Differential Evolution Algorithm with Self-Adaptive Population Resizing Mechanism

Table 6

Experimental results of SapsDE and ATPS-DEs.

Function	𝑗DE-APTS	CoDE-APTS	JADE-APTS	SapsDE
	Mean error (std Dev)	Mean error (std Dev)	Mean error (std Dev)	Mean error (std Dev)
9	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	8.82𝑒−17(7.06𝑒−16)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
10	7.93𝑒−11(2.31𝑒−11)+	2.70𝑒−03(6.73𝑒−03)+	𝟐.𝟏𝟎𝐞−𝟐𝟗(𝟒.𝟖𝟔𝐞−𝟐𝟗)−	1.17𝑒−28(1.07𝑒−28)
11	9.83𝑒+04(4.42𝑒+04)+	1.06𝑒+05(8.03𝑒+05)+	7.43𝑒+03(6.04𝑒+03)=	𝟕.𝟎𝟎𝐞+𝟎𝟑(𝟒.𝟐𝟗𝐞+𝟎𝟑)
12	9.17𝑒−02(8.02𝑒−02)+	1.55𝑒−03(3.98𝑒−02)=	𝟏.𝟕𝟗𝐞−𝟐𝟑(𝟗.𝟕𝟔𝐞−𝟐𝟑)=	4.22𝑒−15(1.25𝑒−14)
13	𝟑.𝟖𝟕𝐞−𝟎𝟏(𝟕.𝟐𝟐𝐞−𝟎𝟏)=	6.12𝑒+00(4.39𝑒+00)+	8.59𝑒+00(3.08𝑒+01)+	1.49𝑒+00(5.68𝑒+00)
14	2.09𝑒+01(1.09𝑒−02)+	𝟐.𝟎𝟕𝐞+𝟎𝟏(𝟐.𝟒𝟒𝐞−𝟎𝟏)+	2.09𝑒+01(6.43𝑒−02)+	𝟐.𝟎𝟕𝐞+𝟎𝟏(𝟑.𝟗𝟖𝐞−𝟎𝟏)
15	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	5.01𝑒−01(3.40𝑒−01)+	5.42𝑒−12(2.24𝑒−12)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
16	5.59𝑒+01(2.47𝑒+01)+	5.10𝑒+01(1.55𝑒+01)+	3.94𝑒+01(1.16𝑒+01)+	𝟐.𝟏𝟖𝐞+𝟎𝟏(𝟑.𝟓𝟖𝐞+𝟎𝟎)
17	𝟕.𝟗𝟎𝐞+𝟎𝟎(𝟔.𝟗𝟗𝐞+𝟎𝟎)−	1.22𝑒+01(6.30𝑒+00)−	2.19𝑒+01(2.84𝑒+00)−	2.42𝑒+01(1.68𝑒+00)
Total score	𝑗DE-APTS	CoDE-APTS	JADE-APTS	SapsDE
+	5	7	4	*
−	1	1	2	*
=	3	1	3	*