README.md

Test Functions for Global Optimization

Uni-modal: unimodal_test_functions.py

Name	Function	Dimension	Range	Global minima
f1	$f(x)=\sum_{i=1}^nx_i^2$	30	[-100, 100]	0
f2	$f(x)=\sum_{i=1}^n	x_i	+\prod_{i=1}^n	x_i
f3	$f(x)=\sum_{i=1}^n(\sum_{j=1}^ix_j)^2$	30	[-100, 100]	0
f4	$f(x)=\max_i{	x_i	,1\leq i\leq n}$	30
f5	$f(x)=\sum_{i=1}^{n-1}[100(x_{i+1}-x_i)^2+(x_i-1)^2]^2$	30	[-30, 30]	0
f6	$f(x)=([x_i+0.5])^2$	30	[-100, 100]	0
f7	$f(x)=\sum_{i=1}^nix_i^4+random[0,1)$	30	[-1.28, 1.28]	0

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Multi-modal: multimodal_test_functions.py

Name	Function	Dimension	Range	Global peaks
two-peak trap	$f(x)=\left{\begin{aligned}&\frac{160}{15}(15-x),0\leq x<15\&\frac{200}{5}(x-15),15\leq x\leq 20\end{aligned}\right.$	1	[0, 20]	1
central two-peak trap	$f(x)=\left{\begin{aligned}x=1\x=2\end{aligned}\right.$	1	[0, 20]	1
equal maxima	$f(x)=\sin^6(5\pi x)$	1	[0, 1]	5
uneven maxima	$f(x)=\sin^6(5\pi(x^{3/4}-0.05))$	1	[0, 1]	5
inverted Shubert function	$f(x)=-\prod_{i=1}^n\sum{j=1}^5j\times\cos[(j+1)x_i+j]$	$n$	[-10, 10]	$n\times3^n$
inverted Vincent function	$f(x)=\frac{1}{n}\sum_{i=1}^n\sin(10\log(x_i))$	$n$	[0.25, 10]	$6^n$
inverted Rastrigin function	$f(x)=-\sum_{i=1}^n(x_i^2-10\cos(2\pi x_i)+10)$	$n$	[-1.5, 1.5]	1