Cellular Harmony Search for Optimization Problems

Table 5

The effect of varying the HMS parameter on HS and cHS for ten functions (𝑓₁--𝑓₁₀).

Function	Alg.	16	25	36	100
Sphere	cHS	1.188𝐸−04	1.323𝐸−04	8.506𝐸−04	6.950𝐸−01
		(2.204𝐸−05)	(3.285𝐸−05)	(2.744𝐸−03	(5.385𝐸−01)
	HS	𝟕.𝟗𝟔𝟏𝐄−𝟎𝟓	6.086𝐸−03	3.934𝐸−03	7.274𝐸−01
		(𝟏.𝟓𝟏𝟏𝐄−𝟎𝟓)	(1.40654𝐸−03)	(1.721𝐸−02)	(5.510𝐸−01)
Schwefel's 2.22	cHS	3.011𝐸−02	2.738𝐸−02	2.869𝐸−02	3.850𝐸−01
		(3.522𝐸−03)	(2.542𝐸−03)	(3.043𝐸−03)	(1.391𝐸−01)
	HS	𝟐.𝟐𝟎𝟖𝐄−𝟎𝟐	2.200𝐸−01	2.447𝐸−02	3.210𝐸−02
		(𝟐.𝟔𝟓𝟖𝐄−𝟎𝟑)	(2.495𝐸−02)	(5.482𝐸−03)	(3.840𝐸−03)
Step	cHS	1.225𝐸−04	1.288𝐸−04	1.637𝐸−02	7.698𝐸−01
		(2.373𝐸−05)	(3.421𝐸−05)	(6.139𝐸−02)	(5.098𝐸−01)
	HS	𝟕.𝟗𝟖𝟖𝐄−𝟎𝟓	6.510𝐸−03	3.161𝐸−03	8.057𝐸−01
		(𝟏.𝟏𝟐𝟑𝐄−𝟎𝟓)	(1.019𝐸−03)	(9.481𝐸−03)	(4.692𝐸−01)
Rosenbrock	cHS	1.106𝐸+02	1.328𝐸+02	1.025𝐸+02	2.738𝐸+02
		(1.449𝐸+02)	(2.425𝐸+02)	(8.530𝐸+01)	(4.751𝐸+02)
	HS	8.418𝐸+02	𝟗.𝟖𝟗𝟐𝐄+𝟎𝟏	1.148𝐸+02	2.573𝐸+02
		(7.497𝐸+02)	(𝟏.𝟐𝟐𝟎𝐄+𝟎𝟐)	(1.278𝐸+02)	(4.789𝐸+02)
Rotated hyper	cHS	𝟐.𝟔𝟎𝟒𝐄−𝟎𝟐	8.421𝐸−01	2.883𝐸+00	1.649295𝐸+01
		(𝟑.𝟎𝟒𝟐𝐄−𝟎𝟐)	(1.381𝐸+00)	(2.572𝐸+00)	(2.234042𝐸+01)
	HS	1.661𝐸−01	2.647𝐸+00	1.808𝐸+00	1.259𝐸+02
		(1.835𝐸−01)	(1.531𝐸+00)	(4.377𝐸+00)	(1.060𝐸+02)
Schwefel's 2.26	cHS	−1.075𝐸+04	−1.256𝐸+04	−1.256𝐸+04	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒
		(1.163𝐸+00)	(1.190𝐸+00)	(2.122𝐸+00)	(3.050𝐸+00)
	HS	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒	−1.256𝐸+04	−1.256𝐸+04
		(𝟏.𝟐𝟎𝟗𝐄+𝟎𝟎)	(1.300𝐸+00)	(2.125𝐸+00)	(2.263𝐸+00)
Rastrigin	cHS	𝟐.𝟏𝟓𝟗𝐄−𝟎𝟐	2.380𝐸−02	3.625𝐸−02	1.010𝐸−01
		(𝟕.𝟑𝟒𝟖𝐄−𝟎𝟑)	(2.852𝐸−02)	(7.533𝐸−02)	(2.517𝐸−01)
	HS	3.268𝐸−02	1.418𝐸+01	5.107𝐸−02	2.503𝐸−02
		(1.956𝐸−03)	(2.376𝐸+00)	(1.816𝐸−01)	(8.612𝐸−03)
Ackley	cHS	𝟑.𝟒𝟗𝟓𝐄−𝟎𝟑	3.890𝐸−02	3.369𝐸−02	2.636𝐸−02
		(𝟐.𝟒𝟓𝟐𝐄−𝟎𝟑)	(1.686𝐸−01)	(1.006𝐸−01)	(4.388𝐸−02)
	HS	6.760𝐸−03	1.060𝐸−01	2.313𝐸−02	8.757𝐸−02
		(8.735𝐸−04)	(5.763𝐸−02)	(8.375𝐸−02)	(1.395𝐸−01)
Griewank	cHS	6.481𝐸−01	7.437𝐸−01	8.571𝐸−01	9.878𝐸−01
		(2.614𝐸−01)	(2.086𝐸−01)	(1.486𝐸−01)	(5.487𝐸−02)
	HS	𝟓.𝟎𝟏𝟎𝐄−𝟎𝟏	6.566𝐸−01	8.020𝐸−01	9.907𝐸−01
		(𝟐.𝟒𝟎𝟗𝐄−𝟎𝟏)	(2.352𝐸−01)	(1.658𝐸−01)	(5.565𝐸−02)
Six-Hump	cHS	−1.031𝐸+00	−1.031𝐸+00	−1.031𝐸+00	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(5.325𝐸−11)	(4.15028𝐸−11)	(6.052𝐸−11)	(𝟐.𝟎𝟎𝟏𝐄−𝟏𝟏)
	HS	−1.031𝐸+00	−1.031𝐸+00	−1.031𝐸+00	−1.030𝐸+00
		(1.897𝐸−11)	(2.922𝐸−09)	(4.793𝐸−10)	(2.235𝐸−10)