优化算法的python实现——粒子群算法（PSO）
粒子群算法
- 2023.6.13 版本（eval()函数 & 动态变量定义与调用）
- 2023.6.11 版本
用处：用于优化连续非线性方程
特点：收敛速度快，参数少，算法简单
问题：可能陷入局部最优
我认为在中文互联网上找到的对于粒子群算法讲解得最详细的
粒子群优化算法(Particle Swarm Optimization, PSO)的详细解读
根据算法的定义，自己写出来的 Demo 如下, 优化的例子是
max x , y − ( x − 1 ) 2 − ( y − 2 ) 2 \max_{x,y} ~ -(x-1)^2-(y-2)^2 x,ymax −(x−1)2−(y−2)2
2023.6.13 版本（eval()函数 & 动态变量定义与调用）
把函数外置了！这样就能不用在类里改方程了。主要用到的就是 eval()函数 和 动态变量名定义与调用。虽然这样，但是还不是很清楚为什么用 exec 的时候会报错orz
#import sympy
import numpy as np
class PSODemo:
def __init__(self,N,dim,weight,learn,itermax,fun):
self.num = N # num of initial paricles
self.dim = dim# dim of variable
self.minweight = weight[0]
self.maxweight = weight[1]
self.person = learn[0] #personal_learn
self.group = learn[1] #group_learn
self.itermax = itermax
self.fun = fun
# objective function
def Function_Value(self,state):
names = locals()
for i in range(self.dim):
names['x'+str(i+1)] = state[...,i]
value = eval(self.fun)
return value
# intertia weight w
def In_weight(self,iter):
w = self.maxweight-(self.maxweight-self.minweight)*iter/self.itermax
return w
# update velocity and state
def Update_VeloState(self,w,old_velo,old_state,old_pbest,old_gbest):
r = np.random.rand(1,2)
velo = w*old_velo+self.person*r[0,0]*(old_pbest-old_state)+self.group*r[0,1]*(np.ones((self.num,2))*old_gbest-old_state)
state = old_state+velo
return velo,state
# update pbest and gbest
def Update_Best(self,old_state,state,pbest,gbest,value_pbest,value_gbest):
value = self.Function_Value(state)
for i in range(0,self.num-1):
if value[i] > value_pbest[i]:
pbest[i,...] = state[i,...]
value_pbest[i] = value[i]
if max(value) > value_gbest:
value_gbest = max(value)
value_li = value.tolist()
index = value_li.index(max(value_li))
gbest = state[index,...]
value_gbest = value[index]
return pbest,gbest,value_pbest,value_gbest
# loop
def Loop(self):
new_state = np.random.rand(self.num,self.dim)
new_pbest = new_state
new_value_pbest = self.Function_Value(new_state)
value_li = new_value_pbest.tolist()
index = value_li.index(max(value_li))
new_gbest = new_state[index,...]
new_value_gbest = new_value_pbest[index]
new_velo = np.ones((self.num,self.dim))
for idx in range(1,self.itermax):
old_state = new_state
old_pbest = new_pbest
old_value_pbest = new_value_pbest
old_gbest = new_gbest
old_value_gbest = new_value_gbest
old_velo = new_velo
w = self.In_weight(idx)
new_velo,new_state = self.Update_VeloState(w,old_velo,old_state,old_pbest,old_gbest)
new_pbest,new_gbest,new_value_pbest,new_value_gbest = self.Update_Best(old_state,new_state,old_pbest,old_gbest,old_value_pbest,old_value_gbest)
return new_gbest,new_value_gbest
if __name__ == '__main__':
num = 40
dim = 2
weight = [0.9,0.1]# [maxweight,minweight]
learn = [1.8,2]
itermax = 1000
fun = '-(x1-1)**2-(x2-2)**2'
# objective function [maximize], the [nth] variable is defined as [xn]
PSO = PSODemo(num,dim,weight,learn,itermax,fun)
new_gbest,new_value_gbest = PSO.Loop()
print('the optimal solution = ',new_gbest)
print('the optimal value = ',new_value_gbest)
2023.6.11 版本
很简单的凸问题。代码有个问题，优化目标函数需要每次都在 class 里修改，还在思考代码在这方面的优化（自己对 python 实在不是很熟悉，如果有大佬经过，指点一下就好了（跪
import sympy
import numpy as np
class PSODemo:
def __init__(self,N,dim,weight,learn):
self.num = N # num of initial paticles
self.dim = dim # dim of variables
self.minweight = weight[0]
self.maxweight = weight[1]
self.person = learn[0] #personal_learn
self.group = learn[1] #group_learn
# objective function
def Function_Value(self,state):
# max -(x-1)^2-(y-2)^2
# x,y = sympy.symbols('x y')
value = -(state[...,0]-1)**2-(state[...,1]-2)**2
return value
# intertia weight w
def In_weight(self,iter,intermax):
w = self.maxweight-(self.maxweight-self.minweight)*iter/itermax
return w
# update velocity and state
def Update_VeloState(self,w,old_velo,old_state,old_pbest,old_gbest):
r = np.random.rand(1,2)
velo = w*old_velo+self.person*r[0,0]*(old_pbest-old_state)+self.group*r[0,1]*(np.ones((self.num,2))*old_gbest-old_state)
state = old_state+velo
return velo,state
# update pbest and gbest
def Update_Best(self,old_state,state,pbest,gbest,value_pbest,value_gbest):
value = self.Function_Value(state)
for i in range(0,self.num-1):
if value[i] > value_pbest[i]:
pbest[i,...] = state[i,...]
value_pbest[i] = value[i]
if max(value) > value_gbest:
value_gbest = max(value)
value_li = value.tolist()
index = value_li.index(max(value_li))
gbest = state[index,...]
value_gbest = value[index]
return pbest,gbest,value_pbest,value_gbest
停止条件是设置的最大迭代次数
num = 40
dim = 2
weight = [0.9,0.1]
learn = [1.6,2]
PSO = PSODemo(num,dim,weight,learn)
if __name__ == '__main__':
itermax = 1000
# num of interation
new_state = np.random.rand(num,dim)
new_pbest = new_state
new_value_pbest = PSO.Function_Value(new_state)
value_li = new_value_pbest.tolist()
index = value_li.index(max(value_li))
new_gbest = new_state[index,...]
new_value_gbest = new_value_pbest[index]
new_velo = np.ones((num,dim))
for idx in range(1,itermax):
old_state = new_state
old_pbest = new_pbest
old_value_pbest = new_value_pbest
old_gbest = new_gbest
old_value_gbest = new_value_gbest
old_velo = new_velo
w = PSO.In_weight(idx,itermax)
new_velo,new_state = PSO.Update_VeloState(w,old_velo,old_state,old_pbest,old_gbest)
new_pbest,new_gbest,new_value_pbest,new_value_gbest = PSO.Update_Best(old_state,new_state,old_pbest,old_gbest,old_value_pbest,old_value_gbest)
print(new_gbest,new_value_gbest)
输出的结果为
[1.00000008 1.99999998] -6.9334143407325055e-15
试过几次之后感觉跟参数的选择有很大的关系，也不懂是不是我写得代码问题。希望有大佬能指导指导。