An Improved Beetle Antennae Search Algorithm Based on Inertia Weight and Attenuation Factor

Table 3

The comparison of two-dimensional function optimization results.

The name of function	Index	BAS	WABAS	PSO	NBAS	RBAS	VBAS
Ackley function		1.97E + 01	1.58E-04	1.82E-04	4.44E-15	8.32E-16	1.27E-11
	Mean	1.65E + 01	9.50E-03	3.06E-01	5.27E-15	7.20E-15	5.60E-11
	Std	5.48E + 00	2.34E-03	1.26E + 00	1.67E-15	9.19E-12	3.78E-12
Griewank function		7.40E-03	5.12E-06	1.16E-07	0	0	0
	Mean	5.69E + 01	3.38E-06	5.94E-02	0	0	0
	Std	3.88E + 01	1.63E-06	3.47E-01	0	0	0
Rastrigin function		1.47E-03	2.03E-04	3.36E-08	0	0	0
	Mean	4.51E + 00	2.36E-03	1.62E-01	0	0	0
	Std	4.54E + 00	8.96E-04	4.17E-01	0	0	0
Rotated hyperellipsoid function		3.69E-06	1.39E-05	8.48E-11	8.91E-32	3.30E-52	3.60E-24
	Mean	2.36E + 03	1.45E-05	3.12E-01	1.73E-30	2.12E-40	7.22E-23
	Std	2.02E + 03	7.11E-06	2.61E + 00	1.27E-30	2.83E-39	5.15E-23
Sphere function		7.30E-06	1.29E-05	7.98E-10	8.56E-33	4.26E-63	3.62E-26
	Mean	3.55E-02	1.11E-05	7.55E-03	3.61E-33	2.02E-37	1.98E-25
	Std	1.53E-01	4.78E-06	4.89E-02	3.87E-33	2.85E-36	1.68E-25
Sum squares function		9.18E + 06	4.50E-03	5.43E + 02	0	0	0
	Mean	1.21E + 07	5.64E-03	8.03E + 02	0	0	0
	Std	1.17E + 06	4.68E-04	2.40E + 02	0	0	0
Zakharov function		4.08E + 00	9.54E-06	8.58E-11	3.38E-36	3.13E-80	7.12E-28
	Mean	3.38E + 00	2.23E-05	2.06E-02	1.96E-32	1.90E-41	1.08E-24
	Std	7.50E + 00	8.28E-06	1.07E-01	2.33E-32	2.01E-40	1.12E-24
Bohachevsky function		2.10E-01	2.03E-05	7.49E-08	0	0	0
	Mean	7.21E + 02	2.52E-04	2.33E + 00	0	0	0
	Std	5.65E + 03	1.09E-04	2.07E + 01	0	0	0
Schaffer function		9.20E-02	3.23E-11	7.86E-13	0	0	0
	Mean	4.57E-01	3.87E-09	7.13E-03	0	0	0
	Std	7.99E-02	3.83E-09	3.82E-02	0	0	0
Sum of different powers function		6.45E-10	2.87E-09	2.07E-12	1.98E-40	4.73E-81	4.84E-32
	Mean	7.30E-07	4.50E-07	1.40E-04	2.26E-34	3.89E-42	6.27E-27
	Std	1.45E-06	4.50E-07	7.53E-04	4.14E-34	5.48E-41	9.65E-27