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智能優(yōu)化算法23個標(biāo)準(zhǔn)測試函數(shù)（Python）

2022-03-31 00:00 作者:吾所求 0人讀過 | 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

單峰測試函數(shù)

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

多峰測試函數(shù)

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

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

固定維多峰測試函數(shù)

F14：Shekel's Foxholes Function

固定2維

F15：Kowalik's Function

固定4維

F16：Six-Hump Camel-Back Function

固定2維

F17：Branin Function

固定2維

F18：Goldstein-Price Function

固定2維

F19&F20：Hartman's Family

固定3維及6維

F21&F22&F23：Shekel's Family

固定4維

該代碼主要用于自用記錄，若有紕漏錯誤，是本人能力有限或是疏忽在此提前表達(dá)歉意，感謝批評指正。

參考來自知乎用戶valley的matlab程序（地址如下）

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

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