Improved Whale Optimization Algorithm for Solving Constrained Optimization Problems

Table 3

Comparison of IWOA with other algorithms.

Function/optimal	Methods	Best	Mean	Std.	FEs
g01/−15.000	IPES	−14.999	−14.999	—	240000
	IFOA	−15	−15	0	164111
	COMDE	−15	−15	7.4E − 01	130000
	ICA	−15	−15	0	200000
	IWOA	−15	−14.998	1.97E − 13	80000
g02/−0.803619	IPES	−0.803607	−0.792771	—	240000
	IFOA	−0.803603	−0.803617	2.4E − 06	553916
	COMDE	−0.803619	−0.801238	5.0E − 03	200000
	ICA	−0.803619	−0.791906	5.1E − 02	200000
	IWOA	−0.803576	−0.801395	6.9E − 03	80000
g03/−1.000	IPES	−1	−1	—	240000
	IFOA	−1.00052	− 1.00052	9.9E − 16	434916
	COMDE	−1.0000	−1.0000	3.03E − 08	150000
	ICA	−1.0005	−1.0004	6.2E − 05	200000
	IWOA	−1.0001	−0.9973	3.9E − 03	80000
g04/−30665.539	IPES	−30665.539	−30665.539	—	240000
	IFOA	−30665.538	−30665.538	2.2E − 11	134756
	COMDE	−30665.539	−30665.539	0	50000
	ICA	−30665.539	−30665.539	0	200000
	IWOA	−30665.539	−30664.771	1.7E − 01	64000
g05/5126.498	IPES	5126.498	5139.003	—	240000
	IFOA	5126.495	5126.495	2.5E − 08	786696
	COMDE	5126.498	5126.498	0	200000
	ICA	5126.498	5126.498	3.8E − 01	200000
	IWOA	5126.498	5126.804	3.5 E + 00	64000
g06/−6961.814	IPES	−6961.814	−6961.814	—	240000
	IFOA	−6961.814	−6961.814	1.8E − 12	129950
	COMDE	−6961.814	−6961.814	0	12000
	ICA	−6961.814	−6961.814	0	200000
	IWOA	−6961.814	−6952.593	9.9 E + 00	64000
g07/24.306	IPES	24.307	24.316	—	240000
	IFOA	24.3068	24.3064	1.29E − 04	695875
	COMDE	24.3062	24.3062	4.7E − 07	200000
	ICA	24.306	24.3704	3.2E − 01	200000
	IWOA	24.3056	24.3705	2.4E − 02	80000
g08/−0.095825	IPES	−0.095825	−0.095825	—	240000
	IFOA	−0.095825	−0.095825	8.33E − 17	10331
	COMDE	−0.095825	−0.095825	9.0E − 18	4000
	ICA	−0.095825	−0.095825	0	200000
	IWOA	−0.095825	−0.095823	4.8E − 06	64000
g09/680.630	IPES	680.630	680.630	—	240000
	IFOA	680.632	680.647	2.02E − 08	559717
	COMDE	680.632	680.630	4.07E − 13	70000
	ICA	680.630	679.429	4.5E − 02	200000
	IWOA	680.630	680.616	9.1E − 02	64000
g10/7049.331	IPES	7051.341	7210.360	—	240000
	IFOA	7049.2844	7049.2607	6.4E − 03	883825
	COMDE	7049.248	7049.248	1.5E − 04	200000
	ICA	7049.248	7053.721	1.7E + 02	200000
	IWOA	7049.331	7046.627	3.1 E + 01	64000
g11/0.7499	IPES	0.75	0.75	—	240000
	IFOA	0.75	0.75	2.7E − 11	372647
	COMDE	0.7499	0.7499	0	50000
	ICA	0.74990	0.74995	0	200000
	IWOA	0.7499	0.7495	2.9E − 06	64000
g12/−1.000	IPES	−1.000	−1.000	—	240000
	IFOA	−1.000	−1.000	0	4505
	COMDE	−1	−1	0	6000
	ICA	−1	−1	0	200000
	IWOA	−1.000	−0.998	2.3E − 03	64000
g13/0.05395	IPES	0.053950	0.0514626	—	240000
	IFOA	0.0543003	0.0539588	6.98E − 05	904975
	COMDE	0.0539415	0.0539415	1.4E − 17	150000
	ICA	—	—	—	—
	IWOA	0.05395	0.05394	3.4E − 05	64000