Component Thermodynamical Selection Based Gene Expression Programming for Function Finding

Table 1

Experimental results of GEP, IGEP, AMACGEP, Mod-GEP, and CTSGEP over 30 independent runs for the 15 test instances.

Instance	GEP; Mean MSE ± Std Dev	IGEP; Mean MSE ± Std Dev	AMACGEP; Mean MSE ± Std Dev	Mod-GEP; Mean MSE ± Std Dev	CTSGEP; Mean MSE ± Std Dev
10	2.36𝐸−06±3.17𝐸−07−	1.40𝐸−06±2.71𝐸−06−	1.24𝐸−06±9.38𝐸−07−	4.07𝐸−07±7.21𝐸−08−	𝟗.𝟔𝟏𝐄−𝟎𝟖±𝟔.𝟗𝟐𝐄−𝟎𝟗
21	4.47𝐸−04±1.06𝐸−04−	7.70𝐸−04±8.03𝐸−05−	2.82𝐸−04±4.33𝐸−05−	4.56𝐸−05±6.51𝐸−06−	𝟗.𝟓𝟗𝐄−𝟎𝟔±𝟓.𝟕𝟖𝐄−𝟎𝟕
35	8.24𝐸−03±2.51𝐸−03−	1.83𝐸−03±4.28𝐸−04−	2.41𝐸−03±5.08𝐸−04−	1.04𝐸−03±8.02𝐸−04≈	𝟖.𝟕𝟏𝐄−𝟎𝟒±𝟐.𝟎𝟕𝐄−𝟎𝟓
44	1.13𝐸−04±5.26𝐸−05−	6.56𝐸−05±1.82𝐸−05−	3.52𝐸−05±2.67𝐸−06−	5.35𝐸−05±5.11𝐸−05−	𝟏.𝟗𝟒𝐄−𝟎𝟓±𝟗.𝟔𝟗𝐄−𝟎𝟕
49	8.85𝐸−02±6.13𝐸−03−	7.55𝐸−02±2.61𝐸−02−	𝟒.𝟏𝟕𝐄−𝟎𝟐±𝟏.𝟗𝟑𝐄−𝟎𝟒+	6.69𝐸−02±1.48𝐸−03−	5.22𝐸−02±3.19𝐸−03
52	5.57𝐸−02±4.31𝐸−02−	5.61𝐸−03±2.57𝐸−03−	7.54𝐸−03±4.12𝐸−04−	1.07𝐸−03±1.21𝐸−04−	𝟔.𝟗𝟎𝐄−𝟎𝟒±𝟐.𝟔𝟑𝐄−𝟎𝟓
76b	6.13𝐸−06±2.87𝐸−06−	4.22𝐸−06±8.61𝐸−07−	3.56𝐸−06±9.47𝐸−07−	2.71𝐸−06±6.23𝐸−07−	𝟏.𝟎𝟏𝐄−𝟎𝟔±𝟓.𝟑𝟔𝐄−𝟎𝟕
84b	9.59𝐸−03±2.86𝐸−03−	1.14𝐸−03±6.35𝐸−04−	2.71𝐸−03±6.87𝐸−04−	𝟔.𝟖𝟐𝐄−𝟎𝟒±𝟗.𝟏𝟓𝐄−𝟎𝟔+	7.89𝐸−04±1.95𝐸−05
103	1.85𝐸−06±4.27𝐸−07−	8.59𝐸−08±6.29𝐸−08−	6.58𝐸−08±1.83𝐸−09−	3.75𝐸−08±5.18𝐸−08−	𝟐.𝟕𝟐𝐄−𝟎𝟗±𝟔.𝟏𝟔𝐄−𝟎𝟗
126a	5.10𝐸−04±3.68𝐸−05−	𝟐.𝟑𝟗𝐄−𝟎𝟓±𝟕.𝟓𝟑𝐄−𝟎𝟔+	6.38𝐸−05±4.79𝐸−04≈	6.78𝐸−05±1.63𝐸−06−	5.10𝐸−05±1.96𝐸−06
148c	7.92𝐸−03±5.15𝐸−04−	9.15𝐸−03±6.72𝐸−04−	5.78𝐸−03±7.61𝐸−05−	𝟏.𝟕𝟐𝐄−𝟎𝟑±𝟑.𝟏𝟒𝐄−𝟎𝟒+	2.77𝐸−03±6.52𝐸−05
155	4.66𝐸−02±2.90𝐸−04−	3.77𝐸−02±1.35𝐸−04−	2.78𝐸−02±9.22𝐸−03−	1.66𝐸−02±3.48𝐸−02≈	𝟗.𝟏𝟏𝐄−𝟎𝟑±𝟒.𝟔𝟐𝐄−𝟎𝟔
163	1.49𝐸−04±1.73𝐸−04−	1.16𝐸−04±2.58𝐸−06−	8.10𝐸−05±1.66𝐸−06−	5.82𝐸−05±6.15𝐸−06−	𝟑.𝟒𝟎𝐄−𝟎𝟓±𝟐.𝟖𝟑𝐄−𝟎𝟓
182c	7.97𝐸−05±3.82𝐸−06−	1.08𝐸−06±6.74𝐸−07−	6.36𝐸−06±3.52𝐸−07−	4.95𝐸−07±5.18𝐸−07−	𝟗.𝟐𝟓𝐄−𝟎𝟖±𝟐.𝟓𝟒𝐄−𝟏𝟎
203	3.66𝐸−03±6.47𝐸−04−	1.26𝐸−03±3.75𝐸−04−	1.01𝐸−03±3.87𝐸−05−	𝟑.𝟔𝟕𝐄−𝟎𝟒±𝟏.𝟏𝟗𝐄−𝟎𝟔+	7.73𝐸−04±1.54𝐸−04
−	15	14	13	10
+	0	1	1	3
≈	0	0	1	2

“Mean MSE” and “Std Dev” indicate the average and standard deviation of the mean square error values obtained in 30 independent runs, respectively.
Two-tailed t-test at a 0.05 significance level is conducted between CTSGEP and each of GEP, IGEP, AMACGEP, and Mod-GEP.
“+”, “−”, “≈” denote that the performance of the corresponding algorithm is better than, worse than and similar to that of CTSGEP according to the two-tailed t-test, respectively.
The best results among the five algorithms are typed in bold.