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

Table 3

Standard deviation for test function using LDIW-PSO.

Chaos maps	Dimension = 30					Dimension = 50
	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5
None	𝟐.𝟑𝟏𝟐𝐞−𝟎𝟓	2.095𝑒−02	1.226𝑒+01	1.259𝑒+04	8.589𝑒−09	5.041𝑒−01	1.292𝑒−02	1.737𝑒+01	2.136𝑒+04	9.913𝑒−05
Logistic	2.659𝑒−01	2.020𝑒−02	9.595𝑒+00	3.596𝑒+01	1.592𝑒−19	4.681𝑒−01	2.309𝑒−02	1.879𝑒+01	4.125𝑒+01	2.656𝑒−12
Tent	1.876𝑒−01^∗	1.539𝑒−02^∗	1.322𝑒+01	3.158𝑒+01^∗	1.717𝑒−20^∗	5.704𝑒−01	1.960𝑒−02^∗	2.063𝑒+01	𝟑.𝟓𝟗𝟗𝐞+𝟎𝟏^∗	1.614𝑒−12^∗
Skew Tent	1.824𝑒−01^∗	2.854𝑒−02	𝟕.𝟕𝟎𝟔𝐞+𝟎𝟎^∗	1.260𝑒+04	2.713𝑒−22^∗	3.938𝑒−01^∗	2.635𝑒−02	𝟏.𝟒𝟗𝟐𝐞+𝟎𝟏^∗	4.246𝑒+02	3.658𝑒−13^∗
Sine	2.102𝑒−01^∗	2.096𝑒−02	1.289𝑒+01	4.773𝑒+01	5.897𝑒−21^∗	5.112𝑒−01	2.783𝑒−02	2.032𝑒+01	1.260𝑒+04	7.103𝑒−10
ICMIC	3.043𝑒−01	1.359𝑒−02^∗	1.169𝑒+01	𝟐.𝟗𝟗𝟕𝐞+𝟎𝟏^∗	1.680𝑒−18	5.112𝑒−01	2.483𝑒−02	2.198𝑒+01	1.260𝑒+04	1.722𝑒−10
Circle	2.056𝑒−01^∗	1.997𝑒−02^∗	1.328𝑒+01	3.278𝑒+01^∗	2.914𝑒−22^∗	5.665𝑒−01	𝟏.𝟐𝟓𝟕𝐞−𝟎𝟐^∗	1.732𝑒+01^∗	5.013𝑒+01	1.572𝑒−12^∗
Piecewise	2.787𝑒−01	𝟏.𝟐𝟕𝟏𝐞−𝟎𝟐^∗	1.294𝑒+01	3.422𝑒+01^∗	3.728𝑒−21^∗	𝟑.𝟐𝟔𝟑𝐞−𝟎𝟏^∗	1.767𝑒−02^∗	2.446𝑒+01	7.173𝑒+02	2.610𝑒−13^∗
Gaussian	2.402𝑒−01^∗	1.916𝑒−02^∗	1.296𝑒+01	3.288𝑒+01^∗	𝟑.𝟗𝟖𝟔𝐞−𝟐𝟑^∗	4.304𝑒−01^∗	1.903𝑒−02^∗	1.976𝑒+01	8.620𝑒+01	𝟐.𝟐𝟐𝟕𝐞−𝟏𝟒^∗
Intermittency	3.861𝑒−01	1.817𝑒−02^∗	1.126𝑒+01	3.089𝑒+01^∗	7.894𝑒−23^∗	6.989𝑒−01	2.052𝑒−02^∗	1.633𝑒+01^∗	4.260𝑒+02	2.427𝑒−13^∗
Cubic	1.617𝑒−01^∗	1.760𝑒−02^∗	1.290𝑒+01	8.995𝑒+01	4.637𝑒−20^∗	4.679𝑒−01^∗	1.791𝑒−02^∗	1.910𝑒+01	4.661𝑒+01	5.196𝑒−12

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.