This is a program that can calculate result of optimization functions. And this program is built on a program that is the paper's example code. The paper is called "The Whale Optimization Algorithm."
This is the website of author who published WOA: http://www.alimirjalili.com/WOA.html
We only copied and modified 2 programs from original version:
- Get_Functions_details.m
- func_plot.m
The main purpose of these modification is extend multidimensional test functions.
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Sphere Function (F1)
$f(\textbf{x}) = f(x_1, x_2, ..., x_n) = {\sum_{i=1}^{n} x_i^{2}}$ -
Schwefel Function 2.22 (F2)
$f(\mathbf{x})=f(x_1, ..., x_n)=\sum_{i=1}^{n}|x_i|+\prod_{i=1}^{n}|x_i|$ -
Schwefel Function 1.2 (F3)
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Schwefel Function 2.21 (F4)
$f(\mathbf{x})=f(x_1, ..., x_n)=\max_{i=1,...,n}|x_i| $ -
Rosenbrock Function (F5)
$f(x, y)=\sum_{i=1}^{n}[b (x_{i+1} - x_i^2)^ 2 + (a - x_i)^2]$ -
Step Function (F6)
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Quartic Function (F7)
$f(\mathbf{x})=f(x_1,...,x_n)=\sum_{i=1}^{n}ix_i^4+\text{random}[0,1)$ -
Schwefel Function (F8)
$f(\textbf{x}) = f(x_1, x_2, ..., x_n) = 418.9829d -{\sum_{i=1}^{n} x_i sin(\sqrt{|x_i|})}$ -
Rastrigin Function (F9)
$f(x, y)=10n + \sum_{i=1}^{n}(x_i^2 - 10cos(2\pi x_i))$ -
Ackley Function (F10)
$f(\textbf{x}) = f(x_1, ..., x_n)= -a.exp(-b\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2})-exp(\frac{1}{n}\sum_{i=1}^{n}cos(cx_i))+ a + exp(1)$ -
Griewank Function (F11)
$f(\textbf{x}) = f(x_1, ..., x_n) = 1 + \sum_{i=1}^{n} \frac{x_i^{2}}{4000} - \prod_{i=1}^{n}cos(\frac{x_i}{\sqrt{i}})$ -
Penalized 1 Function (F12)
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Penalized 2 Function (F13)
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Shekel's Foxholes Function (F14)
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Kowalik's Function (F15)
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Six-Hump Camel-Back Function (F16)
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Branin Function (F17)
$a=1, b=\frac{5.1}{4\pi ^2}, c=\frac{5}{\pi}, r=6, s = 10, t = \frac{1}{8\pi}$ -
Goldstein-Price Function (F18)
$f(x,y)=[1 + (x + y + 1)^2(19 − 14x+3x^2− 14y + 6xy + 3y^2)][30 + (2x − 3y)^2(18 − 32x + 12x^2 + 4y − 36xy + 27y^2)]$ -
Hartman's Family (F19)
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Hartman's Family (F20)
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Shekel's Family (F21)
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Shekel's Family (F22)
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Shekel's Family (F23)
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Power Sum Function (F24)
$dim = 4$ $b = [8, 18, 44, 114]$ $global\ minima\rightarrow x^=[1, 2, 2, 3]的所有排列組合$ $f(x^)=0$ -
Zakharov Function (F25)
$global\ minima\rightarrow x^=[0, ..., 0]$ $f(x^)=0$
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Matyas Function (F26)
$global\ minima\rightarrow x^=[0, ..., 0]$ $f(x^)=0$
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Perm Function d, beta (F27)
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Vincent Function (F28)
$f(x)=\sum_{i=1}^n \sin(10 \log(x))$ -
Levy03 Function(F29)
$f(x)=\sin^2(\pi y_1)+\sum_{i=1}^{n-1}(y_i-1)^2[1+10\sin^2(\pi y_{i+1})]+(y_n-1)^2$ -
Qing Function (F30)
$f(x)=f(x_1,x_2,...,x_n)=\sum_{i=1}^{n}(x^2-i)^2$ - n-dimension
$b=(\pm\sqrt{i},\pm\sqrt{i},...,\pm\sqrt{i})$
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(F31)
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(F32)
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(F33)
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Salomon Function (F34)
$f(\mathbf x)=f(x_1, ..., x_n)=1-cos(2\pi\sqrt{\sum_{i=1}^{D}x_i^2})+0.1\sqrt{\sum_{i=1}^{D}x_i^2}$ -
Styblinski-Tank Function (F35)
$f(\textbf{x}) = f(x_1, ..., x_n)= \frac{1}{2}\sum_{i=1}^{n} (x_i^4 -16x_i^2+5x_i)$ -
Xin-She Yang Function (F36)
$f(\mathbf x)=f(x_1, ...,x_n)=\sum_{i=1}^{n}\epsilon_i|x_i|^i$ -
Shubert Function (F37)
$f(\mathbf{x})=f(x_1, ...,x_n)=\prod_{i=1}^{n}{\left(\sum_{j=1}^5{ cos((j+1)x_i+j)}\right)}$ -
Levy Function (F38)
$f(x)=sin^2(\pi w_1)+\sum^{d-1}_{i=1}(w_i-1)^2[1+10sin^2(\pi w_i+1)]+(w_d-1)^2[1+sin^2(2\pi w_d)]$ , where$w_i=1+\frac{x_i-1}{4}$ , for all$i=1,\dots,d$ -
(F39)
