A Novel Self-Adaptive Harmony Search Algorithm

Table 12

The descriptive statistical result of the relative errors of the six algorithms to solve twelve unconstrained benchmark functions with 1000 dimensions.

Function	HS	IHS	HSw	DLHS	SGHS	NSHS
	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)	Mean (std.)
f1	2.65𝐸+04; (5.35𝐸+02)	2.63𝐸+04; (5.15𝐸+02)	2.85𝐸+04; (6.46𝐸+02)	2.63𝐸+04; (1.76𝐸+03)	1.77𝐸+03; (1.33𝐸+02)	𝟕.𝟗𝟑𝐄+𝟎𝟎; (𝟓.𝟑𝟔𝐄−𝟎𝟏)
f2	6.34𝐸+09; (3.62𝐸+08)	6.41𝐸+09; (2.85𝐸+08)	6.43𝐸+09; (3.01𝐸+08)	6.31𝐸+09; (6.22𝐸+08)	5.04𝐸+07; (3.26𝐸+06)	𝟔.𝟗𝟏𝐄+𝟎𝟑; (𝟏.𝟒𝟎𝐄+𝟎𝟑)
f3	1.16𝐸+05; (1.38𝐸+04)	1.17𝐸+05; (1.34𝐸+04)	1.10𝐸+05; (9.12𝐸+03)	8.30𝐸+04; (6.59𝐸+03)	7.01𝐸+04; (1.02𝐸+04)	𝟔.𝟖𝟔𝐄+𝟎𝟒; (𝟕.𝟒𝟓𝐄+𝟎𝟑)
f4	5.58𝐸−01; (7.02𝐸−03)	5.56𝐸−01; (9.08𝐸−03)	5.18𝐸−01; (6.71𝐸−03)	5.43𝐸−01; (7.79𝐸−03)	5.86𝐸−01; (1.19𝐸−02)	5.72𝐸−01; (1.16𝐸−02)
f5	2.61𝐸+00; (3.17𝐸−02)	2.61𝐸+00; (5.05𝐸−02)	2.69𝐸+00; (5.58𝐸−02)	2.60𝐸+00; (5.30𝐸−02)	2.69𝐸+00; (4.96𝐸−02)	3.15𝐸+00; (6.74𝐸−02)
f6	7.83𝐸+03; (2.54𝐸+02)	7.97𝐸+03; (2.55𝐸+02)	8.08𝐸+03; (2.23𝐸+02)	7.78𝐸+03; (3.95𝐸+02)	7.72𝐸+03; (2.70𝐸+02)	1.02𝐸+04; (4.90𝐸+02)
f7	1.04𝐸−01; (5.97𝐸−04)	1.04𝐸−01; (5.02𝐸−04)	1.06𝐸−01; (9.92𝐸−04)	1.04𝐸−01; (1.23𝐸−03)	5.69𝐸−02; (9.70𝐸−04)	𝟒.𝟒𝟕𝐄−𝟎𝟐; (𝟏.𝟑𝟕𝐄−𝟎𝟑)
f8	2.61𝐸+02; (5.43𝐸+00)	2.60𝐸+02; (6.21𝐸+00)	2.79𝐸+02; (7.31𝐸+00)	2.60𝐸+02; (1.43𝐸+01)	1.95𝐸+01; (1.32𝐸+00)	𝟐.𝟎𝟕𝐄+𝟎𝟎; (𝟓.𝟏𝟓𝐄−𝟎𝟐)
f9	4.28𝐸−02; (1.01𝐸−03)	4.26𝐸−02; (1.18𝐸−03)	4.51𝐸−02; (9.60𝐸−04)	4.26𝐸−02; (2.36𝐸−03)	7.97𝐸−03; (1.54𝐸−04)	𝟓.𝟏𝟐𝐄−𝟎𝟒; (𝟑.𝟖𝟎𝐄−𝟎𝟓)
f10	1.10𝐸+02; (1.95𝐸+00)	1.10𝐸+02; (2.46𝐸+00)	1.17𝐸+02; (3.02𝐸+00)	1.12𝐸+02; (5.36𝐸+00)	3.26𝐸+01; (1.09𝐸+00)	𝟐.𝟓𝟒𝐄+𝟎𝟏; (𝟖.𝟐𝟕𝐄−𝟎𝟏)
f11	1.02𝐸+01; (1.06𝐸−01)	9.92𝐸+00; (9.23𝐸−02)	1.04𝐸+01; (9.89𝐸−02)	1.00𝐸+01; (1.54𝐸−01)	𝟔.𝟔𝟖𝐄+𝟎𝟎; (𝟐.𝟏𝟕𝐄−𝟎𝟏)	1.19𝐸+01; (1.03𝐸−01)
f12	1.70𝐸+00; (3.57𝐸−02)	1.68𝐸+00; (3.93𝐸−02)	2.27𝐸+00; (5.14𝐸−02)	1.73𝐸+00; (1.12𝐸−01)	3.21𝐸−01; (2.46𝐸−02)	𝟏.𝟓𝟗𝐄−𝟎𝟏; (𝟕.𝟏𝟖𝐄−𝟎𝟑)
Total	5.29𝐸+08; (1.76𝐸+09)	5.34𝐸+08; (1.77𝐸+09)	5.36𝐸+08; (1.78𝐸+09)	5.26𝐸+08; (1.76𝐸+09)	4.21𝐸+06; (1.40𝐸+07)	𝟕.𝟏𝟒𝐄+𝟎𝟑; (𝟏.𝟗𝟎𝐄+𝟎𝟒)

∗Each group has 30 samples and the experiment has totally 12 * 6 * 30 = 2160 samples. For a solvability, the search ranges of function f5 are renewed in [−1, 1]because 100^∧1000 reaches an infinity even 10^∧1000. The bold represents the significant best.