An Algorithm for Global Optimization Inspired by Collective Animal Behavior

Table 13

Multimodal test functions.

Test function	S	𝑓opt
𝑓8(𝐱)=∑^𝑛𝑖=1−𝑥𝑖sin(|𝑥𝑖|)	[−500,500]^𝑛	−418.98*n
𝑓9(𝐱)=∑^𝑛𝑖=1[𝑥^2𝑖−10cos(2𝜋𝑥𝑖)+10]	[−5.12,5.12]^𝑛	0
𝑓10(𝐱)=−20exp(−0.2(1/𝑛)∑^𝑛𝑖=1𝑥^2𝑖)−exp((1/𝑛)∑^𝑛𝑖=1cos(2𝜋𝑥𝑖))+20	[−32,32]^𝑛	0
𝑓11(𝐱)=(1/4000)∑^𝑛𝑖=1𝑥^2𝑖−∏^𝑛𝑖=1cos(𝑥𝑖/√𝑖)+1	[−600,600]^𝑛	0
𝑓12(𝐱)=(𝜋/𝑛){10sin(𝜋𝑦1)+∑^𝑛−1𝑖=1(𝑦𝑖−1)^2[1+10sin^2(𝜋𝑦𝑖+1)]+(𝑦𝑛−1)^2}+∑^𝑛𝑖=1𝑢(𝑥𝑖𝑦,10,100,4)𝑖=1+(𝑥𝑖+1)/4𝑢(𝑥𝑖,𝑎,𝑘,𝑚)=𝑘(𝑥𝑖−𝑎)^𝑚𝑥𝑖>𝑎0−𝑎<𝑥𝑖<𝑎𝑘(−𝑥𝑖−𝑎)^𝑚𝑥𝑖<−𝑎	[−50,50]^𝑛	0
𝑓13(𝐱)=0.1{sin^2(3𝜋𝑥1)+∑^𝑛𝑖=1(𝑥𝑖−1)^2[1+sin^2(3𝜋𝑥𝑖+1)]+(𝑥𝑛−1)^2[1+sin^2(2𝜋𝑥𝑛)]}+∑^𝑛𝑖=1𝑢(𝑥𝑖,5,100,4)	[−50,50]^𝑛	0