Differential Evolution Algorithm with Self-Adaptive Population Resizing Mechanism

Table 4

Experimental results of 100-dimensional problems 𝑓₁(𝑥)−𝑓₁₇(𝑥), averaged over 30 independent runs with 1 000 000 FES.

Function	DE	JADE	𝑗DE	SaDE	SapsDE
	Mean error (std Dev)	Mean error (std Dev)	Mean error (std Dev)	Mean error (std Dev)	Mean error (std Dev)
1	1.21𝑒−39(1.21𝑒−39)+	6.89𝑒−189(0.00𝑒+00)=	1.15𝑒−97(1.34𝑒−97)+	2.82𝑒−92(1.48𝑒−91)+	𝟏.𝟕𝟎𝐞−𝟏𝟗𝟖(𝟎.𝟎𝟎𝐞+𝟎𝟎)
2	3.81𝑒+08(1.57𝑒+08)+	1.20𝑒+00(1.86𝑒+00)+	1.03𝑒+02(4.06𝑒+01)+	1.75𝑒+02(7.03𝑒+01)+	𝟐.𝟔𝟓𝐞−𝟎𝟏(𝟏.𝟎𝟏𝐞+𝟎𝟎)
3	8.96𝑒+00(7.84𝑒−01)+	9.68𝑒−01(5.18𝑒−01)+	𝟏.𝟐𝟖𝐞−𝟏𝟒(𝟑.𝟕𝟎𝐞−𝟏𝟓) =	2.92𝑒+00(5.56𝑒−01)+	1.36𝑒−14(2.07𝑒−15)
4	3.98𝑒+01(9.40𝑒+00)+	1.97𝑒−03(4.21𝑒−03)=	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎) =	3.82𝑒−02(5.92𝑒−02)+	1.07𝑒−03(3.28𝑒−03)
5	8.52𝑒+02(5.26𝑒+01)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	9.95𝑒+00(2.75𝑒+00)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
6	1.00𝑒+01(7.87𝑒−01)+	7.23𝑒−01(9.71𝑒−02)+	3.67𝑒−01(4.79𝑒−02)+	1.46𝑒+00(2.97𝑒−01)+	𝟐.𝟗𝟔𝐞−𝟎𝟏(𝟑.𝟏𝟕𝐞−𝟎𝟐)
7	5.57𝑒+05(5.85𝑒+05)+	3.73𝑒−02(8.14𝑒−02)=	𝟏.𝟎𝟒𝐞−𝟎𝟑(𝟓.𝟔𝟖𝐞−𝟎𝟑) =	4.36𝑒−02(1.12𝑒−01)=	1.24𝑒−02(3.70𝑒−02)
8	3.69𝑒+06(2.40𝑒+06)+	1.07𝑒−01(4.05𝑒−01)=	1.01𝑒−01(5.52𝑒−01)=	1.62𝑒−01(6.86𝑒−01)=	𝟏.𝟑𝟒𝐞−𝟑𝟐(𝟓.𝟓𝟔𝐞−𝟒𝟖)
9	3.71𝑒+03(9.46𝑒+02)+	1.05𝑒−29(2.43𝑒−29)=	2.73𝑒−29(6.31𝑒−29)=	𝟏.𝟔𝟖𝐞−𝟑𝟎(𝟗.𝟐𝟐𝐞−𝟑𝟎) =	5.47𝑒−30(1.68𝑒−29)
10	3.82𝑒+05(2.72𝑒+04)+	𝟔.𝟓𝟏𝐞−𝟏𝟓(𝟏.𝟐𝟓𝐞−𝟏𝟒) =	3.04𝑒+01(1.84𝑒+01)+	1.15𝑒+02(3.38𝑒+01)+	8.18𝑒−15(1.63𝑒−14)
11	2.29𝑒+09(3.39𝑒+08)+	3.25𝑒+05(1.42𝑒+05)+	2.28𝑒+06(6.14𝑒+05)+	4.26𝑒+06(9.98𝑒+05)+	𝟐.𝟐𝟎𝐞+𝟎𝟓(𝟖.𝟒𝟒𝐞+𝟎𝟒)
12	4.47𝑒+05(3.67𝑒+04)+	𝟕.𝟖𝟎𝐞+𝟎𝟑(𝟑.𝟒𝟔𝐞+𝟎𝟑) =	2.69𝑒+04(9.63𝑒+03)+	4.83𝑒+04(1.06𝑒+04)+	8.59𝑒+03(4.50𝑒+03)
13	2.40𝑒+08(8.93𝑒+07)+	𝟏.𝟐𝟎𝐞+𝟎𝟎(𝟏.𝟖𝟔𝐞+𝟎𝟎) =	9.59𝑒+01(4.48𝑒+01)+	1.73𝑒+02(4.20𝑒+01)+	1.72𝑒+00(2.00𝑒+00)
14	2.13𝑒+01(2.27𝑒−02)+	2.13𝑒+01(8.41𝑒−02)+	2.13𝑒+01(2.47𝑒−02)+	2.13𝑒+01(2.12𝑒−02)+	𝟐.𝟎𝟑𝐞+𝟎𝟏(𝟒.𝟓𝟔𝐞−𝟎𝟏)
15	8.58𝑒+02(5.87𝑒+01)+	1.78𝑒−16(5.42𝑒−16)=	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	2.57𝑒+01(7.00𝑒+00)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
16	1.09𝑒+03(3.06𝑒+01)+	1.55𝑒+02(3.51𝑒+01)+	2.05𝑒+02(2.94𝑒+01)+	4.36𝑒+02(6.18𝑒+01)+	𝟒.𝟖𝟎𝐞+𝟎𝟏(𝟗.𝟎𝟒𝐞+𝟎𝟎)
17	1.60𝑒+02(1.70𝑒+00)+	1.14𝑒+02(9.12𝑒+00)+	1.27𝑒+02(3.55𝑒+00)+	1.05𝑒+02(7.30𝑒+00)+	𝟓.𝟐𝟐𝐞+𝟎𝟏(𝟐.𝟐𝟏𝐞+𝟎𝟎)
Total score	DE	JADE	𝑗DE	SaDE	SapsDE
+	17	7	10	14	*
−	0	0	0	0	*
=	0	10	7	3	*