Improved Quantum-Behaved Particle Swarm Algorithm Based on Levy Flight

Table 3

Test function optimization results.

Dimension	Function	QPSO			G-QPSO			PSO
		Mean values	Worst values	Best values	Mean values	Worst values	Best values	Mean values	Worst values	Best values
2	f9	8.50E−07	1.50E−05	9.19E−12	1.03E−11	5.39E−11	1.98E−21	2.79E−11	5.62E−11	5.13E−17
	f10	0.0025	0.0148	1.37E−07	0.000074054	0.0074	0	0.0034	0.0104	9.94E−11
	f11	1.41E−06	1.63E−05	9.31E−10	8.88E−16	8.88E−16	8.88E−16	5.61E−06	6.07E−05	6.68E−08
	f12	2.88E−04	0.0116	8.66E−07	0	0	0	1.37E−10	2.10E−09	2.13E−14
	f13	1.96E−121	1.96E−119	2.32E−158	0	0	0	1.71E−10	4.73E−09	4.13E−15
	f14	1.48E−132	7.41E−131	8.96E−171	0	0	0	8.32E−16	1.55E−14	1.29E−19
	f15	6.89E−05	0.001	8.50E−10	3.59E−08	5.48E−07	8.04E−17	5.36E−10	4.54E−09	9.46E−15
10	f9	0.0026	0.0086	3.87E−04	3.37E−08	2.82E−07	4.37E−12	0.0022	0.09	3.98E−06
	f10	6.78E−06	2.70E−04	2.41E−14	0	0	0	0.2416	0.5695	0.0672
	f11	5.56E−06	4.57E−04	4.70E−09	9.59E−16	4.44E−15	8.88E−16	0.4529	2.6358	0.0158
	f12	8.15E−05	0.0012	2.01E−11	0	0	0	9.8506	21.7551	3.0815
	f13	2.34E−120	2.19E−118	5.42E−144	3.59E−289	3.54E−287	0	0.102	2.5406	0.0015
	f14	9.48E−142	4.54E−140	6.33E−171	0	0	0	9.42E−10	5.07E−09	1.54E−12
	f15	7.2605	8.0118	5.5239	5.878	6.2673	5.0525	19.8227	142.6981	2.1855
20	f9	0.017	0.0371	0.0044	1.32E−07	1.13E−06	4.98E−10	0.1884	0.7169	0.02
	f10	7.20E−07	1.18E−05	5.25E−14	0	0	0	1.0726	1.2444	0.9007
	f11	1.42E−06	2.68E−05	9.33E−09	8.88E−16	8.88E−16	8.88E−16	2.7984	3.9679	1.6448
	f12	4.34E−05	7.94E−04	7.83E−13	0	0	0	43.0525	83.8204	18.0085
	f13	1.87E−116	1.86E−114	2.06E−143	2.14E−292	9.09E−163	0	40.565	143.7086	10.9991
	f14	2.98E−140	1.48E−138	8.67E−167	0	0	0	1.40E−08	8.78E−08	1.92E−10
	f15	17.7826	18.5267	16.9326	16.7608	17.0947	16.4504	131.9277	341.1925	28.2159
30	f9	0.037	0.0686	0.0088	4.06E−07	2.94E−06	1.39E−09	1.0181	3.1553	0.311
	f10	3.64E−07	7.55E−06	1.48E−14	0	0	0	1.673	2.6495	1.2062
	f11	1.57E−06	1.62E−05	4.58E−08	8.88E−16	8.88E−16	8.88E−16	4.1699	5.8288	2.8203
	f12	4.43E−05	0.0013	4.23E−13	0	0	0	101.4013	167.6426	49.3847
	f13	5.73E−120	4.45E−118	4.05E−143	4.23E−311	4.09E−309	0	528.0399	2020	176.5473
	f14	3.06E−138	3.07E−136	2.78E−172	0	0	0	4.34E−08	3.91E−07	6.44E−10
	f15	27.9465	28.6972	26.5907	27.157	27.5422	26.8536	336.6403	967.2821	159.5259