A Modified Whale Optimization Algorithm and Its Application in Seismic Inversion Problem

Table 2

Results of OCDWOA and compared algorithms.

Function	Algorithm	Best	Mean	Std
F1	WOA	3.45E − 84	1.84E − 74	6.85E − 74
	OWOA	3.67E − 87	1.54E − 72	6.15E − 72
	OEWOA	8.10E − 104	3.41E − 87	1.61E − 86
	IWOA	3.88E − 31	4.18E − 28	1.52E − 27
	OCDWOA	1.16E − 94	2.68E − 82	8.18E − 82
F2	WOA	3.76E − 59	4.29E − 49	2.30E − 48
	OWOA	8.72E − 58	3.71E − 50	9.41E − 50
	OEWOA	8.88E − 68	2.26E − 59	1.15E − 58
	IWOA	6.02E − 20	6.36E − 19	6.72E − 19
	OCDWOA	1.85E − 63	1.86E − 56	4.92E − 56
F3	WOA	29331.39043	46962.31228	11654.1269
	OWOA	23102.63585	45115.1214	9775.63579
	OEWOA	10896.08787	37765.42249	12462.65209
	IWOA	0.0204919	4.761001851	12.20526468
	OCDWOA	9123.146589	30378.88003	11250.945
F4	WOA	2.845944535	53.98492009	28.64604813
	OWOA	0.221683283	54.59717151	28.7671405
	OEWOA	0.395500666	51.05649771	30.09654391
	IWOA	2.53E − 05	1.43E − 03	1.46E − 03
	OCDWOA	0.091259942	27.15705548	22.72468237
F5	WOA	27.05096579	27.98206458	0.492345074
	OWOA	27.0462713	27.8628119	0.3574981
	OEWOA	27.47961584	28.17255965	0.377986162
	IWOA	24.72608991	26.21998458	1.236007685
	OCDWOA	26.94330849	27.75236194	0.519791973
F6	WOA	0.039352423	0.308186276	0.178197178
	OWOA	0.058900257	0.229444501	0.138575416
	OEWOA	0.094203593	0.471932521	0.211010397
	IWOA	0.132553897	0.634850188	0.363709611
	OCDWOA	0.011880743	0.177746121	0.202309313
F7	WOA	7.31E − 05	3.49E − 03	4.08E − 03
	OWOA	9.68E − 06	1.20E − 03	2.15E − 03
	OEWOA	1.78E − 05	8.51E − 04	9.84E − 04
	IWOA	0.001170766	0.004571304	0.003016255
	OCDWOA	1.19E − 05	8.98E − 04	1.21E − 03
F8	WOA	0	5.68E − 15	2.29E − 14
	OWOA	0	0	0
	OEWOA	0	0	0
	IWOA	0	22.36681071	24.91175078
	OCDWOA	0	0	0
F9	WOA	8.88E − 16	4.32E − 15	2.55E − 15
	OWOA	8.88E − 16	3.85E − 15	2.48E − 15
	OEWOA	8.88E − 16	4.20E − 15	2.27E − 15
	IWOA	2.22E − 14	4.29E − 14	1.27E − 14
	OCDWOA	8.88E − 16	4.44E − 15	2.09E − 15
F10	WOA	0	0.014239143	0.055902557
	OWOA	0	0.006369305	0.034886118
	OEWOA	0	0	0
	IWOA	0	0.005601519	0.009188179
	OCDWOA	0	0.00307175	0.016824667
F11	WOA	0.003303307	0.020703883	0.013561528
	OWOA	0.002886391	0.011523424	0.008134223
	OEWOA	0.008832644	0.022931786	0.008957016
	IWOA	0.01289871	0.04121751	0.023964971
	OCDWOA	0.000984744	0.008086227	0.00817336
F12	WOA	0.091759692	0.476972639	0.2731912
	OWOA	0.071293381	0.343978384	0.176667484
	OEWOA	0.264598322	0.558788251	0.219290838
	IWOA	0.360052384	0.826186996	0.250307701
	OCDWOA	0.008972727	0.315016992	0.165937507
F13	WOA	0.998003838	3.087707817	3.643013869
	OWOA	0.998003838	1.527492833	0.770156088
	OEWOA	0.998003838	1.991064676	1.244254244
	IWOA	0.998003838	5.491627348	4.859439425
	OCDWOA	0.998003838	1.328819151	0.7056337
F14	WOA	0.000309354	0.000754701	0.000591433
	OWOA	0.000308046	0.000692785	0.000506369
	OEWOA	0.000308042	0.000599412	0.000433827
	IWOA	0.000307494	0.005763864	0.008959844
	OCDWOA	0.000308015	0.00068318	0.000396378
F15	WOA	−1.031628453	−1.031628453	7.57E − 10
	OWOA	−1.031628453	−1.031628453	1.10E − 09
	OEWOA	−1.031628453	−1.031628453	5.29E − 10
	IWOA	−1.031628453	−1.031628453	2.29E − 10
	OCDWOA	−1.031628453	−1.031628453	3.68E − 11
F16	WOA	0.397887358	0.397894412	1.60E − 05
	OWOA	0.397887358	0.397899721	2.59E − 05
	OEWOA	0.397887358	0.397916992	0.000107977
	IWOA	0.397887358	0.397887585	5.13E − 07
	OCDWOA	0.397887358	0.397888516	2.38E − 06
F17	WOA	3.000000001	3.000043872	7.74E − 05
	OWOA	3.00000002	3.000044635	0.000152146
	OEWOA	3.000000001	3.000123665	0.000226823
	IWOA	3	8.400000042	20.55035867
	OCDWOA	3.00000001	3.000006355	1.60E − 05
F18	WOA	−3.862688519	−3.857262065	0.007143618
	OWOA	−3.862781863	−3.861815423	0.003572799
	OEWOA	−3.862782142	−3.85726697	0.019011496
	IWOA	−3.862782147	−3.862521555	0.001426916
	OCDWOA	−3.862782147	−3.862775916	9.47E − 06
F19	WOA	−3.321580972	−3.223597877	0.10220952
	OWOA	−3.321545137	−3.244143349	0.085289027
	OEWOA	−3.320833167	−3.213034803	0.091087411
	IWOA	−3.32199476	−3.270086944	0.060385879
	OCDWOA	−3.321994702	−3.278324784	0.058345799

The bold values mean the best results.