Seismic Inversion Problem Using a Multioperator Whale Optimization Algorithm

Table 4

Experimental results of WOA, OWOA, OEWOA, DEWOA, and MOWOA on benchmark function.

Function	Algorithm	Best	Mean	Std
F1	WOA	2.83E − 84	4.28E − 74	2.29E − 73
	OWOA	4.59E − 86	7.95E − 75	2.66E − 74
	OEWOA	8.76E − 103	5.13E − 88	1.59E − 87
	DEWOA	6.77E − 31	1.94E − 28	4.52E − 28
	MOWOA	4.98E − 99	2.15E − 83	8.78E − 83
F2	WOA	8.71E − 57	2.85E − 51	9.40E − 51
	OWOA	1.53E − 57	1.89E − 52	4.72E − 52
	OEWOA	2.93E − 66	7.49E − 61	1.83E − 60
	DEWOA	4.31E − 20	1.19E − 18	1.72E − 18
	MOWOA	1.07E − 76	6.88E − 66	3.59E − 65
F3	WOA	11389.1184	50275.4671	16562.2253
	OWOA	26046.7217	47505.5764	13886.3143
	OEWOA	12028.0259	39227.1659	17413.6989
	DEWOA	0.0020014076	10.6482036	36.5865551
	MOWOA	347.571795	5457.18188	4555.64762
F4	WOA	3.5233	51.6101	27.7077
	OWOA	5.2728	45.4761	29.8808
	OEWOA	4.5498	59.497	26.6399
	DEWOA	0.00030451	0.00480735	0.00478835
	MOWOA	0.0071159	2.32151	2.72084
F5	WOA	27.5719	28.1458	0.400962
	OWOA	27.6861	28.2382	0.372579
	OEWOA	27.7523	28.4584	0.308603
	DEWOA	24.9472	28.8163	12.0021
	MOWOA	25.6436	27.2024	1.04652
F6	WOA	0.51965	1.1606	0.34138
	OWOA	0.1364	0.59648	0.27012
	OEWOA	0.15776	0.85447	0.26204
	DEWOA	0.24573	0.82121	0.41509
	MOWOA	0.00015393	0.33703	0.23659
F7	WOA	3.35E − 05	0.0055325	0.0081194
	OWOA	3.15E − 05	0.0016668	0.00317
	OEWOA	4.25E − 05	0.0019736	0.0054556
	DEWOA	0.0013155	0.0068832	0.0039475
	MOWOA	1.85E − 05	0.0036718	0.0035788
F8	WOA	0	3.78E − 15	2.07E − 14
	OWOA	0	1.89E − 15	1.03E − 14
	OEWOA	0	0.528263	2.46821
	DEWOA	5.6843E − 14	34.4122	29.1644
	MOWOA	0	4.95453	17.8488
F9	WOA	8.88E − 16	4.79E − 15	2.52E − 15
	OWOA	8.88E − 16	4.79E − 15	3.14E − 15
	OEWOA	8.88E − 16	4.79E − 15	2.52E − 15
	DEWOA	5.77E − 14	2.26E − 13	2.53E − 13
	MOWOA	8.88E − 16	4.55E − 15	2.37E − 15
F10	WOA	0	0.0043159	0.023639
	OWOA	0	0	0
	OEWOA	0	0.013409	0.073444
	DEWOA	0	0.0074847	0.013641
	MOWOA	0	0.00086761	0.003396
F11	WOA	0.011672	0.064382	0.11014
	OWOA	0.0077861	0.032889	0.03719
	OEWOA	0.020497	0.054975	0.047825
	DEWOA	0.018752	0.076452	0.10195
	MOWOA	0.0018431	0.0302	0.025889
F12	WOA	0.47343	1.0196	0.34191
	OWOA	0.23239	0.6226	0.32139
	OEWOA	0.20696	0.78504	0.3463
	DEWOA	0.3684	1.0457	0.2804
	MOWOA	0.12339	0.59867	0.29991
F13	WOA	0.998003838	3.0904	3.4404
	OWOA	0.998003838	2.1496	1.9772
	OEWOA	0.998003838	2.3481	1.9499
	DEWOA	0.998003838	6.1401	4.9939
	MOWOA	0.998003838	2.0511	1.8885
F14	WOA	0.00031147	0.00066158	0.00047928
	OWOA	0.00031562	0.00069909	0.00048553
	OEWOA	0.00030766	0.00077445	0.00056134
	DEWOA	0.00030754	0.010188	0.015558
	MOWOA	0.00030753	0.00058442	0.00023566
F15	WOA	−1.031628453	−1.031628453	4.06E − 09
	OWOA	−1.031628453	−1.031628453	1.78E − 08
	OEWOA	−1.031628453	−1.031628453	6.47E − 09
	DEWOA	−1.031628453	−1.031628453	4.12E − 10
	MOWOA	−1.031628453	−1.031628453	5.16E − 16
F16	WOA	0.397887358	0.3979244270	5.23E − 05
	OWOA	0.397887358	0.3979029910	2.65E − 05
	OEWOA	0.397887358	0.3979767040	0.00022822
	DEWOA	0.397887358	0.3978875983	4.54E − 07
	MOWOA	0.397887358	0.3978873577	0
F17	WOA	3	3.0011192003	0.00520741
	OWOA	3	3.0001780437	0.00025126
	OEWOA	3	3.0001806154	0.00022324
	DEWOA	3	6.6000003099	15.4264
	MOWOA	3	3.0000001432	1.99E − 07
F18	WOA	−3.862776732	−3.846948573	0.024831771
	OWOA	−3.862782093	−3.851807712	0.025891037
	OEWOA	−3.862781853	−3.837883876	0.054873368
	DEWOA	−3.862782128	−3.861482692	0.002955750
	MOWOA	−3.862782147	−3.861988195	0.002403123
F19	WOA	−3.320772006	−3.237683424	0.14504
	OWOA	−3.321595755	−3.242573715	0.091649
	OEWOA	−3.319657692	−3.209244175	0.09022
	DEWOA	−3.321993785	−3.258288827	0.087085
	MOWOA	−3.321995171	−3.249430550	0.080041