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

Table 7

Mean fitness obtained by RIW-PSO for test problems using the various chaotic maps.

Chaos maps	Dimension = 30					Dimension = 50
	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5	𝑓1	𝑓2	𝑓3	𝑓4	𝑓5
None	3.358𝑒+00	1.496𝑒+00	6.988𝑒+01	4.173𝑒+03	5.512𝑒+01	5.022𝑒+00	4.905𝑒+00	1.884𝑒+02	3.062𝑒+04	4.352𝑒+02
Logistic	8.915𝑒−07	𝟏.𝟒𝟏𝟏𝐞−𝟎𝟐	3.933𝑒+01	5.085𝑒+01	5.404𝑒−13	9.938𝑒−04	1.303𝑒−02	7.041𝑒+01	1.218𝑒+02	2.798𝑒−07
Tent	3.712𝑒−07^∗	1.610𝑒−02	4.555𝑒+01	5.092𝑒+01	2.099𝑒−13^∗	𝟏.𝟕𝟎𝟏𝐞−𝟎𝟒^∗	1.007𝑒−02^∗	7.237𝑒+01	1.344𝑒+02	1.574𝑒−08^∗
Skew Tent	2.309𝑒−02	2.055𝑒−02	4.267𝑒+01	4.710𝑒+01^∗	3.280𝑒−15^∗	3.468𝑒−02	2.172𝑒−02	7.044𝑒+01	1.161𝑒+02^∗	1.443𝑒−09^∗
Sine	5.360𝑒−02	1.496𝑒−02	3.877𝑒+01^∗	5.341𝑒+01	3.498𝑒−13^∗	4.281𝑒−04^∗	1.367𝑒−02	6.922𝑒+01^∗	1.171𝑒+02^∗	7.386𝑒−08^∗
ICMIC	3.798𝑒−02	1.450𝑒−02	4.252𝑒+01	6.736𝑒+01	9.963𝑒−15^∗	2.623𝑒−04^∗	1.885𝑒−02	𝟔.𝟖𝟗𝟒𝐞+𝟎𝟏^∗	1.138𝑒+02^∗	8.323𝑒−09^∗
Circle	5.360𝑒−02	1.577𝑒−02	4.128𝑒+01	1.210𝑒+02	𝟏.𝟏𝟔𝟕𝐞−𝟏𝟕^∗	2.772𝑒−02	1.985𝑒−02	7.641𝑒+01	9.886𝑒+01^∗	2.253𝑒−10^∗
Piecewise	1.913e − 𝟎𝟕^∗	1.686𝑒−02	4.096𝑒+01	5.357𝑒+01	2.019𝑒−14^∗	7.353𝑒−04^∗	𝟗.𝟔𝟐𝟕𝐞−𝟎𝟑^∗	7.256𝑒+01	1.125𝑒+02^∗	5.960𝑒−09^∗
Gaussian	3.002𝑒−02	1.825𝑒−02	4.248𝑒+01	5.155𝑒+01	3.693𝑒−17^∗	2.950𝑒−02	2.072𝑒−02	7.188𝑒+01	1.047𝑒+02^∗	7.502𝑒−11^∗
Intermittency	5.674𝑒−01	1.541𝑒−02	4.239𝑒+01	𝟒.𝟒𝟓𝟑𝐞+𝟎𝟏^∗	1.357𝑒−16^∗	3.831𝑒−01	2.915𝑒−02	7.362𝑒+01	𝟗.𝟒𝟓𝟔𝐞+𝟎𝟏^∗	𝟑.𝟔𝟗𝟗𝐞−𝟏𝟑^∗
Cubic	4.629𝑒−07^∗	1.905𝑒−02	𝟑.𝟖𝟐𝟒𝐞+𝟎𝟏^∗	1.095𝑒+02	2.368𝑒−13^∗	4.757𝑒−04^∗	1.457𝑒−02	6.957𝑒+01^∗	1.785𝑒+02	7.570𝑒−08^∗

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.