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Table 8 shows the statistical results of

\bar{I G D}

⁠,

\bar{S}

and

\bar{H V}

obtained by MOEA-OSD/SRS and other seven compared algorithms. Note, the PF corresponding to the nondominant solutions in the PS obtained by all eight algorithms makes up the real PF of each environment. It is obvious that MOEA-OSD/SRSA is of better performance, that is to say, the control effect of the PID controller optimized by MOEA-OSD/SRS is much better. Therefore, MOEA-OSD/SRS is promising to be applied to tune the parameters of the PID controller of the dynamic system.

Table 8:

The statistical results of $\bar{I G D}$ ⁠, $\bar{S}$ ⁠, and $\bar{H V}$ for different algorithms.

				FPS	PPS				MOEA
		DNSGA	DNSGA	-RM	-RM			Immune	-OSD
Metrics	Statistic	-II-A	-II-B	-MEDA	-MEDA	SGEA	MOEA/D	GDE3	/SRS
$\bar{I G D}$	Mean	4.9289 $†$	4.8479 $†$	3.7097 $†$	3.6284 $†$	3.9999 $†$	4.0811 $†$	4.6840 $†$	3.4995
	Std	0.0579	0.1245	0.1196	0.0373	0.0815	0.1001	0.0968	0.0128
$\bar{S}$	Mean	1.8673 $†$	1.6659 $†$	0.1303 $†$	3.6284 $†$	0.0417 §	0.0639 $†$	0.0491 $†$	0.0451
	Std	0.3479	0.5166	0.1156	0.0373	0.0019	0.0108	0.0030	0.0028
$\bar{H V}$	Mean	2.3793 $†$	2.3823 $†$	2.4038 $†$	2.4050 $†$	2.4005 $†$	2.3891 $†$	2.4089 $†$	2.6319
	Std	0.0093	0.0164	0.0033	0.0011	0.0030	0.0032	0.0125	1.15E-04

				FPS	PPS				MOEA
		DNSGA	DNSGA	-RM	-RM			Immune	-OSD
Metrics	Statistic	-II-A	-II-B	-MEDA	-MEDA	SGEA	MOEA/D	GDE3	/SRS
$\bar{I G D}$	Mean	4.9289 $†$	4.8479 $†$	3.7097 $†$	3.6284 $†$	3.9999 $†$	4.0811 $†$	4.6840 $†$	3.4995
	Std	0.0579	0.1245	0.1196	0.0373	0.0815	0.1001	0.0968	0.0128
$\bar{S}$	Mean	1.8673 $†$	1.6659 $†$	0.1303 $†$	3.6284 $†$	0.0417 §	0.0639 $†$	0.0491 $†$	0.0451
	Std	0.3479	0.5166	0.1156	0.0373	0.0019	0.0108	0.0030	0.0028
$\bar{H V}$	Mean	2.3793 $†$	2.3823 $†$	2.4038 $†$	2.4050 $†$	2.4005 $†$	2.3891 $†$	2.4089 $†$	2.6319
	Std	0.0093	0.0164	0.0033	0.0011	0.0030	0.0032	0.0125	1.15E-04

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