Cellular Harmony Search for Optimization Problems

Table 6

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

Function	Alg.	0.1	0.3	0.7	0.9
Sphere	cHS	1.343𝐸−02	𝟏.𝟑𝟐𝟑𝐄−𝟎𝟒	3.136𝐸−04	4.713𝐸−04
		(3.391𝐸−02)	(𝟑.𝟐𝟖𝟓𝐄−𝟎𝟓)	(4.066𝐸−05)	(5.207𝐸−05)
	HS	2.012𝐸−02	6.086𝐸−03	3.827𝐸−04	5.497𝐸−04
		(6.098𝐸−02)	(1.406𝐸−03)	(5.318𝐸−05)	(7.251𝐸−05)
Schwefel's 2.22	cHS	4.965𝐸−03	2.738𝐸−02	5.784𝐸−02	2.827𝐸−02
		(7.512𝐸−04)	(2.542𝐸−03)	(5.463𝐸−03)	(3.017𝐸−03)
	HS	𝟑.𝟓𝟏𝟖𝐄−𝟎𝟑	2.200𝐸−01	7.583𝐸−02	9.548𝐸−02
		(𝟓.𝟖𝟑𝟕𝐄−𝟎𝟒)	(2.495𝐸−02)	(5.482𝐸−03)	(4.834𝐸−03)
Step	cHS	5.526𝐸−02	𝟏.𝟐𝟖𝟖𝐄−𝟎𝟒	2.929𝐸−04	4.606𝐸−04
		(1.177𝐸−01)	(𝟑.𝟒𝟐𝟏𝐄−𝟎𝟓)	(3.776𝐸−05)	(5.136268𝐸−05)
	HS	1.682𝐸−02	6.510𝐸−03	3.753𝐸−04	5.291𝐸−04
		(3.939𝐸−02)	(1.019𝐸−03)	(5.417𝐸−05)	(4.401𝐸−05)
Rosenbrock	cHS	2.065𝐸+02	9.892𝐸+01	3.114𝐸+02	1.030𝐸+02
		(4.747𝐸+02)	(8.330𝐸+01)	(6.121𝐸+02)	(6.798𝐸+01)
	HS	1.813𝐸+02	1.489𝐸+02	1.312𝐸+02	𝟖.𝟑𝟎𝟏𝐄+𝟎𝟏
		(3.929𝐸+02)	(1.220𝐸+02)	(2.515𝐸+02)	(𝟓.𝟕𝟒𝟖𝐄+𝟎𝟏)
Rotated hyper	cHS	𝟏.𝟎𝟑𝟖𝐄−𝟎𝟐	8.421𝐸−01	1.323𝐸−01	1.970𝐸−01
		(𝟏.𝟔𝟎𝟑𝐄−𝟎𝟐)	(1.381𝐸+00)	(5.359𝐸−02)	(5.845𝐸−02)
	HS	5.404𝐸+00	2.647𝐸+00	4.726𝐸−01	4.660𝐸−01
		(1.507𝐸+01)	(1.531𝐸+00)	(3.248𝐸−01)	(3.479𝐸−01)
Schwefel's 2.26	cHS	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒	−1.256𝐸+04	−1.256𝐸+04	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒
		(2.536𝐸+02)	(1.190𝐸+00)	(3.982𝐸+00)	(2.371𝐸+00)
	HS	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒	−1.256𝐸+04	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒	−𝟏.𝟐𝟓𝟕𝐄+𝟎𝟒
		(2.092𝐸+00)	(1.393𝐸+00)	(𝟏.𝟎𝟖𝟐𝐄+𝟎𝟎)	(1.151𝐸+00)
Rastrigin	cHS	𝟗.𝟑𝟓𝟓𝐄−𝟎𝟒	2.380𝐸−02	5.248𝐸−02	9.029𝐸−02
		(𝟖.𝟖𝟐𝟕𝐄−𝟎𝟒)	(2.852𝐸−02)	(9.304𝐸−03)	(3.178𝐸−02)
	HS	3.468𝐸−03	1.418𝐸+01	7.952𝐸−02	1.092𝐸−01
			(1.763𝐸−03)	(2.376𝐸+00)	(1.720𝐸−02)
Ackley	cHS	𝟓.𝟔𝟓𝟓𝐄−𝟎𝟑	3.890𝐸−02	5.730𝐸−02	3.827𝐸−02
		(𝟏.𝟏𝟗𝟕𝐄−𝟎𝟐)	(1.686𝐸−01)	(1.815𝐸−01)	(1.152𝐸−03)
	HS	(1.878𝐸−02)	1.060𝐸−01	1.585𝐸−02	1.804𝐸−02
		(8.563𝐸−02)	(5.763𝐸−02)	(1.606𝐸−03)	(1.168𝐸−01)
Griewank	cHS	8.866𝐸−01	7.437𝐸−01	7.310𝐸−01	4.982𝐸−01
		(1.306𝐸−01)	(2.086𝐸−01)	(1.826𝐸−01)	(2.712𝐸−01)
	HS	8.542𝐸−01	6.566𝐸−01	4.912𝐸−01	𝟑.𝟖𝟓𝟑𝐄−𝟎𝟏
		(1.270𝐸−01)	(2.352𝐸−01)	(2.591𝐸−01)	(𝟐.𝟒𝟏𝟑𝐄−𝟎𝟏)
Six-Hump	cHS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(1.496𝐸−10)	(4.150𝐸−11)	(3.543𝐸−11)	(𝟑.𝟏𝟗𝟕𝐄−𝟏𝟏)
	HS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(1.897𝐸−10)	(2.922𝐸−09)	(4.793𝐸−11)	(2.235𝐸−10)