An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization

Table 10

The experiment result of comparison of Cauchy distribution with Gaussian distribution for parameter adaptation.

	GEN	Cauchy 𝛾=0.1		Cauchy 𝛾=0.3		Gaussian Std = 0.1		Gaussian Std = 0.3
		Mean	Std	Mean	Std	Mean	Std	Mean	Std
𝐹1	1500	𝟓.𝟎𝐄−𝟑𝟔	𝟗.𝟒𝐄−𝟑𝟔	1.6𝐸−28	1.2𝐸−28	2.8𝐸−32	3.4𝐸−32	2.8𝐸−30	2.8𝐸−30
𝐹2	2000	𝟐.𝟒𝐄−𝟑𝟎	𝟏.𝟔𝐄−𝟑𝟎	3.1𝐸−24	1.3𝐸−24	1.9𝐸−27	2.1𝐸−27	7.4𝐸−26	4.7𝐸−26
𝐹3	5000	𝟐.𝟗𝐄−𝟏𝟐	𝟏.𝟏𝐄−𝟏𝟐	1.3𝐸−02	6.7𝐸−02	1.3𝐸−01	5.6𝐸−01	5.3𝐸−12	9.0𝐸−12
𝐹4	1500	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00
𝐹5	3000	𝟑.𝟎𝐄−𝟎𝟑	𝟔.𝟗𝐄−𝟎𝟒	4.0𝐸−03	1.3𝐸−03	3.4𝐸−03	1.6𝐸−03	3.1𝐸−03	8.4𝐸−04
𝐹6	9000	−12569.5	7.3𝐸−12	−12569.5	7.3𝐸−12	−12569.5	7.3𝐸−12	−12569.5	7.3𝐸−12
𝐹7	5000	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00	0.0𝐸+00
𝐹8	1500	𝟑.𝟑𝐄−𝟏𝟓	𝟕.𝟎𝐄−𝟏𝟔	8.7𝐸−15	2.7𝐸−15	4.2𝐸−15	1.6𝐸−15	6.3𝐸−15	1.1𝐸−15
𝐹9	2000	𝟎.𝟎𝐄+𝟎𝟎	𝟎.𝟎𝐄+𝟎𝟎	2.0𝐸−04	1.4𝐸−03	𝟎.𝟎𝐄+𝟎𝟎	𝟎.𝟎𝐄+𝟎𝟎	𝟎.𝟎𝐄+𝟎𝟎	𝟎.𝟎𝐄+𝟎𝟎
𝐹10	1500	𝟏.𝟔𝐄−𝟑𝟐	𝟓.𝟓𝐄−𝟒𝟖	6.2𝐸−30	4.9𝐸−30	1.9𝐸−32	6.7𝐸−33	2.9𝐸−31	1.9𝐸−31
𝐹11	1500	𝟏.𝟑𝐄−𝟑𝟐	𝟏.𝟏𝐄−𝟒𝟕	1.0𝐸−28	9.4𝐸−29	6.0𝐸−32	7.6𝐸−32	2.3𝐸−30	2.8𝐸−30
𝐹12	3000	𝟔.𝟏𝐄−𝟐𝟐	𝟓.𝟎𝐄−𝟐𝟐	3.7𝐸−17	2.9𝐸−17	1.5𝐸−19	2.1𝐸−19	3.5𝐸−18	2.6𝐸−18
𝐹13	1000	𝟓.𝟎𝐄−𝟐𝟎	𝟑.𝟒𝐄−𝟐𝟎	2.7𝐸−16	1.1𝐸−16	1.6𝐸−17	8.0𝐸−18	6.7𝐸−17	2.8𝐸−17
𝐹14	3000	𝟑.𝟓𝐄−𝟐𝟐	𝟐.𝟓𝐄−𝟐𝟐	4.4𝐸−17	6.6𝐸−17	2.1𝐸−19	2.4𝐸−19	2.9𝐸−18	2.5𝐸−18