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:
image.PNG
来源: http://www.jianshu.com/p/70b4c878917e