python爬山算法求函数值

爬山算法求函数值

$f(x,y)=e^{-x^2-y^2}+2e^{-(x-5)^2-(y-5)^2}$

算法思路说明：

没时间了。。。明天再说


import random, math
import numpy as np
 
def f(x,y):
    def mul(x,y):
        return math.exp(-x**2-y**2)
    return mul(x,y)+2*mul(x-5,y-5)
 
def get_para(x,y,x_delta,y_delta):
    para = [[x,y],[x-x_delta, y],[x+x_delta, y],[x,y+y_delta],[x,y-y_delta],
            [x-x_delta, y-y_delta],[x+x_delta, y-y_delta],[x-x_delta,y+y_delta],[x-x_delta,y-y_delta],
            [x-x_delta, y+y_delta],[x+x_delta, y+y_delta],[x+x_delta,y+y_delta],[x+x_delta,y-y_delta]]
    # print('para',para)
    rs = []
    for xy in para:
        rs.append(f(xy[0],xy[1]))
    # print('rssrsrs',rs)
 
    best_index = rs.index(max(rs))
    # print('best_index',best_index)
    # print('best_para',para[best_index])
    return para[best_index]
 
 
 
if __name__ == '__main__':
    print(f(20,2))
    x_delta=0.1
    y_delta=0.1
    x,y = 1,1
    xy_best = get_para(x,y,0.5,0.5)
    print(111,xy_best)
    rs_best = f(xy_best[0],xy_best[1])
    # print(rs_best)
    for i in range(10000):
        new_xy_best = get_para(xy_best[0],xy_best[1],x_delta,y_delta)
        # print(222,new_xy_best)
        # print(new_xy_best)
        if rs_best == f(new_xy_best[0],new_xy_best[1]):
            x_delta += 0.01
            y_delta += 0.01
        elif rs_best < f(new_xy_best[0],new_xy_best[1]):
            x_delta = 0.1
            y_delta = 0.1
            # print(11,rs_best, f(new_xy_best[0],new_xy_best[1]))
            xy_best = new_xy_best
            rs_best = f(new_xy_best[0],new_xy_best[1])
            print(i,xy_best, rs_best)
 
    print(xy_best, f(5,5))
 
    # print(rs_best,f(xy_best[0],xy_best[1]))

运行结果：

0 [0.4, 0.4] 0.7261490370736908
1 [0.30000000000000004, 0.30000000000000004] 0.835270211411272
2 [0.20000000000000004, 0.20000000000000004] 0.9231163463866358
3 [0.10000000000000003, 0.10000000000000003] 0.9801986733067553
4 [2.7755575615628914e-17, 2.7755575615628914e-17] 1.0
437 [4.41999999999995, 4.41999999999995] 1.0205555955908896
438 [4.51999999999995, 4.51999999999995] 1.261557641094735
439 [4.6199999999999495, 4.6199999999999495] 1.4983240456498703
440 [4.719999999999949, 4.719999999999949] 1.7097500334492415
441 [4.819999999999949, 4.819999999999949] 1.8745097912252862
442 [4.919999999999948, 4.919999999999948] 1.9745631431805484
443 [5.019999999999948, 5.019999999999948] 1.9984006398293757
[5.019999999999948, 5.019999999999948] 2.0

参考：

爬山算法_csuzhucong的博客-CSDN博客_爬山算法

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原文地址：https://blog.csdn.net/java_raylu/article/details/125506485