Cellular Harmony Search for Optimization Problems

Table 4

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

Function	Alg.	0.7	0.9	0.94	0.98
Sphere	cHS	5.514𝐸+03	3.383𝐸+01	2.240𝐸+00	𝟏.𝟑𝟐𝟑𝐄−𝟎𝟒
		(8.887𝐸+02)	(1.164𝐸+01)	(9.216𝐸−01)	(𝟑.𝟐𝟖𝟓𝐄−𝟎𝟓)
	HS	3.750𝐸+03	1.663𝐸+01	1.152𝐸+00	6.086𝐸−03
		(6.455𝐸+02)	(4.716𝐸+00)	(7.069𝐸−01)	(1.406𝐸−03)
Schwefel's 2.22	cHS	1.939𝐸+01	2.584𝐸−01	5.397𝐸−02	𝟐.𝟕𝟑𝟖𝐄−𝟎𝟐
		(1.966𝐸+00)	(1.006𝐸−01)	(8.303𝐸−03)	(𝟐.𝟓𝟒𝟐𝐄−𝟎𝟑)
	HS	1.581𝐸+01	5.359𝐸+00	4.081𝐸−01	2.20087𝐸−01
		(2.380𝐸+00)	(1.036𝐸+00)	(4.914𝐸−01)	(2.49573𝐸−02)
Step	cHS	5.700𝐸+03	3.233𝐸+01	2.437𝐸+00	𝟏.𝟐𝟖𝟖𝐄−𝟎𝟒
		(8.707𝐸+02)	(1.085𝐸+01)	(1.132𝐸+00)	(𝟑.𝟒𝟐𝟏𝐄−𝟎𝟓)
	HS	3.949𝐸+03	1.605𝐸+01	8.041𝐸+00	6.510𝐸−03
		(6.671𝐸+02)	(4.439𝐸+00)	(5.844𝐸−01)	(1.019𝐸−03)
Rosenbrock	cHS	3.578𝐸+06	1.276𝐸+03	1.944𝐸+02	𝟗.𝟖𝟗𝟐𝐄+𝟎𝟏
		(9.728𝐸+05)	(9.524𝐸+02)	(1.177𝐸+02)	(𝟖.𝟑𝟑𝟎𝐄+𝟎𝟏)
	HS	2.143𝐸+06	5.444𝐸+02	1.449𝐸+02	1.489𝐸+02
		(5.423𝐸+05)	(2.240𝐸+02)	(7.499𝐸+01)	(1.22097𝐸+02)
Rotated hyper	cHS	7.206𝐸+05	5.588𝐸+03	4.250𝐸+01	𝟖.𝟒𝟐𝟏𝐄−𝟎𝟏
		(1.122𝐸+05)	(2.071𝐸+03)	(2.364𝐸+02)	(𝟏.𝟑𝟖𝟏𝐄+𝟎𝟎)
	HS	5.155𝐸+05	2.972𝐸+03	1.373𝐸+02	2.647𝐸+00
		(7.586𝐸+04)	(9.061𝐸+02)	(1.137𝐸+02)	(1.531𝐸+00)
Schwefel's 2.26	cHS	−1.075𝐸+04	−1.250𝐸+04	−1.256𝐸+04	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒
		(2.536𝐸+02)	(2.208𝐸+01)	(3.982𝐸+00)	(2.371𝐸+00)
	HS	−1.123𝐸+04	−1.253𝐸+04	−1.256𝐸+04	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒
		(2.643𝐸+02)	(1.389𝐸+01)	(2.465𝐸+00)	(𝟐.𝟏𝟑𝟏𝐄+𝟎𝟎)
Rastrigin	cHS	8.581𝐸+01	4.029𝐸+00	7.068𝐸−02	2.380𝐸−02
		(8.587𝐸+00)	(1.780𝐸+00)	(9.444𝐸−02)	(2.85250𝐸−02)
	HS	6.612𝐸+01	1.548𝐸+00	1.289𝐸−01	𝟏.𝟓𝟖𝟐𝐄−𝟎𝟐
		(8.693𝐸+00)	(1.198𝐸+00)	(3.037𝐸−01)	(𝟕.𝟎𝟐𝟑𝐄−𝟎𝟑)
Ackley	cHS	1.295𝐸+01	2.522𝐸+00	1.891𝐸−01	𝟑.𝟖𝟗𝟎𝐄−𝟎𝟐
		(6.804𝐸−01)	(3.160𝐸−01)	(2.418𝐸−01)	(𝟏.𝟔𝟖𝟔𝐄−𝟎𝟏)
	HS	1.209𝐸+01	1.830𝐸+00	6.493𝐸−01	1.060𝐸−01
		(5.334𝐸−01)	(3.862𝐸−01)	(1.282𝐸−01)	(5.763𝐸−02)
Griewank	cHS	5.234𝐸+01	1.298𝐸+00	1.024𝐸+00	7.870𝐸−01
		(8.732𝐸+00)	(1.066𝐸−01)	(3.995𝐸−02)	(2.086𝐸−01)
	HS	3.895𝐸+01	1.166𝐸+00	1.013𝐸+00	𝟔.𝟓𝟔𝟔𝐄−𝟎𝟏
		(6.677𝐸+00)	(5.312𝐸−02)	(1.920𝐸−02)	(𝟐.𝟑𝟓𝟐𝐄−𝟎𝟏)
Six-Hump	cHS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(𝟐.𝟖𝟖𝟐𝐄−𝟏𝟎)	(2.998𝐸−11)	(9.912𝐸−11)	(4.150𝐸−11)
	HS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(1.291𝐸−10)	(5.571𝐸−11)	(3.175𝐸−11)	(2.922𝐸−09)