A Synchronous-Asynchronous Particle Swarm Optimisation Algorithm

Table 14

Friedman test on the effect of Δ.

		1%	5%	10%	50%	100%
𝑓1	Mean	0.3812	0.3944	0.3839	0.3932	0.3738
	Friedman rank	2	5	3	4	1
𝑓2	Mean	0.0732∗𝑒−12	0.1061∗𝑒−12	0.0612∗𝑒−12	0.1925∗𝑒−12	0.1401∗𝑒−12
	Friedman rank	2	3	1	5	4
𝑓3	Mean	38.4925	40.8531	39.8487	41.5781	40.5706
	Friedman rank	1	4	2	5	3
𝑓4	Mean	0.3428∗𝑒−09	0.2885∗𝑒−09	0.9245∗𝑒−09	0.2542∗𝑒−09	0.2786∗𝑒−09
	Friedman rank	4	3	5	1	2
𝑓5	Mean	0.2956∗𝑒−08	0.2979∗𝑒−08	0.3365∗𝑒−08	0.4385∗𝑒−08	0.4271∗𝑒−08
	Friedman rank	1	2	3	5	4
𝑓6	Mean	0.1400∗𝑒−04	0.1180∗𝑒−04	0.1210∗𝑒−04	0.1339∗𝑒−04	0.1753∗𝑒−04
	Friedman rank	4	1	2	3	5
𝑓7	Mean	0.0072	0.0069	0.0073	0.0070	0.0073
	Friedman rank	3	1	4.5	2	4.5
𝑓8	Mean	44.8242	44.4277	44.0441	43.8860	44.2639
	Friedman rank	5	4	2	1	3
𝑓9	Mean	0.3479	0.3515	0.3457	0.3505	0.3521
	Friedman rank	2	4	1	3	5
Average Friedman rank		2.67	3	2.61	3.22	3.5