
    return fitnessVal;
#-------------------------

#particle class 
class Particle:
  def __init__(self, fitness, dim, minx, maxx, seed):
    self.rnd = random.Random(seed)

    # initialize position of the particle with 0.0 value
    self.position = [0.0 for i in range(dim)]

     # initialize velocity of the particle with 0.0 value
    self.velocity = [0.0 for i in range(dim)]

    # initialize best particle position of the particle with 0.0 value
    self.best_part_pos = [0.0 for i in range(dim)]

    # loop dim times to calculate random position and velocity
    # range of position and velocity is [minx, max]
    for i in range(dim):
      self.position[i] = ((maxx - minx) *
        self.rnd.random() + minx)
      self.velocity[i] = ((maxx - minx) *
        self.rnd.random() + minx)

    # compute fitness of particle
    self.fitness = fitness(self.position) # curr fitness

    # initialize best position and fitness of this particle
    self.best_part_pos = copy.copy(self.position) 
    self.best_part_fitnessVal = self.fitness # best fitness

# particle swarm optimization function
def pso(fitness, max_iter, n, dim, minx, maxx):
  # hyper parameters
  w = 0.729    # inertia
  c1 = 1.49445 # cognitive (particle)
  c2 = 1.49445 # social (swarm)

  rnd = random.Random(0)

  # create n random particles
  swarm = [Particle(fitness, dim, minx, maxx, i) for i in range(n)] 

  # compute the value of best_position and best_fitness in swarm
  best_swarm_pos = [0.0 for i in range(dim)]
  best_swarm_fitnessVal = sys.float_info.max # swarm best

  # computer best particle of swarm and it's fitness
  for i in range(n): # check each particle
    if swarm[i].fitness < best_swarm_fitnessVal:
      best_swarm_fitnessVal = swarm[i].fitness
      best_swarm_pos = copy.copy(swarm[i].position) 

  # main loop of pso
  Iter = 0
  while Iter < max_iter:
    
    # after every 10 iterations 
    # print iteration number and best fitness value so far
    if Iter % 10 == 0 and Iter > 1:
      print("Iter = " + str(Iter) + " best fitness = %.3f" % best_swarm_fitnessVal)

    for i in range(n): # process each particle
      
      # compute new velocity of curr particle
      for k in range(dim): 
        r1 = rnd.random()    # randomizations
        r2 = rnd.random()
    
        swarm[i].velocity[k] = ( 
                                 (w * swarm[i].velocity[k]) +
                                 (c1 * r1 * (swarm[i].best_part_pos[k] - swarm[i].position[k])) +  
                                 (c2 * r2 * (best_swarm_pos[k] -swarm[i].position[k])) 
                               )  


        # if velocity[k] is not in [minx, max]
        # then clip it 
        if swarm[i].velocity[k] < minx:
          swarm[i].velocity[k] = minx
        elif swarm[i].velocity[k] > maxx:
          swarm[i].velocity[k] = maxx


      # compute new position using new velocity
      for k in range(dim): 
        swarm[i].position[k] += swarm[i].velocity[k]
  
      # compute fitness of new position
      swarm[i].fitness = fitness(swarm[i].position)

      # is new position a new best for the particle?
      if swarm[i].fitness < swarm[i].best_part_fitnessVal:
        swarm[i].best_part_fitnessVal = swarm[i].fitness
        swarm[i].best_part_pos = copy.copy(swarm[i].position)

      # is new position a new best overall?
      if swarm[i].fitness < best_swarm_fitnessVal:
        best_swarm_fitnessVal = swarm[i].fitness
        best_swarm_pos = copy.copy(swarm[i].position)
    
    # for-each particle
    Iter += 1
  #end_while
  return best_swarm_pos
# end pso


#----------------------------
# Driver code for rastrigin function

print("\nBegin particle swarm optimization on rastrigin function\n")
dim = 3
fitness = fitness_rastrigin


print("Goal is to minimize Rastrigin's function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim-1):
  print("0, ", end="")
print("0)")

num_particles = 50
max_iter = 100

print("Setting num_particles = " + str(num_particles))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting PSO algorithm\n")



best_position = pso(fitness, max_iter, num_particles, dim, -10.0, 10.0)

print("\nPSO completed\n")
print("\nBest solution found:")
print(["%.6f"%best_position[k] for k in range(dim)])
fitnessVal = fitness(best_position)
print("fitness of best solution = %.6f" % fitnessVal)

print("\nEnd particle swarm for rastrigin function\n")


print()
print()


# Driver code for Sphere function 
print("\nBegin particle swarm optimization on sphere function\n")
dim = 3
fitness = fitness_sphere


print("Goal is to minimize sphere function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim-1):
  print("0, ", end="")
print("0)")

num_particles = 50
max_iter = 100

print("Setting num_particles = " + str(num_particles))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting PSO algorithm\n")



best_position = pso(fitness, max_iter, num_particles, dim, -10.0, 10.0)

print("\nPSO completed\n")
print("\nBest solution found:")
print(["%.6f"%best_position[k] for k in range(dim)])
fitnessVal = fitness(best_position)
print("fitness of best solution = %.6f" % fitnessVal)

print("\nEnd particle swarm for sphere function\n")