（python源码，详细注解）多目标粒子群算法 mopso

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1 本代码功能

用多目标粒子群算法（mopso）寻找pareto最优解集

2 算法介绍

2.1 简单步骤：

(1)初始化群体粒子群的位置和速度，计算适应值

(2)根据pareto支配原则，计算得到Archive 集(存放当前的非劣解)

(3)计算pbest

(4)计算Archive集中的拥挤度

(5)在Archive集选择gbest

(6)更新粒子的速度、位置、适应值

(7)更新Archive集（还要注意防止溢出）

(8)满足结束条件，则结束；否则，转到第(3)步继续循环。

2.2 算法的详解可参考如下博客：

2.2.1 对多目标粒子群算法MOPSO的理解，https://blog.csdn.net/ture_2010/article/details/18180183

2.2.2 MOPSO算法学习总结，https://blog.csdn.net/sbcypress/article/details/50727907

2.2.3 Handling multiple objectives with particle swarm optimization

3 简单图示

为了便于图示观察，本源码使用一组简单的测试函数：输入坐标为2维（input_x1,input_x2），输出适应值为2维（fitness_y1,fitness_y2）。如下图所示，经过10轮迭代后，pareto边界已见轮廓，红色点代表pareto最优解集。

（python源码，详细注解）多目标粒子群算法 mopso

4 代码如下

4.1 main.py

#encoding: utf-8
import numpy as np
from mopso import *

def main():
	w = 0.8 #惯性因子
	c1 = 0.1 #局部速度因子
	c2 = 0.1 #全局速度因子
	particals = 100 #粒子群的数量
	cycle_ = 30 #迭代次数
	mesh_div = 10 #网格等分数量
	thresh = 300 #外部存档阀值
	min_ = np.array([0,0]) #粒子坐标的最小值
	max_ = np.array([10,10]) #粒子坐标的最大值
	mopso_ = Mopso(particals,w,c1,c2,max_,min_,thresh,mesh_div) #粒子群实例化
	pareto_in,pareto_fitness = mopso_.done(cycle_) #经过cycle_轮迭代后，pareto边界粒子
	np.savetxt("./img_txt/pareto_in.txt",pareto_in)#保存pareto边界粒子的坐标
	np.savetxt("./img_txt/pareto_fitness.txt",pareto_fitness) #打印pareto边界粒子的适应值
	print "\n","pareto边界的坐标保存于：/img_txt/pareto_in.txt"
	print "pareto边界的适应值保存于：/img_txt/pareto_fitness.txt"
	print "\n","迭代结束,over"

if __name__ == "__main__":
	main()

4.2 mopso.py

#encoding: utf-8
import numpy as np
from fitness_funs import *
import init
import update
import plot
class Mopso:
	def __init__(self,particals,w,c1,c2,max_,min_,thresh,mesh_div=10):
		self.w,self.c1,self.c2 = w,c1,c2
		self.mesh_div = mesh_div
		self.particals = particals
		self.thresh = thresh
		self.max_ = max_
		self.min_ = min_
		self.max_v = (max_-min_)*0.05  #速度下限
		self.min_v = (max_-min_)*0.05*(-1) #速度上限
		self.plot_ = plot.Plot_pareto()
	def evaluation_fitness(self): 
		#计算适应值
		fitness_curr = []
		for i in range((self.in_).shape[0]):
			fitness_curr.append(fitness_(self.in_[i]))
		self.fitness_ = np.array(fitness_curr) #适应值
	def initialize(self):
		#初始化粒子坐标
		self.in_ = init.init_designparams(self.particals,self.min_,self.max_)
		#初始化粒子速度
		self.v_ = init.init_v(self.particals,self.min_v,self.max_v)
		#计算适应值
		self.evaluation_fitness()
		#初始化个体最优
		self.in_p,self.fitness_p = init.init_pbest(self.in_,self.fitness_)
		#初始化外部存档
		self.archive_in,self.archive_fitness = init.init_archive(self.in_,self.fitness_)
		#初始化全局最优
		self.in_g,self.fitness_g = init.init_gbest(self.archive_in,self.archive_fitness,self.mesh_div,self.min_,self.max_,self.particals)
	def update_(self):
		#更新粒子坐标、粒子速度、适应值、个体最优、外部存档、全局最优
		self.v_ = update.update_v(self.v_,self.min_v,self.max_v,self.in_,self.in_p,self.in_g,self.w,self.c1,self.c2)
		self.in_ = update.update_in(self.in_,self.v_,self.min_,self.max_)
		self.evaluation_fitness()
		self.in_p,self.fitness_p = update.update_pbest(self.in_,self.fitness_,self.in_p,self.fitness_p)
		self.archive_in,self.archive_fitness = update.update_archive(self.in_,self.fitness_,self.archive_in,self.archive_fitness,self.thresh,self.mesh_div,self.min_,self.max_,self.particals)
		self.in_g,self.fitness_g = update.update_gbest(self.archive_in,self.archive_fitness,self.mesh_div,self.min_,self.max_,self.particals)
	def done(self,cycle_):
		self.initialize()
		self.plot_.show(self.in_,self.fitness_,self.archive_in,self.archive_fitness,-1)
		for i in range(cycle_):
			self.update_()
			self.plot_.show(self.in_,self.fitness_,self.archive_in,self.archive_fitness,i)
		return self.archive_in,self.archive_fitness

4.3 init.py

#encoding: utf-8
import random
import numpy as np
import archiving
import pareto
def init_designparams(particals,in_min,in_max):
	in_dim = len(in_max) 	#输入参数的维度
	in_temp = np.zeros((particals,in_dim))
	for i in range(particals):
		for j in range(in_dim):
			in_temp[i,j] = random.uniform(0,1)*(in_max[j]-in_min[j])+in_min[j]	
	return in_temp
def init_v(particals,v_max,v_min):
	v_dim = len(v_max) 	#输入参数的维度
	v_ = np.zeros((particals,v_dim))
	for i in range(particals):
		for j in range(v_dim):
			v_[i,j] = random.uniform(0,1)*(v_max[j]-v_min[j])+v_min[j]
	return v_
def init_pbest(in_,fitness_):
	return in_,fitness_
def init_archive(in_,fitness_):
	pareto_c = pareto.Pareto_(in_,fitness_)
	curr_archiving_in,curr_archiving_fit = pareto_c.pareto()
	return curr_archiving_in,curr_archiving_fit
def init_gbest(curr_archiving_in,curr_archiving_fit,mesh_div,min_,max_,particals):
	get_g = archiving.get_gbest(curr_archiving_in,curr_archiving_fit,mesh_div,min_,max_,particals)
	return get_g.get_gbest()

4.4 update.py

#encoding: utf-8
import numpy as np
import random
import pareto
import archiving
def update_v(v_,v_min,v_max,in_,in_pbest,in_gbest,w,c1,c2):
	#更新速度值
	v_temp = w*v_ + c1*(in_pbest-in_) + c2*(in_gbest-in_)
	#如果粒子的新速度大于最大值，则置为最大值；小于最小值，则置为最小值
	for i in range(v_temp.shape[0]):
		for j in range(v_temp.shape[1]):
			if v_temp[i,j]<v_min[j]:
				v_temp[i,j] = v_min[j]
			if v_temp[i,j]>v_max[j]:
				v_temp[i,j] = v_max[j]
	return v_temp
def update_in(in_,v_,in_min,in_max):
	#更新位置参数
	in_temp = in_ + v_
	#大于最大值，则置为最大值；小于最小值，则置为最小值
	for i in range(in_temp.shape[0]):
		for j in range(in_temp.shape[1]):
			if in_temp[i,j]<in_min[j]:
				in_temp[i,j] = in_min[j]
			if in_temp[i,j]>in_max[j]:
				in_temp[i,j] = in_max[j]
	return in_temp
def compare_pbest(in_indiv,pbest_indiv):
	num_greater = 0
	num_less = 0
	for i in range(len(in_indiv)):
		if in_indiv[i] > pbest_indiv[i]:
			num_greater = num_greater +1
		if in_indiv[i] < pbest_indiv[i]:
			num_less = num_less +1
	#如果当前粒子支配历史pbest，则更新,返回True
	if (num_greater>0 and num_less==0):
		return True
	#如果历史pbest支配当前粒子，则不更新,返回False
	elif (num_greater==0 and num_less>0):
		return False
	else:
		#如果互不支配，则按照概率决定是否更新
		random_ = random.uniform(0.0,1.0)
		if random_ > 0.5:
			return True
		else:
			return False
def update_pbest(in_,fitness_,in_pbest,out_pbest):
	for i in range(out_pbest.shape[0]):
		#通过比较历史pbest和当前粒子适应值，决定是否需要更新pbest的值。
		if compare_pbest(fitness_[i],out_pbest[i]):
			out_pbest[i] = fitness_[i]
			in_pbest[i] = in_[i]
	return in_pbest,out_pbest
def update_archive(in_,fitness_,archive_in,archive_fitness,thresh,mesh_div,min_,max_,particals):
	#首先，计算当前粒子群的pareto边界，将边界粒子加入到存档archiving中
	pareto_1 = pareto.Pareto_(in_,fitness_)
	curr_in,curr_fit = pareto_1.pareto()
	#其次，在存档中根据支配关系进行第二轮筛选，将非边界粒子去除
	in_new = np.concatenate((archive_in,curr_in),axis=0)
	fitness_new = np.concatenate((archive_fitness,curr_fit),axis=0)
	pareto_2 = pareto.Pareto_(in_new,fitness_new)
	curr_archiving_in,curr_archiving_fit = pareto_2.pareto()
	#最后，判断存档数量是否超过了存档阀值。如果超过了阀值，则清除掉一部分（拥挤度高的粒子被清除的概率更大）
	if((curr_archiving_in).shape[0] > thresh):
		clear_ = archiving.clear_archiving(curr_archiving_in,curr_archiving_fit,mesh_div,min_,max_,particals)
		curr_archiving_in,curr_archiving_fit = clear_.clear_(thresh)
	return curr_archiving_in,curr_archiving_fit
def update_gbest(archiving_in,archiving_fit,mesh_div,min_,max_,particals):
	get_g = archiving.get_gbest(archiving_in,archiving_fit,mesh_div,min_,max_,particals)
	return get_g.get_gbest()

4.5 archiving.py

#encoding: utf-8
import numpy as np
import random

class mesh_crowd(object): 
	def __init__(self,curr_archiving_in,curr_archiving_fit,mesh_div,min_,max_,particals):
		self.curr_archiving_in = curr_archiving_in #当前存档中所有粒子的坐标
		self.curr_archiving_fit = curr_archiving_fit #当前存档中所有粒子的坐标
		self.mesh_div = mesh_div #等分因子，默认值为10等分
		
		
		
		self.num_ = self.curr_archiving_in.shape[0] #cundangzhong######粒子数量
		
		self.particals = particals  ########
		
		self.id_archiving = np.zeros((self.num_)) #各个粒子的id编号，检索位与curr_archiving的检索位为相对应
		self.crowd_archiving = np.zeros((self.num_)) #拥挤度矩阵，用于记录当前粒子所在网格的总粒子数，检索位与curr_archiving的检索为相对应
		self.probability_archiving = np.zeros((self.num_)) #各个粒子被选为gbest的概率，检索位与curr_archiving的检索位为相对应
		self.gbest_in = np.zeros((self.particals,self.curr_archiving_in.shape[1])) #初始化gbest矩阵_坐标
		self.gbest_fit = np.zeros((self.particals,self.curr_archiving_fit.shape[1])) #初始化gbest矩阵_适应值
		self.min_ = min_
		self.max_ = max_

	def cal_mesh_id(self,in_):
		#计算网格编号id
		#首先，将每个维度按照等分因子进行等分离散化，获取粒子在各维度上的编号。按照10进制将每一个维度编号等比相加（如过用户自定义了mesh_div_num的值，则按照自定义），计算出值
		id_ = 0
		for i in range(self.curr_archiving_in.shape[1]):
			id_dim = int((in_[i]-self.min_[i])*self.num_/(self.max_[i]-self.min_[i]))
			id_ = id_ + id_dim*(self.mesh_div**i)
		return id_

	def divide_archiving(self):
		#进行网格划分，为每个粒子定义网格编号
		for i in range(self.num_):
			self.id_archiving[i] = self.cal_mesh_id(self.curr_archiving_in[i])

	def get_crowd(self):
		index_ = (np.linspace(0,self.num_-1,self.num_)).tolist()  #定义一个数组存放粒子集的索引号，用于辅助计算
		index_ = map(int, index_)
		while(len(index_) > 0):
			index_same = [index_[0]] #存放本次子循环中与index[0]粒子具有相同网格id所有检索位
			for i in range(1,len(index_)):
				if self.id_archiving[index_[0]] == self.id_archiving[index_[i]]:
					index_same.append(index_[i])
			number_ = len(index_same) #本轮网格中的总粒子数
			for i in index_same: #更新本轮网格id下的所有粒子的拥挤度
				self.crowd_archiving[i] = number_
				index_.remove(i) #删除本轮网格所包含的粒子对应的索引号，避免重复计算

class get_gbest(mesh_crowd):
	def __init__(self,curr_archiving_in,curr_archiving_fit,mesh_div_num,min_,max_,particals):
		super(get_gbest,self).__init__(curr_archiving_in,curr_archiving_fit,mesh_div_num,min_,max_,particals)
		self.divide_archiving()
		self.get_crowd()

	def get_probability(self):
		for i in range(self.num_):
			self.probability_archiving = 10.0/(self.crowd_archiving**3)
		self.probability_archiving = self.probability_archiving/np.sum(self.probability_archiving) #所有粒子的被选概率的总和为1

	def get_gbest_index(self):
		random_pro = random.uniform(0.0,1.0) #生成一个0到1之间的随机数
		for i in range(self.num_): 
			if random_pro <= np.sum(self.probability_archiving[0:i+1]):
				return i #返回检索值

	def get_gbest(self):
		self.get_probability()
		for i in range(self.particals):
			gbest_index = self.get_gbest_index()
			self.gbest_in[i] = self.curr_archiving_in[gbest_index] #gbest矩阵_坐标
			self.gbest_fit[i] = self.curr_archiving_fit[gbest_index] #gbest矩阵_适应值
		return self.gbest_in,self.gbest_fit

class clear_archiving(mesh_crowd):
	def __init__(self,curr_archiving_in,curr_archiving_fit,mesh_div_num,min_,max_,particals):
		super(get_gbest,self).__init__(curr_archiving_in,curr_archiving_fit,mesh_div_num,min_,max_)
		self.divide_archiving()
		self.get_crowd()

	def get_probability(self):
		for i in range(self.num_):
			self.probability_archiving = self.crowd_archiving**2

	def get_clear_index(self): #按概率清除粒子，拥挤度高的粒子被清除的概率越高
		len_clear = (self.curr_archiving_in).shape[0] - self.thresh #需要清除掉的粒子数量
		clear_index = []
		while(len(clear_index)<len_clear):
			random_pro = random.uniform(0.0,np.sum(self.probability_archiving)) #生成一个0到1之间的随机数
			for i in range(self.num_): 
				if random_pro <= np.sum(self.probability_archiving[0:i+1]):
					if i not in clear_index:
						clear_index.append(i) #记录检索值
		return clear_index

	def clear_(self,thresh):
		self.thresh = thresh
		self.archiving_size = archiving_size
		self.get_probability()
		clear_index = get_clear_index()
		self.curr_archiving_in = np.delete(self.curr_archiving_in[gbest_index],clear_index,axis=0) #初始化gbest矩阵_坐标
		self.curr_archiving_fit = np.delete(self.curr_archiving_fit[gbest_index],clear_index,axis=0) #初始化gbest矩阵_适应值
		return self.curr_archiving_in,self.curr_archiving_fit

4.6 pareto.py

#encoding: utf-8
import numpy as np

def compare_ (fitness_curr,fitness_ref):
#判断fitness_curr是否可以被fitness_ref完全支配
	for i in range(len(fitness_curr)):
		if fitness_curr[i] < fitness_ref[i]:
			return True
	return False
def judge_(fitness_curr,fitness_data,cursor):
#当前粒子的适应值fitness_curr与数据集fitness_data进行比较，判断是否为非劣解
	for i in range(len(fitness_data)):
		if i == cursor:
			continue
		#如果数据集中存在一个粒子可以完全支配当前解，则证明当前解为劣解，返回False
		if compare_(fitness_curr,fitness_data[i]) == False:
			return False
	return True

class Pareto_:
	def __init__(self,in_data,fitness_data):
		self.in_data = in_data  #粒子群坐标信息
		self.fitness_data = fitness_data #粒子群适应值信息
		self.cursor = -1 #初始化游标位置
		self.len_ = in_data.shape[0] #粒子群的数量
		self.bad_num = 0 #非优解的个数
	def next(self):
		#将游标的位置前移一步，并返回所在检索位的粒子坐标、粒子适应值
		self.cursor = self.cursor+1
		return self.in_data[self.cursor],self.fitness_data[self.cursor]
	def hasNext(self):
		#判断是否已经检查完了所有粒子
		return self.len_ > self.cursor + 1 + self.bad_num
	def remove(self):
		#将非优解从数据集删除，避免反复与其进行比较。
		self.fitness_data = np.delete(self.fitness_data,self.cursor,axis=0)
		self.in_data = np.delete(self.in_data,self.cursor,axis=0)
		#游标回退一步
		self.cursor = self.cursor-1
		#非优解个数，加1
		self.bad_num = self.bad_num + 1
	def pareto(self):
		while(self.hasNext()):
			#获取当前位置的粒子信息
			in_curr,fitness_curr = self.next()
			#判断当前粒子是否pareto最优
			if judge_(fitness_curr,self.fitness_data,self.cursor) == False :
				self.remove()
		return self.in_data,self.fitness_data

4.7 fitness_funs.py

#encoding: utf-8
import numpy as np
#为了便于图示观察，试验测试函数为二维输入、二维输出
#适应值函数：实际使用时请根据具体应用背景自定义
def fitness_(in_):
    degree_45 = ((in_[0]-in_[1])**2/2)**0.5
    degree_135 = ((in_[0]+in_[1])**2/2)**0.5
    fit_1 = 1-np.exp(-(degree_45)**2/0.5)*np.exp(-(degree_135-np.sqrt(200))**2/250)
    fit_2 = 1-np.exp(-(degree_45)**2/5)*np.exp(-(degree_135)**2/350)
    return [fit_1,fit_2]

4.8 plot.py

#encoding: utf-8
import numpy as np
import os
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import fitness_funs as fit
class Plot_pareto:
	def __init__(self):
		#绘制测试函数的曲面，（x1，x2）表示两位度的输入，（y1，y2）表示两位的适应值，
		self.x1 = np.linspace(0,10,100)
		self.x2 = np.linspace(0,10,100)
		self.x1,self.x2 = np.meshgrid(self.x1,self.x2)
		self.m,self.n = np.shape(self.x1)
		self.y1,self.y2 = np.zeros((self.m,self.n)),np.zeros((self.m,self.n))
		for i in range(self.m):
			for j in  range(self.n):
				[self.y1[i,j],self.y2[i,j]] = fit.fitness_([self.x1[i,j],self.x2[i,j]])
		if os.path.exists('./img_txt') == False:
			os.makedirs('./img_txt')
			print '创建文件夹img_txt:保存粒子群每一次迭代的图片' 
	def show(self,in_,fitness_,archive_in,archive_fitness,i):
		#共3个子图，第1、2/子图绘制输入坐标与适应值关系，第3图展示pareto边界的形成过程
		fig = plt.figure(13,figsize = (17,5))

		ax1 = fig.add_subplot(131, projection='3d')
		ax1.set_xlabel('input_x1')
		ax1.set_ylabel('input_x2')
		ax1.set_zlabel('fitness_y1')
		ax1.plot_surface(self.x1,self.x2,self.y1,alpha = 0.6)
		ax1.scatter(in_[:,0],in_[:,1],fitness_[:,0],s=20, c='blue', marker=".")
		ax1.scatter(archive_in[:,0],archive_in[:,1],archive_fitness[:,0],s=50, c='red', marker=".")
		ax2 = fig.add_subplot(132, projection='3d')
		ax2.set_xlabel('input_x1')
		ax2.set_ylabel('input_x2')
		ax2.set_zlabel('fitness_y2')
		ax2.plot_surface(self.x1,self.x2,self.y2,alpha = 0.6)
		ax2.scatter(in_[:,0],in_[:,1],fitness_[:,1],s=20, c='blue', marker=".")
		ax2.scatter(archive_in[:,0],archive_in[:,1],archive_fitness[:,1],s=50, c='red', marker=".")
		ax3 = fig.add_subplot(133)
		ax3.set_xlim((0,1))
		ax3.set_ylim((0,1))
		ax3.set_xlabel('fitness_y1')
		ax3.set_ylabel('fitness_y2')
		ax3.scatter(fitness_[:,0],fitness_[:,1],s=10, c='blue', marker=".")
		ax3.scatter(archive_fitness[:,0],archive_fitness[:,1],s=30, c='red', marker=".",alpha = 1.0)
		#plt.show()
		plt.savefig('./img_txt/第'+str(i+1)+'次迭代.png')
		print '第'+str(i+1)+'次迭代的图片保存于 img_txt 文件夹'
		plt.close()

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