An Investigation into the Performance of Particle Swarm Optimization with Various Chaotic Maps

Table 4

Success rate for test problems using LDIW-PSO.

Chaos maps	Dimension = 30					Dimension = 50
	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5
None	50/50	25/50	32/50	38/50	50/50	37/50	34/50	1/50	17/50	50/50
Logistic	49/50	29/50	42/50	45/50	50/50	44/50	27/50	0/50	36/50	50/50
Tent	49/50	25/50	33/50	𝟒𝟗/𝟓𝟎^∗	50/50	41/50	30/50*	1/50*	𝟒𝟏/𝟓𝟎^∗	50/50
Skew Tent	48/50	23/50	𝟒𝟑/𝟓𝟎^∗	48/50*	50/50	45/50*	27/50	1/50*	30/50	50/50
Sine	49/50	25/50	38/50	48/50*	50/50	43/50	35/50*	1/50*	31/50	50/50
ICMIC	47/50	29/50	39/50	47/50*	50/50	41/50	28/50*	1/50*	34/50	50/50
Circle	48/50	24/50	36/50	48/50*	50/50	39/50	𝟑𝟔/𝟓𝟎^∗	0/50	37/50*	50/50
Piecewise	48/50	25/50	37/50	46/50*	50/50	𝟒𝟕/𝟓𝟎^∗	32/50*	1/50*	34/50	50/50
Gaussian	47/50	29/50	36/50	48/50*	50/50	44/50	31/50*	1/50*	37/50*	50/50
Intermittency	46/50	25/50	38/50	𝟒𝟗/𝟓𝟎^∗	50/50	36/50	33/50*	0/50	36/50	50/50
Cubic	49/50	25/50	42/50	46/50*	50/50	44/50	29/50*	0/50	36/50	50/50

The values in bold are the best results obtained by the algorithms using the corresponding chaotic map incorporated into it compared with others.
*are the better results obtained by the algorithms relative to the corresponding chaotic maps, compared to Logistic map.