Optimizing High-Dimensional Functions with an Efficient Particle Swarm Optimization Algorithm

Table 6

The performance of PSOTS, the traditional PSO algorithm (PSO), the AsynLnPSO algorithm (APSO), the LinWPSO algorithm (LPSO), GPSO, CCAS, and VPSO on 9 functions in the benchmark dataset when the dimensionality is 1000.

Function		Ackley	Cigar	Griewank	Rastrigin	Rosenbrock	Noncon-rast	Sphere	Tablet	Ellipse
PSOTS	Best	0.551	58336.090	0.013	1049.727	1583.446	1036.363	5.691	7.021	4561.731
	Mean	0.654	66590.620	0.017	1206.143	1695.683	1224.481	6.641	8.866	6034.033
	STD	0.066	8530.537	0.003	108.670	80.271	122.191	0.872	1.767	1089.670
PSO	Best	0.883	101581.400	0.022	1856.572	2091.178	2176.873	10.588	12.760	8299.737
	Mean	0.959	119206.001	0.030	3752.308	2202.001	7460.916	12.395	13.751	9268.079
	STD	0.052	10297.240	0.004	2558.991	100.112	2777.144	1.500	1.345	1063.982
APSO	Best	0.903	114610.100	0.019	2051.027	2102.363	2168.402	11.284	12.864	8528.893
	Mean	0.976	126324.800	0.029	3395.736	2268.229	8025.089	12.318	16.518	10217.47
	STD	0.044	5550.201	0.005	2225.827	119.697	2069.662	0.623	1.783	1131.887
LPSO	Best	0.840	96167.060	0.022	1844.305	1959.617	8590.621	9.892	12.613	6859.916
	Mean	0.864	105884.300	0.028	4760.095	2053.572	8861.428	10.804	15.071	8193.032
	STD	0.029	7576.268	0.003	3024.811	75.338	135.469	0.814	1.484	916.128
GPSO	Best	0.671	63817.053	0.018	1630.047	2305.846	1779.136	6.781	9.207	6002.318
	Mean	0.827	84967.952	0.031	4267.252	2552.418	2407.985	8.051	13.506	8425.598
	STD	0.052	10801.034	0.003	1479.187	85.12814	132.854	0.833	2.204	1820.534
CCAS	Best	0.676	58706.483	0.013	1363.015	1847.001	1681.628	6.632	9.931	6127.127
	Mean	0.820	82986.121	0.027	4717.921	2528.346	2605.835	7.767	15.745	7943.676
	STD	0.092	9234.537	0.007	843.3347	113.5974	1637.341	0.825	1.039	755.427
VPSO	Best	0.657	57804.753	0.014	1330.581	1915.181	1661.348	6.568	8.420	5118.947
	Mean	0.741	85502.262	0.029	3187.537	2146.646	2969.365	7.753	12.515	7077.191
	STD	0.027	8076.055	0.008	676.163	93.69879	1248.472	0.848	1.956	672.217