Steady Modeling for an Ammonia Synthesis Reactor Based on a Novel CDEAS-LS-SVM Model

Table 1

The comparison results of the CDEAS algorithm and original DE algorithm.

	Original DE	CDEAS
Sphere function 𝑓1
Best	1.1746×10^−65	𝟓.𝟎𝟏𝟒𝟕×𝟏𝟎^−𝟕𝟗
Worst	1.0815×10^−23	𝟗.𝟑𝟐𝟒𝟒×𝟏𝟎^−𝟕𝟓
Mean	3.6052×10^−25	𝟏.𝟔𝟑𝟗𝟎×𝟏𝟎^−𝟕𝟓
Std.	1.9746×10^−24	𝟐.𝟐𝟑𝟏𝟓×𝟏𝟎^−𝟕𝟓
Success rate (%)	100	100
Times (s)	1.8803	14.6017
Shifted sphere function 𝑓2
Best	0	0
Worst	8.0779×10^−28	0
Mean	3.3658×10^−29	0
Std.	1.5078×10^−28	0
Success rate (%)	100	100
Times (s)	2.1788	18.1117
Schwefel’s Problem 1.2 𝑓3
Best	2.4386×10^−65	𝟑.𝟎𝟑𝟔𝟖×𝟏𝟎^−𝟕𝟖
Worst	2.4820×10^−22	𝟗.𝟐𝟗𝟎𝟐×𝟏𝟎^−𝟕𝟑
Mean	8.2736×10^−24	𝟕.𝟐𝟑𝟒𝟏×𝟏𝟎^−𝟕𝟒
Std.	4.5316×10^−23	𝟐.𝟎𝟏𝟖𝟕×𝟏𝟎^−𝟕𝟑
Success rate (%)	100	100
Times (s)	3.1647	24.1178
Shifted Schwefel’s Problem 1.2 𝑓4
Best	0	0
Worst	5.6545×10^−27	𝟑.𝟒𝟑𝟑𝟏×𝟏𝟎^−𝟐𝟕
Mean	2.0868×10^−28	𝟏.𝟖𝟖𝟒𝟖×𝟏𝟎^−𝟐𝟖
Std.	1.0323×10^−27	𝟕.𝟗𝟖𝟏𝟑×𝟏𝟎^−𝟐𝟖
Success rate (%)	100	100
Times (s)	3.3956	27.7058
Rosenbrock’s function 𝑓5
Best	13.0060	5.2659
Worst	166.1159	139.1358
Mean	70.9399	39.4936
Std.	40.0052	31.2897
Success rate (%)	86.67	96.67
Times (s)	1.9594	16.7233
Schwefel’s Problem 1.2 with noise in fitness 𝑓6
Best	3.1344×10^−39	𝟑.𝟗𝟖𝟖𝟑𝟖×𝟏𝟎^−𝟒𝟗
Worst	3.61389×10^−36	𝟏.𝟔𝟏𝟐𝟒×𝟏𝟎^−𝟒𝟑
Mean	5.7744×10^−37	𝟕.𝟒𝟔𝟓𝟔×𝟏𝟎^−𝟒𝟓
Std.	9.5348×10^−37	𝟐.𝟗𝟕𝟐𝟐×𝟏𝟎^−𝟒𝟒
Success rate (%)	100	100
Times (s)	3.2141	24.2426
Shifted Schwefel’s Problem 1.2 with noise in fitness 𝑓7
Best	0	0
Worst	0	0
Mean	0	0
Std.	0	0
Success rate (%)	100	100
Times (s)	3.3374	28.5638
Ackley’s function 𝑓8
Best	7.1054×10^−15	3.5527×10^−15
Worst	𝟒.𝟖𝟗𝟗𝟗×𝟏𝟎^−𝟕	1.3404
Mean	𝟏.𝟔𝟑𝟑𝟐×𝟏𝟎^−𝟖	0.1763
Std.	𝟖.𝟗𝟒𝟓𝟕×𝟏𝟎^−𝟖	0.4068
Success rate (%)	100	83.33
Times (s)	2.4820	20.9353
Shifted Ackley’s function 𝑓9
Best	7.1054×10^−15	𝟑.𝟓𝟓𝟐𝟕×𝟏𝟎^−𝟏𝟓
Worst	0.9313	0.9313
Mean	0.0310	0.0620
Std.	0.1700	0.2362
Success rate (%)	96.67	93.33
Times (s)	2.7337	21.6841
Griewank’s function 𝑓10
Best	0	0
Worst	0.0367	0.0270
Mean	0.0020	0.0054
Std.	0.0074	0.0076
Success rate (%)	90	56.67
Times (s)	2.535	20.7793
Shifted Griewank’s function 𝑓11
Best	0	0
Worst	0.0319	0.0343
Mean	0.0056	0.0060
Std	0.0089	0.0088
Success rate (%)	80	76.67
Times (s)	2.7768	22.8541
Rastrigin’s function 𝑓12
Best	8.1540	1.9899
Worst	35.5878	12.9344
Mean	20.3594	6.5003
Std.	6.3072	2.6612
Success rate (%)	3.33	90
Times (s)	2.7264	22.3237
Shifted Rastrigin’s function 𝑓13
Best	5.9725	0.9949
Worst	36.9923	6.7657
Mean	19.4719	8.2581
Std.	8.9164	3.8680
Success rate (%)	16.67	76.67
Times (s)	2.9313	23.8838
Noncontiguous Rastrigin’s function 𝑓14
Best	20.7617	3.9949
Worst	29.9112	11.9899
Mean	25.4556	8.1947
Std.	2.9078	2.2473
Success rate (%)	0	86.67
Times (s)	3.1663	25.5374
Shifted noncontiguous Rastrigin’s function 𝑓15
Best	0	0
Worst	16	6
Mean	6.7666	1.5333
Std.	3.4509	1.8519
Success rate (%)	40	96.67
Times (s)	3.3374	25.9430
Schwefel’s function 𝑓16
Best	118.4387	236.8770
Worst	710.6303	1362.0521
Mean	357.61725	676.4166
Std.	144.41244	324.2317
Success rate (%)	90	40
Times (s)	2.5028	19.0009
Schwefel’s Problem 2.21 𝑓17
Best	0.1640	0.3254
Worst	4.5102	4.7086
Mean	1.1077	1.9849
Std.	0.8652	1.16418
Success rate (%)	53.33	23.33
Times (s)	2.3806	19.2505
Schwefel’s Problem 2.22 𝑓18
Best	1.2706×10^−35	𝟖.𝟓𝟗𝟒𝟔×𝟏𝟎^−𝟒𝟓
Worst	1.6842×10^−34	𝟏.𝟖𝟑𝟔𝟐×𝟏𝟎^−𝟒𝟐
Mean	6.1883×10^−35	𝟐.𝟔𝟗𝟗𝟐×𝟏𝟎^−𝟒𝟑
Std.	3.4937×10^−35	𝟒.𝟔𝟐𝟓𝟕×𝟏𝟎^−𝟒𝟑
Success rate (%)	100	100
Times (s)	2.6297	20.8573