Human Behavior-Based Particle Swarm Optimization

Table 3

Experimental results obtained by SPSO and HPSO on functions from 𝐹₁₁ to 𝐹₂₀.

Fun	Dim		Best	Worst	Median	Mean	SD	Significant
𝐹11	30	SPSO	0.0043	19.9630	0.0595	2.3935	5.4041
		HPSO	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	0	+
	50	SPSO	0.0598	19.9646	12.6912	10.5673	6.3042
		HPSO	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	0	+
	100	SPSO	15.4237	20.2143	19.5200	19.4135	0.8672
		HPSO	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	𝟖.𝟖𝟖𝟏𝟖𝐞−𝟏𝟔	0	+
𝐹12	30	SPSO	7.0274𝑒−04	90.8935	0.0178	12.0794	31.2763
		HPSO	0	0	0	0	0	+
	50	SPSO	0.0014	270.8170	0.0415	45.1971	70.1274
		HPSO	0	0	0	0	0	+
	100	SPSO	1.1140	721.0594	361.0858	376.1758	158.6584
		HPSO	0	0	0	0	0	+
𝐹13	30	SPSO	0.1403	4.3952	0.3210	1.0567	1.4863
		HPSO	0	0	0	0	0	+
	50	SPSO	0.8657	15.2389	7.5828	8.2388	3.6607
		HPSO	0	0	0	0	0	+
	100	SPSO	27.6235	64.4826	49.3984	47.7138	10.0126
		HPSO	0	0	0	0	0	+
𝐹14	30	SPSO	6.4114𝑒−05	2.2031	0.4202	0.5373	0.5730
		HPSO	0.0710	0.2803	0.1301	0.1444	0.0513	+
	50	SPSO	0.1882	6.9784	2.2774	2.3889	1.5688
		HPSO	0.1016	0.3137	0.1652	0.1702	0.0438	+
	100	SPSO	32.5063	5.1200𝑒+08	457.9143	7.6801𝑒+07	1.5257𝑒+08
		HPSO	0.1866	0.5097	0.2703	0.2736	0.0653	+
𝐹15	30	SPSO	−3.0000	−2.8522	−3.0000	−2.9507	0.0709
		HPSO	−3	−3	−3	−3	0	+
	50	SPSO	−5.0000	−2.3044	−4.4827	−4.2127	0.6865
		HPSO	−5	−5	−5	−5	0	+
	100	SPSO	−7.9165	4.7637	−5.2127	−4.6977	2.8465
		HPSO	−10	−10	−10	−10	0	+
𝐹16	30	SPSO	2.3604𝑒+03	3.8233𝑒+04	3.8233𝑒+04	1.2375𝑒+04	9.2463𝑒+03
		HPSO	0	5.8369𝑒+03	0	390.6710	1.2756𝑒+03	+
	50	SPSO	7.1213𝑒+03	1.0427𝑒+05	3.3195𝑒+04	3.4891𝑒+04	2.2914𝑒+04
		HPSO	0	4.0529𝑒+03	0	224.6749	873.6249	+
	100	SPSO	6.2317𝑒+04	2.7386𝑒+05	1.4222𝑒+05	1.4697𝑒+05	5.7699𝑒+04
		HPSO	0	1.9403𝑒+04	0	1.0583𝑒+03	3.8088𝑒+03	+
𝐹17	30	SPSO	6.7986𝑒+03	9.7587𝑒+03	8.3387𝑒+03	8.2508𝑒+03	739.7223
		HPSO	8.3590𝑒+03	9.8803𝑒+03	9.0866𝑒+03	9.0790𝑒+03	442.4330	−
	50	SPSO	1.3020𝑒+04	1.7080𝑒+04	1.4999𝑒+04	1.5149𝑒+04	1.0581𝑒+03
		HPSO	1.5003𝑒+04	1.7349𝑒+04	1.6514𝑒+04	1.6310𝑒+04	669.3538	−
	100	SPSO	2.7400𝑒+04	2.7400𝑒+04	3.1087𝑒+04	3.1149𝑒+04	2.1654𝑒+03
		HPSO	3.0329𝑒+04	3.5493𝑒+04	3.4226𝑒+04	3.3586𝑒+04	1.5320𝑒+03	−
𝐹18	30	SPSO	20.7888	21.0951	21.0053	20.9848	0.0712
		HPSO	8.8818𝑒−16	21.1210	20.9931	11.2354	10.6894	+
	50	SPSO	21.0515	21.2478	21.1455	21.1436	0.0536
		HPSO	8.8818𝑒−16	21.2404	21.1366	12.0016	10.6745	+
	100	SPSO	21.2367	21.3931	21.3368	21.3358	0.0364
		HPSO	8.8818𝑒−16	21.3949	21.3545	15.6658	9.6084	+
𝐹19	30	SPSO	1.0517	495.3131	273.6408	243.6176	154.3551
		HPSO	0	0	0	0	0	+
	50	SPSO	265.0558	1.4393𝑒+03	798.8065	786.0782	289.8401
		HPSO	0	0	0	0	0	+
	100	SPSO	1.9937𝑒+03	4.0158𝑒+03	2.9388𝑒+03	2.9263𝑒+03	543.9053
		HPSO	0	0	0	0	0	+
𝐹20	30	SPSO	22.5705	34.8494	28.6842	28.8734	3.5028
		HPSO	0	39.9834	0	3.1393	9.7817	+
	50	SPSO	45.9462	70.7399	55.5532	55.6014	5.7839
		HPSO	0	66.4051	0	2.2135	12.1239	+
	100	SPSO	106.4483	139.8394	120.6118	121.4481	7.8030
		HPSO	0	129.4941	0	8.3487	31.7918	+