Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis

Table 1

High dimensional benchmark functions used in experiments.

Test function	Range
𝑓1(𝑥)=^𝑛𝑖=1𝑥^2𝑖	[−100,100]^𝑛
𝑓2(𝑥)=^𝑛𝑖=1(10^6)^(𝑖−1)/(𝑛−1)𝑥^2𝑖	[−100,100]^𝑛
𝑓3(𝑥)=^𝑛𝑖=1𝑖𝑥^2𝑖	[−10,10]^𝑛
𝑓4(𝑥)=^𝑛𝑖=1𝑥𝑖^(𝑖+1)	[−10,10]^𝑛
𝑓5(𝑥)=^𝑛𝑖=1(𝑥𝑖+0.5)^2	[−100,100]^𝑛
𝑓6(𝑥)=−20exp−0.21𝑛^𝑛𝑖=1𝑥^2𝑖1−exp𝑛^𝑛𝑖=1cos(2𝜋𝑥𝑖)+20+𝑒	[−32,32]^𝑛
𝑓7(𝑥)=^𝑛−1𝑖=1100(𝑥𝑖+1−𝑥^2𝑖)^2+(𝑥𝑖−1)^2	[−10,10]^𝑛
𝑓8(𝑥)=^𝑛𝑖=1𝑥^2𝑖−10cos(2𝜋𝑥𝑖)+10	[−5.12,5.12]^𝑛
𝑓9(𝑥)=^𝑛𝑖=1𝑦^2𝑖−10cos(2𝜋𝑦𝑖)+10 𝑦^2𝑖𝑥𝑖,𝑥𝑖<12round2𝑥𝑖2,𝑥𝑖≥12	[−5.12,5.12]^𝑛
𝑓101(𝑥)=𝑛^𝑛𝑖=1(𝑥^4𝑖−16𝑥^2𝑖+5𝑥𝑖)	[−5,5]^𝑛
𝑓11(𝑥)=^𝑛𝑖=1𝑥𝑖sin(𝑥𝑖)+0.1𝑥𝑖	[−10,10]^𝑛
𝑓12(𝑥)=^𝑛−1𝑖=1(𝑥𝑖−1)^21+𝑥𝑖sin^2(3𝜋𝑥𝑖)	[−10,10]^𝑛