A Free Search Krill Herd Algorithm for Functions Optimization

Table 4

Simulation results for 𝐹₁∼𝐹₉ in high dimension.

Benchmark function	Result	Method
		PSO	DE	KH II	FSKH	HS	FS	BA
𝐹1(𝐷=1000)	Best	1.7539𝐸+02	1.1046𝐸+02	2.2325𝐸+02	𝟎	5.5839𝐸+03	1.9398𝐸+03	4.6377𝐸+00
	Mean	4.2055𝐸+02	1.2990𝐸+02	2.3419𝐸+02	𝟒.𝟔𝟎𝟖𝟐𝐄−𝟑𝟏𝟔	5.8593𝐸+03	2.1829𝐸+03	5.1666𝐸+00
	Worst	8.7083𝐸+02	1.4698𝐸+02	2.4475𝐸+02	𝟒.𝟒𝟔𝟗𝟏𝐄−𝟑𝟏𝟓	6.0746𝐸+03	2.2895𝐸+03	5.7013𝐸+00
	Std.	1.5335𝐸+02	8.4319𝐸+00	8.0663𝐸+00	𝟎	9.3024𝐸+01	7.1875𝐸+01	2.4083𝐸−01
	Rank	4	3	5	1	7	6	2
𝐹2(𝐷=200)	Best	1.7420𝐸+03	5.8630𝐸+03	3.8140𝐸+03	𝟎	2.0879𝐸+05	3.6160𝐸+03	5.1312𝐸+05
	Mean	5.6810𝐸+03	7.6012𝐸+03	6.4365𝐸+03	𝟎	2.4108𝐸+05	4.2361𝐸+03	5.5451𝐸+05
	Worst	1.2432𝐸+04	9.4600𝐸+03	9.4830𝐸+03	𝟎	1.3406𝐸+04	4.8140𝐸+03	6.0191𝐸+05
	Std.	2.4260𝐸+03	7.9567𝐸+02	1.2702𝐸+03	𝟎	2.5040𝐸+05	2.8971𝐸+02	1.8030𝐸+04
	Rank	2	5	4	1	6	3	7
𝐹3(𝐷=100)	Best	2.2607𝐸+02	1.8958𝐸+02	1.0216𝐸+02	𝟗.𝟖𝟎𝟕𝟎𝐄+𝟎𝟏	4.8892𝐸+03	1.1008𝐸+02	9.9091𝐸+01
	Mean	1.2251𝐸+03	2.3327𝐸+02	1.1403𝐸+02	𝟗.𝟖𝟕𝟎𝟏𝐄+𝟎𝟏	6.6060𝐸+03	1.1743𝐸+02	1.0747𝐸+02
	Worst	4.3896𝐸+03	2.8370𝐸+02	1.3766𝐸+02	𝟗.𝟖𝟗𝟒𝟐𝐄+𝟎𝟏	8.4203𝐸+03	1.2626𝐸+02	1.6127𝐸+02
	Std.	1.1701𝐸+03	2.0992𝐸+01	9.4142𝐸+00	𝟐.𝟏𝟕𝟐𝟒𝐄−𝟎𝟏	9.0378𝐸+02	2.8202𝐸+00	2.0822𝐸+01
	Rank	6	5	3	1	7	4	2
𝐹4(𝐷=1000)	Best	2.9336𝐸+00	2.1517𝐸−01	1.3101𝐸+00	𝟔.𝟑𝟓𝟒𝟑𝐄−𝟎𝟔	2.6746𝐸+02	7.7482𝐸+01	6.9964𝐸+00
	Mean	2.7344𝐸+01	3.0597𝐸−01	1.5941𝐸+00	𝟒.𝟒𝟎𝟒𝟖𝐄−𝟎𝟒	2.9365𝐸+02	8.4210𝐸+01	8.4533𝐸+00
	Worst	6.4757𝐸+01	4.0618𝐸−01	2.0862𝐸+00	𝟗.𝟖𝟎𝟒𝟎𝐄−𝟎𝟒	3.1329𝐸+02	8.9597𝐸+01	9.7956𝐸+00
	Std.	1.3793𝐸+01	4.7306𝐸−02	2.5818𝐸−01	𝟑.𝟎𝟎𝟒𝟏𝐄−𝟎𝟒	9.2166𝐸+00	3.2374𝐸+00	5.4824𝐸−01
	Rank	4	2	3	1	7	6	5
𝐹5(𝐷=500)	Best	2.7456𝐸+03	4.0397𝐸+03	2.0311𝐸+03	𝟎	6.1828𝐸+03	6.3281𝐸+03	3.8981𝐸+03
	Mean	3.9835𝐸+03	4.2471𝐸+03	2.3252𝐸+03	𝟎	6.5147𝐸+03	6.5574𝐸+03	4.2476𝐸+03
	Worst	4.6952𝐸+03	4.4312𝐸+03	2.5811𝐸+03	𝟎	6.7919𝐸+03	6.7360𝐸+03	4.5534𝐸+03
	Std.	4.2126𝐸+02	8.3027𝐸+01	1.2453𝐸+02	𝟎	1.2874𝐸+02	9.1246𝐸+01	1.3686𝐸+02
	Rank	3	5	2	1	6	7	4
𝐹6(𝐷=300)	Best	6.3274𝐸+00	8.0299𝐸+00	7.0415𝐸+00	𝟖.𝟖𝟖𝟏𝟖𝐄−𝟏𝟔	1.9882𝐸+01	2.0898𝐸+01	1.9386𝐸+01
	Mean	8.2684𝐸+00	8.7293𝐸+00	8.6721𝐸+00	𝟖.𝟖𝟖𝟏𝟖𝐄−𝟏𝟔	2.0099𝐸+01	2.1003𝐸+01	1.9495𝐸+01
	Worst	1.0209𝐸+01	9.4457𝐸+00	1.0111𝐸+01	𝟖.𝟖𝟖𝟏𝟖𝐄−𝟏𝟔	2.0345𝐸+01	2.1056𝐸+01	1.9589𝐸+01
	Std.	8.7857𝐸−01	3.0761𝐸−01	6.4227𝐸−01	𝟎	7.7479𝐸−02	3.3659𝐸−02	3.5615𝐸−02
	Rank	2	4	3	1	6	7	5
𝐹7(𝐷=100)	Best	2.1725𝐸+05	2.7428𝐸+03	4.3171𝐸+05	𝟑.𝟖𝟑𝟑𝟗𝐄−𝟑𝟏𝟗	9.4228𝐸+06	7.1039𝐸+05	7.9254𝐸+05
	Mean	1.5219𝐸+06	5.7789𝐸+03	2.8233𝐸+06	𝟐.𝟐𝟒𝟒𝟐𝐄−𝟐𝟖𝟎	3.0414𝐸+07	1.3329𝐸+06	4.5801𝐸+06
	Worst	6.8641𝐸+06	1.2878𝐸+04	7.0375𝐸+06	𝟏.𝟏𝟐𝟐𝟏𝐄−𝟐𝟕𝟖	7.1585𝐸+07	1.8894𝐸+06	1.6408𝐸+07
	Std.	1.3202𝐸+06	2.5486𝐸+03	1.6109𝐸+06	𝟎	1.3820𝐸+07	2.6259𝐸+05	3.7611𝐸+06
	Rank	3	2	4	1	7	5	6
𝐹8(𝐷=500)	Best	4.7748𝐸+01	1.6294𝐸+02	2.1827𝐸+02	𝟎	7.7044𝐸+03	1.0245𝐸+03	1.1878𝐸+04
	Mean	1.5434𝐸+02	2.0567𝐸+02	2.7742𝐸+02	𝟎	8.3385𝐸+03	1.2015𝐸+03	1.3091𝐸+04
	Worst	3.1407𝐸+02	2.4796𝐸+02	3.3449𝐸+02	𝟎	8.9522𝐸+03	1.4065𝐸+03	1.3825𝐸+04
	Std.	5.9349𝐸+01	1.7027𝐸+01	2.6215𝐸+01	𝟎	2.7756𝐸+02	7.9418𝐸+01	3.3184𝐸+02
	Rank	2	3	4	1	6	5	7
𝐹9(𝐷=200)	Best	𝟎	𝟎	3.4191𝐸−10	𝟎	8.9839𝐸−05	7.9967𝐸−09	2.4396𝐸−10
	Mean	7.9602𝐸−78	9.7855𝐸−19	5.6362𝐸−05	𝟔.𝟏𝟒𝟕𝟏𝐄−𝟏𝟔𝟕	1.0189𝐸−02	4.9600𝐸−07	3.5023𝐸−07
	Worst	2.6973𝐸−76	1.3878𝐸−17	1.7294𝐸−03	𝟐.𝟑𝟓𝟔𝟒𝐄−𝟏𝟔𝟓	1.1317𝐸−01	2.5864𝐸−06	6.8099𝐸−06
	Std.	3.8349𝐸−77	2.9411𝐸−18	2.5904𝐸−04	𝟎	1.9049𝐸−02	5.7052𝐸−07	1.1021𝐸−06
	Rank	2	3	5	1	7	6	4
𝐹10(𝐷=300)	Best	1.2447𝐸+02	1.2043𝐸+02	5.5973𝐸+02	𝟎	9.0756𝐸+03	2.9821𝐸+02	7.3081𝐸+03
	Mean	3.9115𝐸+02	1.5201𝐸+02	8.4831𝐸+02	𝟏.𝟑𝟗𝟎𝟏𝐄−𝟑𝟏𝟕	1.0803𝐸+05	3.6677𝐸+02	8.3861𝐸+03
	Worst	8.1348𝐸+02	1.9321𝐸+02	1.1894𝐸+03	𝟔.𝟒𝟔𝟒𝟕𝐄−𝟑𝟏𝟔	1.9276𝐸+06	4.7007𝐸+02	9.4975𝐸+03
	Std.	1.8186𝐸+02	1.6427𝐸+01	1.6003𝐸+02	𝟎	3.6921𝐸+05	3.4810𝐸+01	4.8766𝐸+02
	Rank	3	2	5	1	7	4	6