Analysis of Population Diversity of Dynamic Probabilistic Particle Swarm Optimization Algorithms

Table 2

The benchmark functions used in this paper.

Sphere	Formula	𝑓(𝑥)=∑^𝑛𝑖=1𝑥^2𝑖
	Dimension	Optimal solution	Optimal value	Range	Accepted error
	30	(0,0,0,…,0)	0	𝑥𝑖<100	0.01
Schaffer F6	Formula	𝑓(𝑥)=sin^2𝑥^21+𝑥^22−0.5[1+0.001(𝑥^21+𝑥^22)]^2−0.5
	Dimension	Optimal solution	Optimal value	Range	Accepted error
	2	(0,0)	0	𝑥𝑖<100	0.00001
Rosenbrock	Formula	𝑓(𝑥)=∑^𝑛−1𝑖=1[(1−𝑥𝑖)^2+100(𝑥𝑖+1−𝑥^2𝑖)^2]
	Dimension	Optimal solution	Optimal value	Range	Accepted error
	30	(1,1,1,…,1)	0	𝑥𝑖≤30	100
Griewank	Formula	1𝑓(𝑥)=1+4000^𝑛𝑖∑=1𝑥^2𝑖−∏^𝑛𝑖=1𝑥cos(^𝑖√𝑖)
	Dimension	Optimal solution	Optimal value	Range	Accepted error
	30	(0,0,0,…,0)	0	𝑥𝑖<600	0.1