python实现爬山算法的思路详解

脚本专栏 2025/11/7 佚名

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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 np
import matplotlib.pyplot as plt
import 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 = 100
def 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：