python实现爬山算法的思路详解

问题

找图中函数在区间[5,8]的最大值

重点思路

爬山算法会收敛到局部最优，解决办法是初始值在定义域上随机取乱数100次，总不可能100次都那么倒霉。

实现

import numpy as npimport matplotlib.pyplot as pltimport math# 搜索步长DELTA = 0.01# 定义域x从5到8闭区间BOUND = [5,8]# 随机取乱数100次GENERATION = 100def F(x):  return math.sin(x*x)+2.0*math.cos(2.0*x)def hillClimbing(x):  while F(x+DELTA)>F(x) and x+DELTA<=BOUND[1] and x+DELTA>=BOUND[0]:    x = x+DELTA  while F(x-DELTA)>F(x) and x-DELTA<=BOUND[1] and x-DELTA>=BOUND[0]:    x = x-DELTA  return x,F(x)def findMax():  highest = [0,-1000]  for i in range(GENERATION):    x = np.random.rand()*(BOUND[1]-BOUND[0])+BOUND[0]    currentValue = hillClimbing(x)    print('current value is :',currentValue)        if currentValue[1] > highest[1]:      highest[:] = currentValue  return highest[x,y] = findMax()print('highest point is x :{},y:{}'.format(x,y))

运行结果：

总结

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