退火算法学习笔记

import math
import numpy  as np

T = 1000
Tmin = 1
sectionl = -4
sectionh = 16
xold = np.random.uniform(sectionl,sectionh)
k = 100
yold = 0
t = 0


def aimFunction(x):
    y = x*math.sin(x)
    return y

def judge(de,tmp):
    if(de < 0):
        return 1
    else:
        p = math.exp(-(de/tmp))
        r = np.random.uniform(low=0,high=1)
        if  p > r :
            return 1
        else:
            return 0

while T > Tmin:
    for i in range(k):
        delta = (np.random.uniform(0,1) - 0.5)*5
        xnew = xold + delta
        if ((xnew < sectionl) or (xnew > sectionh)) :
            xnew = xnew - 2*delta
        else:
            ynew = aimFunction(xnew)
            dE = ynew - yold
            bz= judge(dE,T)
            if bz:
                xold = xnew
                yold = ynew

    t =  t + 1
    
    T = 1000/(1 + t)
    print(yold)

           

感想

如果当前状态比前一个最好的状态好，那么更新当前的状态 但是 如果当前的状态 不比之前的状态好的话 ，当前的状态可以以一定的概率更新之前的概率，这样就能在一定程度上跳出局部最优解 ，从而更好的寻找全局最优解