Z-Shaped Transfer Functions for Binary Particle Swarm Optimization Algorithm

Table 7

Numerical statistics.

Function	Arithmetic	Best	Worst	Ave	Std
	BPSO1	20.0000	25.0000	23.7000	1.4177
	BPSO2	28.0000	34.0000	30.8000	1.8330
	BPSO3	36.0000	41.0000	38.4000	1.6852
	BPSO4	38.0000	44.0000	42.1000	1.5780
	BPSO5	2.0000	14.0000	7.7000	2.9343
	BPSO6	4.0000	9.0000	5.7000	1.5524
	BPSO7	3.0000	7.0000	5.0000	1.3416
	BPSO8	2.0000	7.0000	4.0000	1.4142
	BPSO10	0.0000	0.0000	0.0000	0.0000
	BPSO1	21.0000	28.0000	24.9000	1.9723
	BPSO2	28.0000	35.0000	32.5000	2.1095
	BPSO3	38.0000	42.0000	39.2000	1.1662
	BPSO4	38.0000	43.0000	41.4000	1.7436
	BPSO5	4.0000	12.0000	7.6000	2.3324
	BPSO6	4.0000	10.0000	6.8000	1.8868
	BPSO7	2.0000	7.0000	4.7000	1.6155
	BPSO8	1.0000	6.0000	3.8000	1.6000
	BPSO10	0.0000	0.0000	0.0000	0.0000
	BPSO1	2.0936E + 04	2.9895E + 04	2.4866E + 04	3.0074E + 03
	BPSO2	3.5023E + 04	4.7871E + 04	4.0582E + 04	4.5452E + 03
	BPSO3	4.0798E + 04	7.7036E + 04	6.3317E + 04	9.7782E + 03
	BPSO4	6.1630E + 04	8.7746E + 04	7.4415E + 04	7.9859E + 03
	BPSO5	9.2100E + 02	7.8520E + 03	3.2089E + 03	1.9484E + 03
	BPSO6	2.6700E + 02	4.6020E + 03	2.1907E + 03	1.3673E + 03
	BPSO7	9.2000E + 01	3.1230E + 03	1.0619E + 03	1.0267E + 03
	BPSO8	1.5600E + 02	2.5080E + 03	1.0006E + 03	8.4595E + 02
	BPSO10	0.0000	0.0000	0.0000	0.0000
	BPSO1	3651.0000	4256.0000	3899.0000	155.1722
	BPSO2	4072.0000	4657.0000	4406.2000	159.0540
	BPSO3	4163.0000	4971.0000	4750.7000	219.8095
	BPSO4	4771.0000	5162.0000	4963.3000	103.9173
	BPSO5	1828.0000	3047.0000	2207.5000	324.0522
	BPSO6	1937.0000	2454.0000	2135.4000	210.8327
	BPSO7	1643.0000	2650.0000	2179.6000	355.8585
	BPSO8	1640.0000	2848.0000	2175.5000	386.0337
	BPSO10	149.0000	149.0000	149.0000	0.0000
	BPSO1	85.5000	89.5000	87.5000	1.7889
	BPSO2	97.5000	107.5000	102.5000	3.6056
	BPSO3	105.5000	117.5000	112.3000	3.8158
	BPSO4	115.5000	125.5000	119.9000	3.2000
	BPSO5	37.5000	61.5000	52.1000	6.3906
	BPSO6	45.5000	53.5000	50.3000	2.4000
	BPSO7	41.5000	53.5000	47.7000	4.1425
	BPSO8	43.5000	47.5000	45.5000	1.7889
	BPSO10	37.5000	37.5000	37.5000	0.0000
	BPSO1	1174.2146	1680.9851	1489.1710	149.4409
	BPSO2	1760.8619	2317.8085	1949.8876	155.5235
	BPSO3	2496.6527	2707.5556	2584.3121	63.7418
	BPSO4	2691.9604	2984.0308	2850.7730	103.5472
	BPSO5	225.0052	567.0026	401.3030	109.7147
	BPSO6	162.0050	665.0021	346.3023	133.7193
	BPSO7	145.0009	504.0035	245.7022	113.2767
	BPSO8	144.0011	482.0005	297.3014	114.2555
	BPSO10	0.0001	0.0101	0.0035	0.0028
	BPSO1	22.0000	28.0000	25.3000	2.2383
	BPSO2	29.0000	34.0000	32.0000	1.4142
	BPSO3	36.0000	40.0000	38.1000	1.0440
	BPSO4	35.0000	44.0000	40.8000	2.7129
	BPSO5	4.0000	9.0000	6.4000	1.4283
	BPSO6	1.0000	11.0000	6.5000	2.6926
	BPSO7	2.0000	7.0000	4.8000	1.9391
	BPSO8	1.0000	6.0000	3.3000	1.4866
	BPSO10	0.0000	0.0000	0.0000	0.0000
	BPSO1	1.4420	1.5979	1.5153	0.0418
	BPSO2	1.6837	1.8667	1.7507	0.0513
	BPSO3	1.8418	1.9625	1.9171	0.0450
	BPSO4	1.9153	2.0532	1.9989	0.0400
	BPSO5	0.4566	1.0066	0.7834	0.1726
	BPSO6	0.6426	1.0066	0.8087	0.1022
	BPSO7	0.3239	0.8457	0.6732	0.1405
	BPSO8	0.3239	0.9028	0.6573	0.1738
	BPSO10	8.88178E − 16	8.88178E − 16	8.8818E − 16	0.0000
	BPSO1	1.9687	2.2083	2.0753	0.0814
	BPSO2	2.1886	2.4374	2.3050	0.0850
	BPSO3	2.5578	2.7476	2.6494	0.0629
	BPSO4	2.5683	2.7973	2.7120	0.0743
	BPSO5	1.3666	1.6074	1.4911	0.0771
	BPSO6	1.3666	1.5472	1.4309	0.0552
	BPSO7	1.3666	1.5773	1.4690	0.0634
	BPSO8	1.3365	1.4975	1.4068	0.0486
	BPSO10	1.2108	1.2108	1.2108	0.0000
	BPSO1	833.4458	897.9789	859.9714	23.8603
	BPSO2	797.1630	894.5194	855.8127	29.2840
	BPSO3	822.1992	935.9137	871.3066	31.0668
	BPSO4	801.6173	922.5607	860.1476	40.3582
	BPSO5	819.9967	922.3191	864.5066	32.5671
	BPSO6	798.7684	903.6756	848.3581	32.5885
	BPSO7	803.2907	904.1978	862.3321	35.3385
	BPSO8	833.7166	898.4921	865.7664	24.2585
	BPSO10	732.3788	790.8776	764.5206	20.0896
	BPSO1	811.5518	896.1991	860.3674	26.4694
	BPSO2	797.1630	905.6025	854.5382	29.9453
	BPSO3	822.1992	935.9137	862.4550	36.2997
	BPSO4	801.6173	888.0983	849.7746	28.6370
	BPSO5	819.9967	922.3191	868.3163	29.5430
	BPSO6	798.7684	903.6756	844.8258	35.6381
	BPSO7	803.2907	904.1978	865.2761	29.1488
	BPSO8	788.3447	898.6084	866.7004	37.5416
	BPSO10	732.3788	790.5087	758.0837	22.0786
	BPSO1	761.2894	912.1116	863.0355	43.0973
	BPSO2	803.8999	897.6278	850.4606	32.1798
	BPSO3	835.9801	912.0372	878.0874	23.8546
	BPSO4	772.1731	916.9646	858.7735	44.5248
	BPSO5	765.3802	900.9199	859.8082	41.3350
	BPSO6	810.4896	900.3629	856.8248	28.2321
	BPSO7	820.4377	918.6237	873.2900	30.3881
	BPSO8	811.3776	885.9333	852.6042	20.1360
	BPSO10	693.7516	811.1792	758.9200	38.4465