Multistrategy Improved Whale Optimization Algorithm and Its Application

Table 2

Comparative experimental results of different improvement strategies.

Function		Experimental comparison
		WOA-1	WOA-2	WOA-3	WOA-4
F1	Std	4.51559E − 08	2.09347E − 17	1.84557E − 83	0.00000E + 00
	Mean	2.79484E − 07	1.13353E − 17	8.30331E − 84	5.23562E − 284
	Best	2.29048E − 07	5.67353E − 21	6.23435E − 88	2.03579E − 288
	Worst	3.30405E − 07	4.84395E − 17	4.10483E − 83	1.04979E − 283
F2	Std	1.70153E − 10	1.83991E − 10	1.43226E − 54	1.11454E − 153
	Mean	1.25058E − 10	1.15076E − 10	7.85979E − 55	1.13351E − 153
	Best	2.99584E − 11	7.22843E − 12	4.20392E − 60	8.38538E − 159
	Worst	4.27458E − 10	4.38038E − 10	3.30944E − 54	2.60495E − 153
F3	Std	0.024963674	0.109350354	0.751703418	0.621730369
	Mean	2.89000E + 01	2.80000E + 01	2.80000E + 01	2.63000E + 01
	Best	2.88000E + 01	2.78000E + 01	2.70000E + 01	2.50500E + 01
	Worst	2.89000E + 01	2.81000E + 01	2.88000E + 01	2.70000E + 01
F4	Std	0.555804735	0.374895942	0.007181727	0.016941429
	Mean	4.71000E + 00	2.53000E + 00	2.93000E − 02	5.20688E − 02
	Best	4.06000E + 00	2.02000E + 00	2.20000E − 02	3.33000E − 02
	Worst	5.29000E + 00	2.91000E + 00	3.71000E − 02	7.27000E − 02
F5	Std	0.000538608	0.001572697	0.004444647	9.32354E − 05
	Mean	1.642924E − 03	3.42854E − 03	2.45038E − 03	9.90238E − 05
	Best	9.46000E − 04	1.96257E − 03	2.76048E − 04	4.03043E − 05
	Worst	2.31000E − 03	5.85754E − 03	1.04037E − 02	2.59042E − 04
F6	Std	135.48707911	224.1043362	1645.9890973	1583.1336835
	Mean	−3.63000E + 03	−4.19242E + 03	−1.09483E + 04	−1.18032E + 04
	Best	−3.82000E + 03	−4.52124E + 03	−1.26836E + 04	−1.26023E + 04
	Worst	−3.44000E + 03	−3.98124E + 03	−8.34938E + 03	−9.02012E + 03
F7	Std	4.287032E − 11	1.66405E − 06	0.00000E + 00	0.00000E + 00
	Mean	3.77032E − 11	1.39229E − 06	0.00000E + 00	0.00000E + 00
	Best	3.41023E − 13	8.97492E − 08	0.00000E + 00	0.00000E + 00
	Worst	9.76032E − 11	4.20305E − 06	0.00000E + 00	0.00000E + 00
F8	Std	5.76251E − 06	0.000258291	2.51215E − 15	0.00000E + 00
	Mean	5.34320E − 05	2.03723E − 04	4.44423E − 15	8.88021E − 16
	Best	4.46034E − 05	6.71941E − 06	8.88423E − 16	8.88012E − 16
	Worst	6.04323E − 05	6.46058E − 04	7.99012E − 15	8.88135E − 16
F9	Std	1.52609E − 07	1.55974E − 07	0.00000E + 00	0.00000E + 00
	Mean	2.18044E − 07	1.97474E − 07	0.00000E + 00	0.00000E + 00
	Best	7.35032E − 08	4.30479E − 10	0.00000E + 00	0.00000E + 00
	Worst	4.20234E − 07	4.17068E − 07	0.00000E + 00	0.00000E + 00
F10	Std	0.117121177	0.184990967	0.101764095	0.160370012
	Mean	2.94043E + 00	1.67000E + 00	2.55000E − 01	3.23000E − 01
	Best	2.73043E + 00	1.47000E + 00	1.40000E − 01	9.04000E − 02
	Worst	2.99034E + 00	1.91010E + 00	3.62985E − 01	5.33000E − 01
F11	Std	0.006595458	5.94138E − 05	0.887534913	0.00000E + 00
	Mean	1.00000E + 00	9.98000E − 01	1.59000E + 00	9.98000E − 01
	Best	9.98000E − 01	9.98000E − 01	9.98000E − 01	9.98000E − 01
	Worst	1.01000E + 00	9.98000E − 01	2.98000E + 00	9.98000E − 01
F12	Std	9.35683E − 05	9.72888E − 06	0.000797524	3.85761E − 05
	Mean	5.01044E − 04	3.27153E − 04	7.73325E − 04	3.29173E − 04
	Best	3.63403E − 04	3.16032E − 04	3.11320E − 04	3.09163E − 04
	Worst	5.83340E − 04	3.36011E − 04	2.18264E − 03	3.97427E − 04
F13	Std	0.141889101	0.000134211	4.47202E − 05	0.000207401
	Mean	3.13232E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
	Best	3.00003E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
	Worst	3.30237E + 00	3.00000E + 00	3.00000E + 00	3.00000E + 00
F14	Std	0.072140138	0.001317012	0.010294048	0.000532011
	Mean	−3.76034E + 00	−3.8600E + 00	−3.86000E + 00	−3.86000E + 00
	Best	−3.86043E + 00	−3.8600E + 00	−3.86000E + 00	−3.86000E + 00
	Worst	−3.67001E + 00	−3.8600E + 00	−3.84000E + 00	−3.86000E + 00