Improved Bat Algorithm Based on Multipopulation Strategy of Island Model for Solving Global Function Optimization Problem

Table 2

Simulation results on function optimization problems under different chaotic mappings.

Function	Chaotic mapping	Avg.	Best	Std.
	Chebyshev map	2.46E − 03	6.07E − 07	7.37E − 03
	Circle map	4.08E − 03	9.77E − 07	1.12E − 02
	Gauss/mouse map	1.77E − 04	6.33E − 07	5.25E − 04
	Iterative map	1.92E − 02	1.22E − 06	5.76E − 02
	Logistic map	1.74E − 06	1.10E − 06	5.28E − 07
	Piecewise map	1.91E − 06	5.70E − 07	7.10E − 07
	Sine map	1.60E − 02	9.53E − 07	4.76E − 02
	Singer map	3.38E − 02	1.14E − 06	1.01E − 01
	Sinusoidal map	8.43E − 03	1.07E − 06	2.53E − 02
	Tent map	2.25E − 06	1.21E − 06	7.34E − 07
	Chebyshev map	1.22E − 03	1.67E − 07	3.01E − 03
	Circle map	2.06E − 03	1.27E − 07	5.76E − 03
	Gauss/mouse map	6.44E − 03	1.28E − 07	1.47E − 02
	Iterative map	3.04E − 03	1.28E − 07	6.60E − 03
	Logistic map	7.70E − 05	8.32E − 08	1.66E − 04
	Piecewise map	2.28E − 06	1.33E − 07	6.04E − 06
	Sine map	3.75E − 03	4.52E − 08	1.12E − 02
	Singer map	8.91E − 03	1.16E − 07	1.33E − 02
	Sinusoidal map	4.62E − 03	2.06E − 07	9.24E − 03
	Tent map	9.79E − 04	8.08E − 08	2.58E − 03
	Chebyshev map	2.11E + 00	1.16E + 00	5.77E − 01
	Circle map	2.13E + 00	1.16E + 00	9.04E − 01
	Gauss/mouse map	2.01E + 00	1.42E − 03	7.21E − 01
	Iterative map	2.24E + 00	1.16E + 00	7.99E − 01
	Logistic map	2.23E + 00	1.91E − 03	9.84E − 01
	Piecewise map	1.89E + 00	1.59E − 03	6.80E − 01
	Sine map	2.41E + 00	1.16E + 00	6.13E − 01
	Singer map	1.95E + 00	1.64E − 03	7.85E − 01
	Sinusoidal map	2.22E + 00	1.76E − 03	9.29E − 01
	Tent map	1.90E + 00	1.31E − 03	7.28E − 01
	Chebyshev map	−4.3381	−3.4831	0.4727
	Circle map	−4.2815	−2.8800	0.9298
	Gauss/mouse map	−4.4270	−3.3986	0.7517
	Iterative map	−4.3976	−3.2347	0.7557
	Logistic map	−4.6527	−3.5362	0.9810
	Piecewise map	−3.6912	−3.3934	0.1789
	Sine map	−4.1871	−3.3551	0.5061
	Singer map	−3.9540	−3.2770	0.5729
	Sinusoidal map	−4.1621	−2.6385	0.7561
	Tent map	−4.0751	−2.6231	0.9906
	Chebyshev map	12.3377	6.9650	4.9388
	Circle map	14.6261	6.9650	5.0547
	Gauss/mouse map	13.4322	5.9700	5.1170
	Iterative map	11.6412	4.9750	4.6038
	Logistic map	12.0392	3.9801	4.3472
	Piecewise map	9.6514	6.9649	1.6074
	Sine map	13.1337	4.9750	5.5895
	Singer map	14.0292	7.9600	3.9410
	Sinusoidal map	13.0342	6.9649	6.4242
	Tent map	13.5317	6.9650	5.2686
	Chebyshev map	2.64E − 01	3.69E − 06	2.98E − 01
	Circle map	5.17E − 01	1.08E − 05	8.15E − 01
	Gauss/mouse map	1.84E − 01	4.49E − 05	1.45E − 01
	Iterative map	1.92E − 01	1.64E − 05	1.69E − 01
	Logistic map	3.22E − 01	2.76E − 03	3.84E − 01
	Piecewise map	1.49E − 01	6.80E − 06	1.90E − 01
	Sine map	1.75E − 01	2.25E − 06	2.58E − 01
	Singer map	2.17E − 01	2.46E − 06	2.55E − 01
	Sinusoidal map	1.19E − 01	2.12E − 06	1.72E − 01
	Tent map	2.02E − 01	7.22E − 06	2.21E − 01