Stochastic Constriction Cockroach Swarm Optimization for Multidimensional Space Function Problems

Table 1

Benchmark functions.

Problems	Range	Minimum
Ackley: 𝑓(𝑥) = +20+𝑒−20𝑒^−0.2∑𝑛𝑖=1(𝑥2𝑖/𝑛)−𝑒^∑𝑛𝑖=1cos(2𝜋𝑥𝑖/𝑛)	[−10, 10]	0
Levy: 𝑓(𝑥)=sin^2𝜋𝑦1+∑^𝑛−1𝑖=1(𝑦𝑖−1)^21+10sin^2𝜋𝑦𝑖+1+(𝑦𝑛−1)^21+sin^22𝜋𝑥𝑛,	[−10, 10]	0
where 𝑦𝑖1=1+4(𝑥𝑖−1)
Quadric: 𝑓(𝑥)=∑^𝑛∑𝑖=1^𝑖𝑗=1𝑥𝑗^2	[−10, 10]	0
Rastrigin: 𝑓(𝑥)=10𝑛+∑^𝑛𝑖=1𝑥𝑖^2−4000^𝑛∏𝑖=1𝑥cos^𝑖√𝑖+1	[−5.12, 5.12]	0
Rosenbrock: 𝑓(𝑥)=∑^𝑛−1𝑖=1100𝑥𝑖+1−𝑥^2𝑖^2+1−𝑥𝑖^2	[−5, 10]	0
Schwefel: 𝑓(𝑥)=∑^𝑛𝑖=1|𝑥𝑖|+∏^𝑛𝑖=1|𝑥𝑖|	[−10, 10]	0
Sphere: 𝑓(𝑥)=∑^𝑛𝑖=1𝑥^2𝑖	[−10, 10]	0
Sum Squares: 𝑓(𝑥)=∑^𝑛𝑖=1𝑖𝑥^2𝑖	[−10, 10]	0
Griewank: 1𝑓(𝑥)=4000^𝐷𝑖∑=1𝑥^2𝑖−∏^𝐷𝑖=1𝑥cos^𝑖√𝑖+1	[−600, 600]	0