Cellular Harmony Search for Optimization Problems

Table 8

Mean and standard deviation of ten functions (𝑓₁--𝑓₁₀) when 𝑁=(10,30,50,100).

Function	Alg.	𝑁=10	𝑁=30	𝑁=50	𝑁=100
Sphere	cHS	7.022𝐸−08	1.323𝐸−04	4.776𝐸+02	2.036𝐸+04
		(4.079𝐸−08)	(3.285𝐸−05)	(9.256𝐸+01)	(2.584𝐸+03)
	HS	𝟑.𝟎𝟑𝟑𝐄−𝟎𝟖	6.086𝐸−03	8.746𝐸+02	1.591𝐸+04
		(𝟏.𝟖𝟒𝟐𝐄−𝟎𝟖)	(1.406𝐸−03)	(1.484𝐸+02)	(2.471𝐸+03)
Schwefel's 2.22	cHS	3.548𝐸−04	2.738𝐸−02	8.810𝐸+00	8.500𝐸+01
		(1.327𝐸−04)	(2.542𝐸−03)	(9.866𝐸−01)	(8.610𝐸+00)
	HS	𝟐.𝟕𝟐𝟓𝐄−𝟎𝟒	2.200𝐸−01	1.050𝐸+01	5.479𝐸+01
		(𝟔.𝟓𝟑𝟕𝐄−𝟎𝟓)	(2.495𝐸−02)	(1.323𝐸+00)	(3.951𝐸+00)
Step	cHS	6.297𝐸−08	1.288𝐸−04	3.771𝐸+02	1.960𝐸+04
		(3.292𝐸−08)	(3.42100𝐸−05)	(1.029𝐸+02)	(2.260𝐸+03)
	HS	𝟑.𝟓𝟎𝟏𝐄−𝟎𝟖	6.510𝐸−03	7.214𝐸+02	1.551𝐸+04
		(𝟐.𝟖𝟕𝟑𝐄−𝟎𝟖)	(1.019𝐸−03)	(1.364𝐸+02)	(1.169𝐸+03)
Rosenbrock	cHS	3.758𝐸+01	9.892𝐸+01	2.090𝐸+04	1.359𝐸+07
		(7.344𝐸+01)	(8.330𝐸+01)	(9.488𝐸+03)	(2.397𝐸+06)
	HS	𝟏.𝟔𝟓𝟏𝐄+𝟎𝟏	1.489𝐸+02	9.093𝐸+04	1.730𝐸+07
		(𝟑.𝟖𝟎𝟗𝐄+𝟎𝟏)	(1.220𝐸+02)	(2.346𝐸+04)	(2.195𝐸+06)
Rotated hyper-ellipsoid	cHS	2.351𝐸−06	8.421𝐸−01	1.993𝐸+05	3.097𝐸+07
		(1.799𝐸−06)	(1.381𝐸+00)	(4.916𝐸+04)	(3.408𝐸+06)
	HS	𝟖.𝟓𝟓𝟒𝐄−𝟎𝟕	2.647𝐸+00	2.825𝐸+05	2.723𝐸+07
		(𝟕.𝟎𝟓𝟗𝐄−𝟎𝟕)	(1.531𝐸+00)	(4.035𝐸+04)	(3.321𝐸+06)
Schwefel's 2.26	cHS	−𝟒.𝟏𝟗𝟎𝐄+𝟎𝟑	−1.256𝐸+04	9.019𝐸+02	8.874𝐸+03
		(1.040𝐸−01)	(1.190𝐸+00)	(2.182𝐸+02)	(8.167𝐸+02)
	HS	−𝟒.𝟏𝟗𝟎𝐄+𝟎𝟑	−1.256𝐸+04	8.594𝐸+02	5.119𝐸+03
		(𝟑.𝟖𝟔𝟏𝐄−𝟎𝟑)	(1.393𝐸+00)	(1.645𝐸+02)	(5.619𝐸+02)
Rastrigin	cHS	8.538𝐸−06	2.380𝐸−02	3.594𝐸+01	3.575𝐸+02
		(4.752𝐸−06)	(2.852𝐸−02)	(4.537𝐸+00)	(4.352𝐸+01)
	HS	𝟒.𝟗𝟑𝟖𝐄−𝟎𝟔	1.418𝐸+01	4.766𝐸+01	2.325𝐸+02
		(𝟓.𝟐𝟏𝟓𝐄−𝟎𝟔)	(2.376𝐸+00)	(4.308𝐸+00)	(1.703𝐸+01)
Ackley	cHS	𝟗.𝟑𝟔𝟔𝐄−𝟎𝟔	3.890𝐸−02	5.168𝐸+00	1.385𝐸+01
		(𝟒.𝟑𝟖𝟓𝐄−𝟎𝟔)	(1.686𝐸−01)	(4.202𝐸−01)	(3.524𝐸−01)
	HS	2.101𝐸−04	1.060𝐸−01	6.197𝐸+00	1.277𝐸+01
		(1.146𝐸−04)	(5.763𝐸−02)	(3.790𝐸−01)	(3.405𝐸−01)
Griewank	cHS	9.958𝐸−02	7.437𝐸−01	5.828𝐸+00	1.931𝐸+02
		(4.819𝐸−02)	(2.086𝐸−01)	(1.398𝐸+00)	(2.241𝐸+01)
	HS	𝟕.𝟎𝟖𝟐𝐄−𝟎𝟐	6.566𝐸−01	8.641𝐸+00	1.470𝐸+02
		(𝟒.𝟎𝟓𝟑𝐄−𝟎𝟐)	(2.352𝐸−01)	(1.330𝐸+00)	(1.583𝐸+01)
Six-Hump Camel-Back	cHS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−1.03163𝐸+00	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(3.927𝐸−11)	(4.150𝐸−11)	(𝟎)	(𝟎)
	HS	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−1.03163𝐸+00	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎	−𝟏.𝟎𝟑𝟐𝐄+𝟎𝟎
		(6.526𝐸−11)	(2.922𝐸−09)	(𝟎)	(𝟎)