Multistrategy Improved Whale Optimization Algorithm and Its Application

Table 3

Comparative experimental results of different optimization algorithms.

Function		Experimental Comparison
		BOA	AO	SSA	WOA	CFAWOA	DE	DECWOA
F1	Std	1.15689E − 07	7.17623E − 129	5.76465E − 82	1.09694E − 77	0.00000E + 00	1.10035E − 227	0.00000E + 00
	Mean	3.75375E − 07	3.59224E − 129	2.88294E − 82	1.03964E − 77	1.50843E − 199	2.65158E − 177	7.57439E − 281
	Best	2.63837E − 07	5.76183E − 150	0.00000E + 00	1.99046E − 82	9.43048E − 204	2.6923E − 199	1.24974E − 284
	Worst	4.93932E − 07	1.44945E − 128	1.15446E − 81	2.32947E − 77	5.38249E − 199	7.95564E − 177	2.40433E − 280
F2	Std	3.78976E − 10	8.84757E − 75	6.85326E − 46	1.74286E − 54	1.14893E − 122	1.83797E − 107	2.75246E − 150
	Mean	3.02274E − 10	6.71386E − 75	3.43464E − 46	8.76034E − 55	6.79042E − 123	1.29946E − 107	1.38049E − 150
	Best	2.23027E − 14	1.24559E − 77	0.0000E + 00	2.14797E − 57	3.43868E − 126	1.71259E − 126	2.59043E − 155
	Worst	8.00049E − 10	1.82578E − 74	1.37856E − 45	3.49578E − 54	2.39786E − 122	3.89803E − 107	5.54661E − 150
F3	Std	1.46819E − 07	4.82826E − 143	1.33095E − 97	3.63932E − 56	5.02996E − 130	1.70936E − 133	0.00000E + 00
	Mean	3.42043E − 07	4.84945E − 143	6.65032E − 98	4.81636E + 04	2.59746E − 130	1.22267E − 133	6.97643E − 195
	Best	2.36235E − 07	1.29869E − 149	9.49000E − 149	3.25000E + 04	1.86978E − 135	9.38623E − 156	2.03225E − 204
	Worst	5.58263E − 07	1.10898E − 142	2.66000E − 97	5.50000E + 04	1.01958E − 129	3.64865E − 133	2.77642E − 194
F4	Std	1.45389E − 05	2.51446E − 57	2.75065E − 46	26.26153745	1.33868E − 102	6.14682E − 103	2.26475E − 135
	Mean	7.62368E − 05	1.26467E − 57	1.38455E − 46	2.71000E + 01	6.70849E − 103	4.70798E − 103	1.13954E − 135
	Best	5.81373E − 05	4.15866E − 80	0.00000E + 00	1.89000E + 00	4.40275E − 107	0.00000E + 00	9.25859E − 139
	Worst	9.16575E − 05	5.03978E − 57	5.50768E − 46	5.59000E + 01	2.68957E − 102	1.33957E − 102	4.53684E − 135
F5	Std	0.000304159	0.000129661	0.000371841	0.001796123	1.12746E − 05	2.38558E − 05	6.25793E − 05
	Mean	1.70355E − 03	1.44979E − 04	4.59000E − 04	1.61000E − 03	4.57038E − 05	6.40005E − 05	7.08953E − 05
	Best	1.39358E − 03	7.107979E − 05	1.27000E − 04	2.02000E − 04	3.42012E − 05	3.62615E − 05	2.16964E − 05
	Worst	2.05245E − 03	3.39456E − 04	9.32000E − 04	4.24000E − 03	6.12065E − 05	9.45679E − 05	1.61964E − 04
F6	Std	340.3553381	4159.246398	1334.570924	1829.634873	2634.429438	1279.258654	1795.295025
	Mean	−3.54224E + 03	−1.05375E + 04	−7.59000E + 03	−1.13000E + 04	−1.13375E + 04	−1.19745E + 04	−1.16957E + 04
	Best	−3.91246E + 03	−1.26278E + 04	−9.57000E + 03	−1.26000E + 04	−1.26276E + 04	−1.28452E + 04	−1.26857E + 04
	Worst	−3.09146E + 03	−4.21386E + 03	−6.70000E + 03	−8.64000E + 03	−7.30859E + 03	−8.64000E + 03	−8.02895E + 03
F7	Std	2.84157E − 10	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Mean	1.60364E − 10	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Best	2.33275E − 12	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Worst	5.85463E − 10	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00
F8	Std	9.99847E − 06	0.00000E + 00	0.00000E + 00	3.52342E − 15	2.05116E − 15	1.45039E − 15	1.77636E − 15
	Mean	5.51047E − 05	8.88570E − 16	8.88000E − 16	3.44585E − 15	2.66796E − 15	2.66454E − 15	1.78648E − 16
	Best	4.51607E − 05	8.80000E − 16	8.88000E − 16	4.41738E − 16	8.88075E − 16	8.88618E − 16	3.88357E − 16
	Worst	6.89840E − 05	8.88093E − 16	8.88000E − 16	7.99965E − 15	4.44796E − 15	4.44069E − 15	4.44686E − 15
F9	Std	1.46303E − 07	0.00000E + 00	0.00000E + 00	0.043835506	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Mean	2.09702E − 07	0.00000E + 00	0.00000E + 00	2.19000E − 02	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Best	7.93603E − 08	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00	0.00000E + 00
	Worst	3.66570E − 07	0.00000E + 00	0.00000E + 00	8.77000E − 02	0.00000E + 00	0.00000E + 00	0.00000E + 00
F10	Std	0.001515476	6.19254E − 05	2.78732E − 07	0.314675773	0.344948649	0.04999952	0.172051704
	Mean	2.99030E + 00	4.72000E − 05	3.09759E − 07	4.29000E − 01	7.77000E − 01	9.62645E − 01	3.38000E − 01
	Best	2.99000E + 00	1.81000E − 06	2.26556E − 08	1.15000E − 01	4.21000E − 01	3.06721E − 01	1.49000E − 01
	Worst	2.99000E + 00	1.33000E − 04	5.85685E − 07	8.49000E − 01	1.25000E + 00	6.9980E − 01	5.34000E − 01
F11	Std	0.012411974	0.949646322	5.8362500000	4.647013825	0.00000E + 00	4.603359426	0.00000E + 00
	Mean	1.00000E + 00	2.24000E + 00	9.75000E + 00	3.94467E + 00	9.98000E − 01	4.253066667	9.98000E − 01
	Best	9.98000E − 01	9.98000E − 01	9.98000E − 01	9.98876E − 01	9.98000E − 01	9.98000E − 01	9.98000E − 01
	Worst	1.02000E + 00	2.98000E + 00	1.27000E + 01	1.08869E + 01	9.98000E − 01	1.07632E + 01	9.98000E − 01
F12	Std	4.23456E − 05	0.000135416	4.46346E − 07	0.000738262	0.000201337	3.67346E − 05	8.69472E − 06
	Mean	5.06000E − 04	5.94000E − 04	3.08000E − 04	1.32000E − 03	5.67000E − 04	0.000348965	3.20538E − 04
	Best	4.67000E − 04	3.97000E − 04	3.08000E − 04	3.87000E − 04	3.62000E − 04	0.000307718	3.13043E − 04
	Worst	5.51000E − 04	6.98000E − 04	3.08000E − 04	2.16000E − 03	7.42000E − 04	0.000396938	3.31835E − 04
F13	Std	0.091946882	0.021166877	0.00011547	0.000163299	0.00000E + 00	0.00000E + 00	0.000150000
	Mean	3.08000E + 00	3.01000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
	Best	3.01063E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
	Worst	3.21969E + 00	3.05000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
F14	Std	0.366127815	0.001438749	0.00000E + 00	0.003880185	0.000141421	0.000164992	0.000732575
	Mean	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00
	Best	−3.83954E + 00	−3.86267E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00
	Worst	−3.89554E + 00	−3.86467E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00	−3.86268E + 00