# coding=utf-8
import numpy as np
import copy
import matplotlib.pyplot as plt
import math
def GrieFunc(vardim, x, bound):
"""
Griewangk function
"""
s1 = 0.
s2 = 1.
for i in range(1, vardim + 1):
s1 = s1 + x[i - 1] ** 2
s2 = s2 * math.cos(x[i - 1] / math.sqrt(i))
y = (1. / 4000.) * s1 - s2 + 1
y = 1. / (1. + y)
return y
#
# def RastFunc(vardim, x, bound):
# """
# Rastrigin function
# """
# s = 10 * 25
# for i in range(1, vardim + 1):
# s = s + x[i - 1] ** 2 - 10 * math.cos(2 * math.pi * x[i - 1])
# return s
class PSOIndividual:
"""
individual of PSO
"""
def __init__(self, vardim, bound):
"""
vardim: dimension of variables
bound: boundaries of variables
"""
self.vardim = vardim
self.bound = bound
self.fitness = 0.
def generate(self):
"""
generate a rondom chromsome
"""
len = self.vardim
rnd = np.random.random(size=len)
self.chrom = np.zeros(len)
self.velocity = np.random.random(size=len)
for i in range(0, len):
self.chrom[i] = self.bound[0, i] + \
(self.bound[1, i] - self.bound[0, i]) * rnd[i]
self.bestPosition = np.zeros(len)
self.bestFitness = 0.
def calculateFitness(self):
"""
calculate the fitness of the chromsome
"""
self.fitness = GrieFunc(self.vardim, self.chrom, self.bound)
class ParticleSwarmOptimization:
"""
the class for Particle Swarm Optimization
"""
def __init__(self, sizepop, vardim, bound, MAXGEN, params):
"""
sizepop: population sizepop
vardim: dimension of variables
bound: boundaries of variables
MAXGEN: termination condition
params: algorithm required parameters, it is a list which is consisting of[w, c1, c2]
"""
self.sizepop = sizepop
self.vardim = vardim
self.bound = bound
self.MAXGEN = MAXGEN
self.params = params
self.population = []
self.fitness = np.zeros((self.sizepop, 1))
self.trace = np.zeros((self.MAXGEN, 2))
def initialize(self):
"""
initialize the population of pso
"""
for i in range(0, self.sizepop):
ind = PSOIndividual(self.vardim, self.bound)
ind.generate()
self.population.append(ind)
def evaluation(self):
"""
evaluation the fitness of the population
"""
for i in range(0, self.sizepop):
self.population[i].calculateFitness()
self.fitness[i] = self.population[i].fitness
if self.population[i].fitness > self.population[i].bestFitness:
self.population[i].bestFitness = self.population[i].fitness
self.population[i].bestIndex = copy.deepcopy(
self.population[i].chrom)
def update(self):
"""
update the population of pso
"""
for i in range(0, self.sizepop):
self.population[i].velocity = self.params[0] * self.population[i].velocity + self.params[1] * np.random.random(self.vardim) * (
self.population[i].bestPosition - self.population[i].chrom) + self.params[2] * np.random.random(self.vardim) * (self.best.chrom - self.population[i].chrom)
self.population[i].chrom = self.population[
i].chrom + self.population[i].velocity
def solve(self):
"""
the evolution process of the pso algorithm
"""
self.t = 0
self.initialize()
self.evaluation()
best = np.max(self.fitness)
bestIndex = np.argmax(self.fitness)
self.best = copy.deepcopy(self.population[bestIndex])
self.avefitness = np.mean(self.fitness)
self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness
self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness
print("Generation %d: optimal function value is: %f; average function value is %f" % (
self.t, self.trace[self.t, 0], self.trace[self.t, 1]))
while self.t < self.MAXGEN - 1:
self.t += 1
self.update()
self.evaluation()
best = np.max(self.fitness)
bestIndex = np.argmax(self.fitness)
if best > self.best.fitness:
self.best = copy.deepcopy(self.population[bestIndex])
self.avefitness = np.mean(self.fitness)
self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness
self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness
print("Generation %d: optimal function value is: %f; average function value is %f" % (
self.t, self.trace[self.t, 0], self.trace[self.t, 1]))
print("Optimal function value is: %f; " % self.trace[self.t, 0])
print("Optimal solution is:")
print(self.best.chrom)
self.printResult()
def printResult(self):
"""
plot the result of pso algorithm
"""
x = np.arange(0, self.MAXGEN)
y1 = self.trace[:, 0]
y2 = self.trace[:, 1]
plt.plot(x, y1, 'r', label='optimal value')
plt.plot(x, y2, 'g', label='average value')
plt.xlabel("Iteration")
plt.ylabel("function value")
plt.title("Particle Swarm Optimization algorithm for function optimization")
plt.legend()
plt.show()
if __name__ == "__main__":
bound = np.tile([[-600], [600]], 25)
pso = ParticleSwarmOptimization(60, 25, bound, 1000, [0.7298, 1.4962, 1.4962])
pso.solve()
