Improved Gradient-Based Optimizer for Modelling Thermal and Hydropower Plants

Table 1

Results of unimodal benchmark functions.

Function		IGBO	GBO	HPO	WOA	SDO	GWO
F1	Best	1E − 249	9.06E − 52	1.17E − 77	1.92E − 40	1.39E − 55	4.47E − 12
	Mean	4.1E − 215	4.1E − 46	1.49E − 69	7.2E − 34	1.37E − 51	3.12E − 11
	Median	1.7E − 234	1.73E − 49	3.09E − 72	2.28E − 35	3.74E − 54	2.46E − 11
	Worst	6.4E − 214	4.79E − 45	1.92E − 68	4.34E − 33	8.43E − 51	8.73E − 11
	STD	0.00	1.27E − 45	4.51E − 69	1.34E − 33	2.74E − 51	2.31E − 11
F2	Best	5.1E − 126	2.03E − 28	5.41E − 41	4.41E − 24	1.83E − 29	1.42E − 07
	Mean	7.1E − 109	1.95E − 24	2.69E − 38	5.82E − 21	3.76E − 25	2.77E − 07
	Median	1.6E − 118	1.77E − 25	1.64E − 39	1.34E − 21	1.13E − 26	2.66E − 07
	Worst	1.4E − 107	1.95E − 23	2.64E − 37	5.99E − 20	3.98E − 24	4.78E − 07
	STD	3.2E − 108	4.64E − 24	6.13E − 38	1.34E − 20	9.1E − 25	9.9E − 08
F3	Best	4.2E − 226	3.42E − 42	4.64E − 68	30005.81	6.27E − 46	0.008462
	Mean	1.1E − 190	2.56E − 38	1.72E − 59	55046.4	6.91E − 34	0.610441
	Median	3.2E − 210	5.51E − 40	5.21E − 63	53305.88	1.4E − 39	0.185412
	Worst	2.1E − 189	2.05E − 37	3.12E − 58	83830.83	1.38E − 32	3.567009
	STD	0	5.68E − 38	6.95E − 59	13707.83	3.09E − 33	0.827115
F4	Best	6.5E − 120	1.54E − 24	2.1E − 35	0.99528	1.11E − 26	0.002608
	Mean	1.2E − 102	8.59E − 22	7.25E − 32	53.18395	4.52E − 23	0.008
	Median	1.3E − 111	1.22E − 22	1.31E − 32	60.93168	1.14E − 23	0.007092
	Worst	1.3E − 101	1.08E − 20	7.27E − 31	89.09969	1.94E − 22	0.016667
	STD	3.5E − 102	2.47E − 21	1.69E − 31	29.69543	6.34E − 23	0.003845
F5	Best	22.76424	24.25387	23.80007	27.88483	27.90967	25.92515
	Mean	24.56508	25.13063	24.34554	28.27419	28.65096	27.18903
	Median	24.48176	25.117	24.16784	28.43647	28.74726	27.09814
	Worst	28.509	26.10917	25.98622	28.7227	28.98699	28.79035
	STD	1.407275	0.565603	0.511546	0.28925	0.295026	0.72182
F6	Best	6.99E − 08	0.00018	3.7E − 07	0.303542	0.039957	0.252254
	Mean	2.1E − 05	0.00108	0.000811	0.655907	2.568541	0.647554
	Median	1.17E − 07	0.000875	1.8E − 06	0.62203	2.038779	0.611378
	Worst	0.000417	0.002836	0.015867	1.16408	7.250251	1.172757
	STD	9.32E − 05	0.000702	0.003544	0.210811	1.852701	0.280888
F7	Best	0.000201	0.000111	2.71E − 05	0.0004	8.66E − 05	0.001477
	Mean	0.001124	0.001192	0.000529	0.00542	0.002356	0.004433
	Median	0.001127	0.000985	0.000167	0.003763	0.001136	0.003685
	Worst	0.002789	0.004017	0.001566	0.019069	0.013813	0.01033
	STD	0.000717	0.001008	0.000569	0.005011	0.003331	0.002554
The best obtained values are in bold.