Differential Evolution Algorithm with Self-Adaptive Population Resizing Mechanism

Table 3

Experimental results of 50-dimensional problems 𝑓₁(𝑥)−𝑓₁₇(𝑥), averaged over 30 independent runs with 500 000 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	3.51𝑒−35(4.71𝑒−35)+	1.99𝑒−184(0.00𝑒+00)+	5.98𝑒−62(7.49𝑒−62)+	1.67𝑒−118(7.81𝑒−118)+	𝟑.𝟎𝟓𝐞−𝟐𝟎𝟐(𝟎.𝟎𝟎𝐞+𝟎𝟎)
2	1.82𝑒+08(1.16𝑒+08)+	5.32𝑒−01(1.38𝑒+00)+	2.61𝑒+01(1.56𝑒+01)+	6.79𝑒+01(3.58𝑒+01)+	𝟏.𝟕𝟎𝐞−𝟐𝟖(𝟓.𝟓𝟓𝐞−𝟐𝟖)
3	2.69𝑒−02(7.63𝑒−03)+	5.98𝑒−15(9.01𝑒−16)=	6.21𝑒−15(0.00𝑒+00)+	1.18𝑒+00(4.68𝑒−01)+	𝟓.𝟑𝟖𝐞−𝟏𝟓(𝟏.𝟓𝟐𝐞−𝟏𝟓)
4	6.35𝑒−02(1.62𝑒−01)+	1.56𝑒−03(5.46𝑒−03)=	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)−	1.39𝑒−02(3.26𝑒−02)+	2.46𝑒−04(1.35𝑒−03)
5	2.02𝑒+02(5.08𝑒+01)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	5.97𝑒−01(7.20𝑒−01)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
6	1.78𝑒+00(2.00𝑒−01)+	3.07𝑒−01(3.65𝑒−02)+	𝟐.𝟎𝟎𝐞−𝟎𝟏(𝟑.𝟓𝟓𝐞−𝟏𝟏)−	5.37𝑒−01(1.13𝑒−01)+	2.73𝑒−01(3.05𝑒−02)
7	1.24𝑒−02(4.73𝑒−02)+	6.22𝑒−03(1.90𝑒−02)+	1.57𝑒−32(5.57𝑒−48)+	5.39𝑒−02(1.04𝑒−01)+	𝟗.𝟒𝟐𝐞−𝟑𝟑(𝟐.𝟕𝟖𝐞−𝟒𝟖)
8	1.37𝑒−32(9.00𝑒−34)=	1.35𝑒−32(5.57𝑒−48)=	1.35𝑒−32(5.57𝑒−48)=	5.43𝑒−02(2.91𝑒−01)+	𝟏.𝟑𝟒𝐞−𝟑𝟐(𝟓.𝟓𝟔𝐞−𝟒𝟖)
9	1.40𝑒−28(1.34𝑒−28)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	1.68𝑒−30(9.22𝑒−30)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
10	3.08𝑒+00(1.90𝑒+00)+	4.20𝑒−27(2.47𝑒−27)=	6.20𝑒−07(7.93𝑒−07)+	1.22𝑒−01(1.98𝑒−01)+	𝟑.𝟓𝟒𝐞−𝟐𝟕(𝟐.𝟗𝟕𝐞−𝟐𝟕)
11	4.61𝑒+08(8.15𝑒+07)+	3.63𝑒+04(2.18𝑒+04)+	5.31𝑒+05(2.42𝑒+04)+	1.07𝑒+06(3.67𝑒+05)+	𝟏.𝟐𝟑𝐞+𝟎𝟒(𝟓.𝟕𝟖𝐞+𝟎𝟑)
12	2.36𝑒+02(1.52𝑒+02)+	8.77𝑒−01(2.10𝑒+00)=	4.83𝑒+02(4.62𝑒+02)+	6.49𝑒+03(2.89𝑒+03)+	𝟓.𝟐𝟒𝐞−𝟎𝟏(𝟔.𝟖𝟑𝐞−𝟎𝟏)
13	2.99𝑒+01(1.97𝑒+01)+	1.26𝑒+01(4.03𝑒+01)+	2.63𝑒+01(2.70𝑒+01)+	8.97𝑒+01(4.56𝑒+01)+	𝟗.𝟑𝟎𝐞−𝟎𝟏(𝟏.𝟕𝟏𝐞+𝟎𝟎)
14	2.11𝑒+01(2.82𝑒−02)+	2.11𝑒+01(2.01𝑒−01)+	2.10𝑒+01(5.57𝑒−02)+	2.11𝑒+01(3.94𝑒−02)+	𝟐.𝟎𝟕𝐞+𝟎𝟏(𝟓.𝟎𝟑𝐞−𝟎𝟏)
15	1.93𝑒+02(3.67𝑒+01)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)	1.89𝑒+00(9.90𝑒−01)+	𝟎.𝟎𝟎𝐞+𝟎𝟎(𝟎.𝟎𝟎𝐞+𝟎𝟎)
16	3.57𝑒+02(1.19𝑒+01)+	4.84𝑒+01(7.99𝑒+00)=	5.47𝑒+01(1.03𝑒+01)+	1.26𝑒+02(2.10𝑒+01)+	𝟒.𝟕𝟎𝐞+𝟎𝟏(𝟕.𝟖𝟔𝐞+𝟎𝟎)
17	7.29𝑒+01(1.19𝑒+00)+	5.19𝑒+01(2.17𝑒+00)+	5.40𝑒+01(2.94𝑒+00)+	𝟑.𝟖𝟓𝐞+𝟎𝟏(𝟒.𝟎𝟕𝐞+𝟎𝟎)−	5.00𝑒+01(2.69𝑒+00)
Total score	DE	JADE	𝑗DE	SADE	SAPSDE
+	16	8	11	16	*
−	0	0	2	1	*
=	1	9	4	0	*