A Free Search Krill Herd Algorithm for Functions Optimization

Table 3

Simulation results for 𝐹₁₀∼𝐹₁₃.

Benchmark function	Result	Method
		PSO	DE	KH II	FSKH	HS	FS	BA
𝐹11(𝐷=2)	Best	−𝟏	−9.999984𝐸−01	−9.999997𝐸−01	−𝟏	−9.880465𝐸−01	−9.982745𝐸−01	−9.627759𝐸−01
	Mean	−9.961136𝐸−01	−9.996264𝐸−01	−9.999894𝐸−01	−𝟏	−8.445035𝐸−01	−9.921680𝐸−01	−7.407210𝐸−01
	Worst	−9.902840𝐸−01	−9.941573𝐸−01	−9.999449𝐸−01	−𝟏	−5.830062𝐸−01	−9.902681𝐸−01	−5.482243𝐸−01
	Std.	4.808128𝐸−03	8.981117𝐸−04	1.209463𝐸−05	𝟎	9.752777𝐸−02	2.869464𝐸−03	1.250904𝐸−01
	Rank	2	4	3	𝟏	6	5	7
𝐹12(𝐷=2)	Best	−𝟏	−𝟏	−𝟏	−𝟏	−9.756697𝐸−01	−9.999931𝐸−01	−9.999997𝐸−01
	Mean	−9.961747𝐸−01	−9.999996𝐸−01	−9.821486𝐸−01	−𝟏	−8.443158𝐸−01	−9.983692𝐸−01	−7.368404𝐸−01
	Worst	−9.362453𝐸−01	−9.999938𝐸−01	−9.362453𝐸−01	−𝟏	−5.856036𝐸−01	−9.948806𝐸−01	−2.888120𝐸−01
	Std.	1.529461𝐸−02	1.113912𝐸−06	2.891639𝐸−02	𝟎	9.704192𝐸−02	1.421345𝐸−03	1.667622𝐸−01
	Rank	3	2	4	𝟏	7	6	5
𝐹13(𝐷=2)	Best	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−1.031587𝐸+00	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎
	Mean	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−1.031510𝐸+00	−9.719758𝐸−01	−1.031628𝐸+00	−9.989818𝐸−01
	Worst	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟏𝟔𝟐𝟖𝐄+𝟎𝟎	−1.031071𝐸+00	−6.378180𝐸−01	−1.031627𝐸+00	−2.154637𝐸−01
	Std.	𝟔.𝟕𝟐𝟖𝟗𝟔𝟕𝐄−𝟏𝟔	8.535156𝐸−16	2.176352𝐸−09	1.420660𝐸−04	7.340586𝐸−02	1.353951𝐸−07	1.615586𝐸−01
	Rank	𝟏	2	3	5	7	4	6
𝐹14(𝐷=2)	Best	−𝟏	−𝟏	−𝟏	−𝟏	−9.938758𝐸−01	−9.999999𝐸−01	−1
	Mean	−𝟏	−𝟏	−9.999999𝐸−01	−9.998070𝐸−01	−5.496989𝐸−01	−9.997912𝐸−01	−6.000308𝐸−01
	Worst	−𝟏	−𝟏	−9.999999𝐸−01	−9.995538𝐸−01	−1.236216𝐸−05	−9.984373𝐸−01	−8.743099𝐸−12
	Std.	𝟎	𝟎	2.026218𝐸−09	1.291856𝐸−03	4.099494𝐸−01	2.968278𝐸−04	4.948335𝐸−01
	Rank	𝟏	𝟏	3	4	7	6	5