智能优化算法23个标准测试函数（Python）

2022-03-31 00:00 作者:吾所求 0人读过 | 我要投稿

原文：

Evolutionary programming made faster

IEEE Transactions on Evolutionary Computation ( IF 11.554 ) Pub Date : 1999-07-01 , DOI: 10.1109/4235.771163

单峰测试函数

F1：Sphere Function

$%0A%5Cbegin%7Baligned%7D%0Af_%7B1%7D(x)%3D%20%26%5Csum_%7Bi%3D1%7D%5E%7B30%7D%5Cleft(x_i%5Cright)%5E2%20%2C-100%20%5Cleq%20x_i%20%5Cleq%20100%5C%5C%0A%26%5Cquad%20%5Cmin%20%5Cleft(f_%7B1%7D%5Cright)%3Df_%7B1%7D(0%2C%20%5Cldots%2C%200)%3D0%0A%5Cend%7Baligned%7D%0A$

F2：Schwefel's Problem 2.22

F3：Schwefel's Problem 1.2

F4：Schwefel's Problem 2.21

F5：Generalized Rosenbrock's Function

F6：Step Function

F7：Quartic Function i.e. Noise

多峰测试函数

F8：Generalized Schwefel's Problem 2.26

F9：Generalized Rastrigin's Function

F10：Ackley's Function

F11：Generalized Griewank's Function

F12：Generalized Penalized Function 1

$%0A%5Cbegin%7Baligned%7D%0A%26%20u%5Cleft(x_i%2C%20a%2C%20k%2C%20m%5Cright)%3D%20%5Cbegin%7Bcases%7Dk%5Cleft(x_i-a%5Cright)%5Em%2C%20%26%20x_i%3Ea%2C%20%5C%5C%0A0%2C%20%26%20-a%20%5Cleq%20x_i%20%5Cleq%20a%2C%20%5C%5C%0Ak%5Cleft(-x_i-a%5Cright)%5Em%2C%20%26%20x_i%3C-a%20.%5Cend%7Bcases%7D%20%5C%5C%0A%5Cend%7Baligned%7D$

$%5Cbegin%7Baligned%7D%0Af_%7B12%7D(x)%3D%20%26%20%5Cfrac%7B%5Cpi%7D%7B30%7D%20%5Cleft%5C%7B10%20%5Csin%20%5E2%5Cleft(%5Cpi%20y_1%5Cright)%2B%20%5Csum_%7Bi%3D1%7D%5E%7B29%7D%5Cleft(y_i-1%5Cright)%5E2%20%5Ccdot%5Cleft%5B1%2B10%20%5Csin%20%5E2%5Cleft(%5Cpi%20y_%7Bi%2B1%7D%5Cright)%5Cright%5D%2B%5Cleft(y_n-1%5Cright)%5E2%5Cright%5C%7D%2B%5Csum_%7Bi%3D1%7D%5E%7B30%7D%20u%5Cleft(x_i%2C%2010%2C100%2C4%5Cright)%20%5C%5C%0A%26-50%20%5Cleq%20x_i%20%5Cleq%2050%2C%20%5Cquad%20%5Cmin%20%5Cleft(f_%7B12%7D%5Cright)%3Df_%7B12%7D(1%2C%20%5Cldots%2C%201)%3D0%5C%5C%0A%20%5Ctext%20%7B%20where%20%7D%20%5C%5C%0A%26y_i%3D1%2B%5Cfrac%7B1%7D%7B4%7D%5Cleft(x_i%2B1%5Cright)%20%5Ctext%20%7B.%20%7D%20%5C%5C%0A%5Cend%7Baligned%7D$

F13：Generalized Penalized Function 2

$%5Cbegin%7Baligned%7D%0A%26%20f_%7B13%7D(x)%3D0.1%5Cleft%5C%7B%5Csin%20%5E2%5Cleft(%5Cpi%203%20x_1%5Cright)%2B%5Csum_%7Bi%3D1%7D%5E%7B29%7D%5Cleft(x_i-1%5Cright)%5E2%5Cleft%5B1%2B%5Csin%20%5E2%5Ccdot%5Cleft(3%20%5Cpi%20x_%7Bi%2B1%7D%5Cright)%5Cright%5D%2B%5Cleft(x_n-1%5Cright)%5E2%5Cleft%5B1%2B%5Csin%20%5E2%5Cleft(2%20%5Cpi%20x_%7B30%7D%5Cright)%5Cright%5D%5Cright%5C%7D%2B%5Csum_%7Bi%3D1%7D%5E%7B30%7D%20u%5Cleft(x_i%2C%205%2C100%2C4%5Cright)%20%5C%5C%0A%26%20-50%20%5Cleq%20x_i%20%5Cleq%2050%2C%20%5Cquad%20%5Cmin%20%5Cleft(f_%7B13%7D%5Cright)%3Df_%7B13%7D(1%2C%20%5Cldots%2C%201)%3D0%20%5C%5C%0A%5Cend%7Baligned%7D$

固定维多峰测试函数

F14：Shekel's Foxholes Function

固定2维

F15：Kowalik's Function

固定4维

F16：Six-Hump Camel-Back Function

固定2维

F17：Branin Function

固定2维

F18：Goldstein-Price Function

固定2维

F19&F20：Hartman's Family

固定3维及6维

F21&F22&F23：Shekel's Family

固定4维

该代码主要用于自用记录，若有纰漏错误，是本人能力有限或是疏忽在此提前表达歉意，感谢批评指正。

参考来自知乎用户valley的matlab程序（地址如下）

https://zhuanlan.zhihu.com/p/397505364

标签：python 智能优化算法测试函数

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