A Novel Self-Adaptive Harmony Search Algorithm

Table 10

The descriptive statistical result of the relative errors of the six algorithms to solve twelve unconstrained benchmark functions with 100 dimensions.

Function	HS	IHS	HSw	DLHS	SGHS	NSHS
	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)
f1	2.30𝐸+02; (2.34𝐸+01)	2.38𝐸+02; (3.29𝐸+01)	2.06𝐸+02; (2.57𝐸+01)	1.30𝐸+02; (3.60𝐸+01)	5.23𝐸−02; (8.03𝐸−03)	𝟏.𝟓𝟔𝐄−𝟎𝟑; (𝟑.𝟓𝟖𝐄−𝟎𝟒)
f2	8.24𝐸+06; (1.82𝐸+06)	7.97𝐸+06; (1.77𝐸+06)	5.60𝐸+06; (1.14𝐸+06)	2.21𝐸+06; (1.08𝐸+06)	4.91𝐸+00; (2.32𝐸+00)	𝟐.𝟒𝟒𝐄+𝟎𝟎; (𝟕.𝟎𝟑𝐄+𝟎𝟎)
f3	8.94𝐸+02; (1.30𝐸+02)	9.46𝐸+02; (1.04𝐸+02)	8.68𝐸+02; (1.29𝐸+02)	5.79𝐸+02; (7.58𝐸+01)	7.99𝐸+02; (1.66𝐸+02)	8.04𝐸+02; (1.83𝐸+02)
f4	3.27𝐸−01; (2.30𝐸−02)	3.22𝐸−01; (2.08𝐸−02)	2.43𝐸−01; (1.91𝐸−02)	2.69𝐸−01; (2.65𝐸−02)	4.22𝐸−01; (4.47𝐸−02)	4.24𝐸−01; (3.39𝐸−02)
f5	2.09𝐸+10; (7.98𝐸+10)	1.50𝐸+12; (8.23𝐸+12)	6.56𝐸+00; (7.28𝐸−01)	3.84𝐸+00; (6.54𝐸−01)	𝟏.𝟑𝟖𝐄+𝟎𝟎; (𝟐.𝟏𝟐𝐄−𝟎𝟏)	4.78𝐸+00; (1.05𝐸+00)
f6	9.32𝐸+01; (1.32𝐸+01)	8.88𝐸+01; (9.45𝐸+00)	8.59𝐸+01; (1.28𝐸+01)	6.79𝐸+01; (1.38𝐸+01)	2.40𝐸+01; (4.48𝐸+00)	𝟏.𝟏𝟗𝐄+𝟎𝟎; (𝟐.𝟑𝟕𝐄+𝟎𝟎)
f7	4.93𝐸−02; (1.90𝐸−03)	4.88𝐸−02; (2.15𝐸−03)	4.79𝐸−02; (1.87𝐸−03)	4.21𝐸−02; (4.51𝐸−03)	𝟑.𝟔𝟎𝐄−𝟎𝟒; (𝟐.𝟑𝟔𝐄−𝟎𝟒)	5.01𝐸−04; (1.20𝐸−03)
f8	2.63𝐸+00; (2.85𝐸−01)	2.66𝐸+00; (2.34𝐸−01)	2.38𝐸+00; (2.72𝐸−01)	1.50𝐸+00; (4.14𝐸−01)	1.23𝐸−02; (3.98𝐸−03)	𝟏.𝟏𝟎𝐄−𝟎𝟐; (𝟓.𝟔𝟑𝐄−𝟎𝟑)
f9	5.86𝐸−03; (8.71𝐸−05)	5.87𝐸−03; (5.18𝐸−05)	5.74𝐸−03; (1.10𝐸−04)	4.46𝐸−03; (9.65𝐸−04)	3.07𝐸−05; (5.04𝐸−05)	𝟏.𝟕𝟕𝐄−𝟎𝟓; (𝟐.𝟒𝟎𝐄−𝟎𝟓)
f10	2.40𝐸+00; (1.83𝐸−01)	2.41𝐸+00; (1.66𝐸−01)	2.69𝐸+00; (1.59𝐸−01)	1.52𝐸+00; (4.14𝐸−01)	1.54𝐸−01; (2.06𝐸−02)	𝟑.𝟑𝟓𝐄−𝟎𝟏; (𝟑.𝟖𝟗𝐄−𝟎𝟐)
f11	4.62𝐸−01; (3.03𝐸−02)	4.26𝐸−01; (2.40𝐸−02)	4.59𝐸−01; (1.79𝐸−02)	3.89𝐸−01; (3.40𝐸−02)	1.24𝐸−01; (1.64𝐸−02)	5.57𝐸−01; (1.08𝐸−01)
f12	1.32𝐸−02; (1.59𝐸−03)	1.26𝐸−02; (1.73𝐸−03)	3.86𝐸−02; (3.18𝐸−03)	7.20𝐸−03; (2.15𝐸−03)	𝟒.𝟕𝟑𝐄−𝟎𝟓; (𝟐.𝟐𝟑𝐄−𝟎𝟓)	2.93𝐸−04; (6.85𝐸−05)
Total	1.74𝐸+09; (2.34𝐸+10)	1.25𝐸+11; (2.37𝐸+12)	4.67𝐸+05; (1.58𝐸+06)	1.85𝐸+05; (6.86𝐸+05)	6.92𝐸+01; (2.25𝐸+02)	𝟔.𝟕𝟖𝐄+𝟎𝟏; (𝟐.𝟐𝟖𝐄+𝟎𝟐)

∗Each group has 30 samples and the experiment has totally 12 * 6 * 30 = 2160 samples. The bold represents the significant best.