An Adaptive Hybrid Algorithm Based on Particle Swarm Optimization and Differential Evolution for Global Optimization

Table 4

Convergence speed and algorithm reliability comparisons.

Functions		Algorithms
		PSO	PSO-w	PSO-FDR	PSO-TVAC	DE	jDE	HPSO-DE
𝑓1	FESS	4.5056𝐸+4	2.3642+𝐸5	1.4738𝐸+5	1.0142𝐸+5	1.1055𝐸+5	1.0883𝐸+5	𝟐.𝟐𝟎𝟕𝟓𝐄+𝟒
	SR	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%
𝑓2	FESS	4.9428𝐸+4	2.4217𝐸+5	1.5194𝐸+5	1.0435𝐸+5	1.1905𝐸+5	6.4498𝐸+4	𝟐.𝟑𝟎𝟎𝟐𝐄+𝟒
	SR	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%
𝑓3	FESS	6.8336𝐸+4	2.5089𝐸+5	1.6382𝐸+5	1.1524𝐸+5	1.8979𝐸+5	7.6644𝐸+4	𝟑.𝟐𝟕𝟔𝟐𝐄+𝟒
	SR	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%	𝟏𝟎𝟎%
𝑓4	FESS	2.907𝐸+5	—	—	2.4757𝐸+5	1.1041𝐸+5	5.9383𝐸+4	𝟐.𝟐𝟎𝟕𝟓𝐄+𝟒
	SR	12%	0%	0%	100%	100%	100%	𝟏𝟎𝟎%
𝑓5	FESS	2.987𝐸+5	—	—	2.8725𝐸+5	—	—	𝟑.𝟐𝟔𝟐𝟗𝐄+𝟒
	SR	4%	0%	0%	24%	0%	0%	𝟏𝟎𝟎%
𝑓8	FESS	—	—	—	—	—	7.3477𝐸+4	𝟐.𝟑𝟎𝟖𝟒𝐄+𝟒
	SR	0%	0%	0%	0%	0%	100%	𝟏𝟎𝟎%
𝑓9	FESS	—		—	—	—	8.7133𝐸+4	𝟐.𝟐𝟑𝟓𝟔𝐄+𝟒
	SR	0%		0%	0%	0%	96%	𝟏𝟎𝟎%
𝑓10	FESS	7.337𝐸+4	2.7072𝐸+5	1.7226𝐸+5	1.2118𝐸+5	1.7113𝐸+5	9.0429𝐸+4	𝟑.𝟐𝟓𝟎𝟐𝐄+𝟒
	SR	92%	100%	100%	100%	100%	100%	𝟏𝟎𝟎%
𝑓11	FESS	4.6325𝐸+4	2.3907𝐸+5	1.5296𝐸+5	1.0411𝐸+5	1.1398𝐸+5	6.2468𝐸+4	2.0659𝐸+4
	SR	32%	28%	36%	36%	100%	100%	100%
𝑓12	FESS	4.6978𝐸+4	2.4440𝐸+5	1.3834𝐸+5	1.0872𝐸+5	1.0199𝐸+5	𝟓.𝟎𝟐𝟎𝟏𝐄+𝟒	—
	SR	72%	96%	100%	80%	100%	100%	0%
𝑓13	FESS	—	2.975𝐸+5	1.6684𝐸+5	1.4981𝐸+5	2.5882𝐸+5	𝟓.𝟕𝟐𝟕𝟏𝐄+𝟒	—
	SR	0%	4%	100%	60%	52%	100%	0%
𝑓14	FESS	—	2.7346𝐸+5	—	—	—	8.435𝐸+4	3.85E+4
	SR	0%	88%	0%	0%	0%	100%	𝟏𝟎𝟎%
𝑓15	FESS	—	—	—	—	—	—	𝟐.𝟏𝟎𝟐𝟓𝐄+𝟒
	SR	0%	0%	0%	0%	0%	0%	𝟏𝟎𝟎%
𝑓16	FESS	—	—	—	—	—	—	𝟐.𝟐𝟓𝟔𝟑𝐄+𝟒
	SR	0%	0%	0%	0%	0%	0%	𝟏𝟎𝟎%
𝑓17	FESS	—	—	—	—	—	—	𝟔.𝟖𝟖𝟕𝟖𝐄+𝟒
	SR	0%	0%	0%	0%	0%	0%	𝟖𝟎%
𝑓18	FESS	1.0931𝐸+5	—	—	1.4448𝐸+5	1.834𝐸+5	—	𝟐.𝟐𝟔𝟖𝐄+𝟒
	SR	36%	0%	0%	20%	100%	0%	100%