Improved Gradient-Based Optimizer for Modelling Thermal and Hydropower Plants

Table 2

Results of multimodal benchmark functions.

Function		IGBO	GBO	HPO	WOA	SDO	GWO
F8	Best	−1909.05	−1872.79	−1795.63	−1909.05	−1655	−1495.31
	Mean	−1761.77	−1743.83	−1675.9	−1786.9	−1312.83	−1245.57
	Median	−1751.43	−1732.31	−1684.22	−1907.06	−1385.86	−1224.18
	Worst	−1650.19	−1659.76	−1452.47	−1632.06	−598.802	−1123.85
	STD	81.08657	58.4135	73.47505	138.0759	294.008	104.0153
F9	Best	0	0	0	0	4.33E − 30	1.062467
	Mean	0	0	0	1.14E − 14	1.75E − 22	9.801018
	Median	0	0	0	0	4.17E − 25	9.824713
	Worst	0	0	0	1.14E − 13	3.02E − 21	24.96968
	STD	0	0	0	2.97E − 14	6.75E − 22	5.565812
F10	Best	8.88E − 16	8.88E − 16	8.88E − 16	4.44E − 15	8.88E − 16	20.76487
	Mean	8.88E − 16	8.88E − 16	8.88E − 16	1.33E − 14	8.88E − 16	20.92344
	Median	8.88E − 16	8.88E − 16	8.88E − 16	1.15E − 14	8.88E − 16	20.94465
	Worst	8.88E − 16	8.88E − 16	8.88E − 16	3.29E − 14	8.88E − 16	21.06309
	STD	0	0	0	8.11E − 15	0	0.083433
F11	Best	0	0	0	0	0	6.56E − 13
	Mean	0	0	0	0.021832	0	0.009891
	Median	0	0	0	0	0	4.55E − 12
	Worst	0	0	0	0.26626	0	0.055407
	STD	0	0	0	0.068973	0	0.015766
F12	Best	2.76E − 09	5.1E − 06	5.47E − 09	0.006052	0.001152	0.006066
	Mean	1.13E − 08	3.6E − 05	0.005183	0.022239	0.23467	0.026151
	Median	1.02E − 08	2.19E − 05	2.8E − 08	0.015529	0.067805	0.023474
	Worst	2.16E − 08	0.000217	0.103669	0.087947	1.492821	0.047176
	STD	5.16E − 09	4.68E − 05	0.023181	0.018774	0.352063	0.013414
F13	Best	1.09E − 07	0.000369	9.49E − 07	0.400281	0.046216	0.09955
	Mean	0.107892	0.014006	0.111506	0.687522	1.867552	0.613832
	Median	0.010988	0.008366	0.110589	0.598054	1.934246	0.609981
	Worst	0.600317	0.052319	0.296493	1.321352	2.999924	1.044
	STD	0.184008	0.016889	0.101889	0.248523	0.961284	0.280029
The best obtained values are in bold.