Improved Whale Optimization Algorithm for Solving Constrained Optimization Problems

Table 4

Statistical features of the results obtained by various versions of IWOA.

Problem	Features	IWOA	IWOA-1	IWOA-2	IWOA-3	IWOA-4	IWOA-5
g01	Best	−15	−14.998	−14.999	−15	−14.998	−14.999
	Mean	−14.998	−14.998	−14.991	−14.997	−14.994	−14.998
	Std.	1.97E − 13	3.24E − 04	9.85E − 03	7.46E − 04	5.27E − 03	2.13E − 04
g02	Best	−0.803572	−0.8038	−0.7997	−0.8034	−0.8017	−0.8038
	Mean	−0.801395	−0.8006	−0.8076	−0.8012	−0.8007	−0.8023
	Std.	6.9E − 03	7.05E − 03	1.65E − 02	6.67E − 03	7.69E − 02	6.5E − 03
g03	Best	−1.0001	−0.9997	−0.9958	−1.0001	−0.9979	−0.9999
	Mean	−0.9973	−0.9956	−0.9842	−1.0034	−0.9528	−0.9921
	Std.	3.9E − 03	2.62E − 03	4.8E − 03	3.6E − 03	5.3E − 03	5.3E − 03
g04	Best	−30665.539	−30664.66	−30664.41	−30665.88	−30664.32	−30665.51
	Mean	−30664.771	−30663.86	−30664.02	−30664.85	−30661.36	−30664.72
	Std.	1.7E − 01	3.5E − 01	2.1E − 02	2.4E − 01	8.6E − 01	2.6E − 01
g05	Best	5126.498	5126.697	5124.071	5126.421	5125.535	5125.386
	Mean	5126.804	5126.022	5129.948	5126.977	5127.811	5125.846
	Std.	3.5 E + 00	4.5 E + 00	6.2 E + 00	5.4 E + 00	7.4 E + 00	1.2 E + 00
g06	Best	−6961.814	−6961.814	−6958.081	−6961.814	−6959.795	−6961.814
	Mean	−6952.593	−6959.795	−6950.981	−6951.057	−6953.327	−6950.333
	Std.	9.9 E + 00	6.0 E + 00	7.3 E + 00	10E + 00	4.6 E + 00	11E + 00
g07	Best	24.3056	24.3037	24.3421	24.3184	24.3228	24.3106
	Mean	24.3705	24.3674	24.4065	24.3436	24.3788	24.3428
	Std.	2.4E − 02	1.3E − 01	5.2 E + 00	2.7E − 01	1.3 E + 00	2.2E − 02
g08	Best	−0.095825	−0.095825	−0.095802	−0.095824	−0.095822	−0.095825
	Mean	−0.095823	−0.095820	−0.095822	−0.095821	−0.095820	−0.095821
	Std.	4.8E − 06	2.7E − 05	3.2E − 04	6.5E − 06	5.2E − 05	6.7E − 06
g09	Best	680.630	680.638	682.241	680.630	680.633	680.630
	Mean	680.616	680.882	687.076	681.300	683.533	680.605
	Std.	9.1E − 02	0.499	3.942	0.291	2.438	8.6E − 01
g010	Best	7049.331	7047.405	7058.088	7050.038	7056.534	7049.148
	Mean	7046.627	7043.326	7051.038	7041.397	7042.572	7047.406
	Std.	3.1 E + 01	5.2 E + 02	6.3 E + 02	3.7 E + 01	2.7 E + 02	1.8 E + 01
g011	Best	0.7499	0.7499	0.7501	0.7499	0.7499	0.7499
	Mean	0.7495	0.7487	0.7416	0.7499	0.7494	0.7491
	Std.	2.9E − 06	3.5E − 06	4.3E − 05	3.1E − 06	2.5E − 06	7.4E − 06
g012	Best	−1.000	−1.000	−0.997	−1.000	−1.000	−0.999
	Mean	−0.998	−0.996	−0.991	−0.997	−0.993	−0.995
	Std.	2.3E − 03	5.3E − 03	3.5E − 02	2.6E − 03	9.2E − 03	6.3E − 03
g013	Best	0.05395	0.05396	0.05398	0.05396	0.05393	0.05395
	Mean	0.05394	0.05393	0.05388	0.05392	0.05390	0.05391
	Std.	3.4E − 05	2.5E − 04	1.7E − 03	4.2E − 05	4.8E − 04	3.7E − 05