An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

Table 2

Performance comparison of the E-MOEA and MOSADE on the test problems.

Test problems	GD		SP
	E-MOEA	MOSADE	E-MOEA	MOSADE
ZDT1	𝟐.𝟐𝟏𝟓𝟏e− 4	1.2485𝑒−3	0.19677	𝟎.𝟏𝟑𝟏𝟓𝟗
	±4.88744𝑒−5	±9.7574𝑒−5	±1.7614𝑒−2	±5.6921𝑒−3
ZDT2	𝟏.𝟏𝟕𝟖𝟗e− 4	9.8051𝑒−4	0.18056	𝟎.𝟏𝟐𝟎𝟗𝟗
	±4.14203𝑒−5	±4.9107𝑒−5	±2.2941𝑒−2	±7.9444𝑒−3
ZDT3	𝟏.𝟖𝟏𝟓𝟖e− 4	2.1620𝑒−3	0.49072	𝟎.𝟒𝟑𝟕𝟖𝟑
	±4.08439𝑒−5	±1.9962𝑒−4	±1.5302𝑒−2	±8.0801𝑒−3
ZDT6	𝟑.𝟒𝟒𝟎𝟐e− 5	2.5156𝑒−3	0.36294	𝟎.𝟏𝟑𝟑𝟏𝟗
	±3.25𝑒−6	±1.0967𝑒−4	±1.5114𝑒−2	±9.8303𝑒−3
DTLZ1	𝟏.𝟗𝟔𝟑𝟓e− 3	5.2512𝑒−3	𝟎.𝟐𝟒𝟏𝟏𝟏	0.63755
	±1.0045𝑒−3	±1.5650𝑒−4	±1.1527𝑒−2	±3.0464𝑒−2
DTLZ2	𝟖.𝟕𝟑𝟕𝟒e− 4	5.3344𝑒−3	𝟎.𝟐𝟕𝟗𝟑𝟗	0.61323
	±5.6621𝑒−5	±1.7429𝑒−4	±1.1527𝑒−2	±3.6732𝑒−2
DTLZ3	𝟐.𝟓𝟗𝟓𝟒e− 3	6.4632𝑒−3	𝟎.𝟑𝟎𝟗𝟒𝟒	0.58601
	±3.0169𝑒−3	±3.3253𝑒−4	±0.10179	±2.9955𝑒−2
DTLZ4	𝟓.𝟑𝟔𝟖𝟖𝟕e− 4	4.7736𝑒−3	𝟎.𝟓𝟏𝟒𝟏𝟏	0.93230
	±2.0186𝑒−5	±2.7427𝑒−4	±0.1810𝑒−2	±1.0819𝑒−1
DTLZ5	𝟑.𝟔𝟗𝟕𝟗e − 4	3.8930𝑒−3	0.42787	𝟎.𝟑𝟓𝟓𝟐𝟗
	±1.0853𝑒−4	±2.0137𝑒−3	±1.5032𝑒−2	±2.2054𝑒−1
DTLZ6	𝟏.𝟎𝟖𝟎𝟎e − 5	3.7701𝑒−3	0.43264	𝟎.𝟑𝟎𝟕𝟐𝟎
	±9.9346𝑒−7	±3.1470𝑒−4	±1.35959	±4.7503𝑒−2
DTLZ7	4.7858𝑒−3	𝟐.𝟑𝟕𝟑𝟕e−3	𝟎.𝟓𝟗𝟏𝟎𝟕	0.85454
	±2.1121𝑒−3	±0.001303	±9.4664𝑒−2	±3.8634𝑒−2