Improved Gradient-Based Optimizer for Modelling Thermal and Hydropower Plants

Table 3

Results of composite benchmark functions.

Function		IGBO	GBO	HPO	WOA	SDO	GWO
F14	Best	0.998004	0.998004	0.998004	0.998004	0.998004	0.998004
	Mean	1.14691	1.097209	2.371342	2.230204	3.494696	3.892106
	Median	0.998004	0.998004	0.998004	1.495017	1.495017	2.982105
	Worst	2.982105	2.982105	10.76318	10.76318	12.67051	12.67051
	STD	0.485651	0.443659	2.980135	2.241367	3.953203	3.727681
F15	Best	0.000307	0.000307	0.000307	0.000311	0.000307	0.00031
	Mean	0.001448	0.000446	0.003462	0.000626	0.00067	0.003547
	Median	0.000307	0.000307	0.000308	0.000578	0.000527	0.000546
	Worst	0.020363	0.001223	0.020363	0.001528	0.002121	0.020363
	STD	0.004465	0.000335	0.007292	0.000342	0.000473	0.007255
F16	Best	−1.03163	−1.03163	−1.03163	−1.03163	−1.03163	−1.03163
	Mean	−1.03163	−1.03163	−1.03163	−1.03163	−1.03005	−1.03158
	Median	−1.03163	−1.03163	−1.03163	−1.03163	−1.03163	−1.03163
	Worst	−1.03163	−1.03163	−1.03163	−1.03163	−1.00046	−1.03063
	STD	1.97E − 16	1.61E − 16	7.2 E − 17	1.94E − 08	0.006966	0.000223
F17	Best	0.397887	0.397887	0.397887	0.397887	0.397887	0.397888
	Mean	0.397887	0.397887	0.397887	0.397896	0.397987	0.397891
	Median	0.397887	0.397887	0.397887	0.39789	0.397887	0.397891
	Worst	0.397887	0.397887	0.397887	0.397967	0.399795	0.397897
	STD	0	0	0	1.78E − 05	0.000426	3.01E − 06
F18	Best	3	3	3	3.000001	3	3
	Mean	3	3	3	3.000069	4.371758	3.000068
	Median	3	3	3	3.000026	3	3.000036
	Worst	3	3	3	3.000668	30.41145	3.000238
	STD	1.71E − 15	1.56E − 15	1.46E − 14	0.000147	6.129111	6.53E − 05
F19	Best	−0.30048	−0.30048	−0.30048	−0.30048	−0.30048	−0.30048
	Mean	−0.30048	−0.30048	−0.30048	−0.30048	−0.2893	−0.30048
	Median	−0.30048	−0.30048	−0.30048	−0.30048	−0.30038	−0.30048
	Worst	−0.30048	−0.30048	−0.30048	−0.30048	−0.19165	−0.30048
	STD	1.14E − 16	1.14E − 16	1.14E − 16	1.14E − 16	0.026531	1.14E − 16
F20	Best	−3.322	−3.322	−3.322	−3.31923	−3.322	−3.32198
	Mean	−3.28633	−3.29822	−3.19159	−2.98949	−3.09697	−3.22876
	Median	−3.322	−3.322	−3.20024	−3.15019	−3.2031	−3.26239
	Worst	−3.2031	−3.2031	−2.84042	−1.57922	−0.89904	−2.84039
	STD	0.055899	0.048793	0.1241	0.479795	0.550986	0.125558
F21	Best	−10.1532	−10.1532	−10.1532	−10.1528	−10.1532	−10.1502
	Mean	−8.24766	−7.8591	−7.36173	−7.35262	−8.703	−8.51218
	Median	−10.1532	−10.1532	−7.6042	−10.0113	−10.1532	−10.1413
	Worst	−2.63047	−5.0552	−2.63047	−2.59723	−4.99677	−2.62918
	STD	2.713589	2.602111	2.94916	3.245445	2.23952	2.963153
F22	Best	−10.4029	−10.4029	−10.4029	−10.4008	−10.4029	−10.4024
	Mean	−7.81002	−9.07412	−5.67655	−7.90953	−8.45822	−10.0134
	Median	−10.4029	−10.4029	−5.08767	−10.2376	−10.4029	−10.3959
	Worst	−2.7659	−5.08767	−1.83759	−3.69711	−1.0677	−2.76526
	STD	2.990142	2.36137	3.035943	2.779744	3.128689	1.706042
F23	Best	−10.5364	−10.5364	−10.5364	−10.5297	−10.5364	−10.5348
	Mean	−8.57898	−8.37899	−7.29165	−7.3919	−7.90449	−9.74305
	Median	−10.5364	−10.5364	−5.12848	−7.79854	−10.5357	−10.5274
	Worst	−3.83543	−2.42173	−5.12848	−1.67334	−3.79083	−2.42135
	STD	2.750568	3.074069	2.718159	3.33909	3.015319	2.418464
The best obtained values are in bold.