An Adaptive Hybrid Algorithm Based on Particle Swarm Optimization and Differential Evolution for Global Optimization

Table 5

Results of the comparison between HPSO-DE and JADE.

Functions	Gen	HPSO-DE; Mean (Std Dev.)	JADE w/o archive; Mean (Std Dev.)	JADE with archive; Mean (Std Dev.)
𝑓1	1500	𝟐.𝟗𝐄−𝟏𝟐𝟏    (𝟏.𝟎𝐄−𝟐𝟒𝟎)	1.8𝐸−60 (8.4𝐸−60)	1.3𝐸−54 (9.2𝐸−54)
𝑓3	2000	𝟏.𝟕𝐄−𝟕𝟖   (𝟒.𝟓𝐄−𝟏𝟓𝟓)	1.8𝐸−25 (8.8𝐸−25)	3.9𝐸−22 (2.7𝐸−21)
𝑓4	5000	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	5.7𝐸−61 (2.7𝐸−60)	6.0𝐸−87 (1.9𝐸−86)
𝑓5	5000	𝟏.𝟕𝐄−𝟏𝟖𝟓   (𝟎𝟎.𝟎𝐄+𝟎𝟎)	8.2𝐸−24 (4.0𝐸−23)	4.3𝐸−66 (1.2𝐸−65)
𝑓6	3000	2.9+𝐸2 (1.1𝐸−2)	𝟖.𝟎𝐄−𝟎𝟐   (𝟓.𝟔𝐄−𝟎𝟏)	3.2𝐸−01 (1.1𝐸+00)
	20000	2.9+𝐸2 (3.4𝐸−2)	𝟖.𝟎𝐄−𝟎𝟐   (𝟓.𝟔𝐄−𝟎𝟏)	3.2𝐸−01 (1.1𝐸+00)
𝑓7	3000	𝟐.𝟏𝐄−𝟓   (𝟐.𝟐𝐄−𝟏𝟎)	6.4𝐸−04 (2.5𝐸−04)	6.8𝐸−04 (2.5𝐸−04)
𝑓8	1000	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	1.0𝐸−04 (6.0𝐸−05)	1.4𝐸−04 (6.5𝐸−05)
	5000	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)
𝑓10	500	𝟖.𝟗𝐄−𝟏𝟔   ( 𝟎.𝟎𝐄+𝟎𝟎)	8.2𝐸−10 (6.9𝐸−10)	3.0𝐸−09 (2.2𝐸−09)
	2000	𝟖.𝟗𝐄−𝟏𝟔   (𝟎.𝟎𝐄+𝟎𝟎)	4.4𝐸−15 (0.0𝐸+00)	4.4𝐸−15 (0.0𝐸+00)
𝑓11	500	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	9.9𝐸−08 (6.0𝐸−07)	2.0𝐸−04 (1.4𝐸−03)
	3000	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	𝟎.𝟎𝐄+𝟎𝟎   (𝟎.𝟎𝐄+𝟎𝟎)	2.0𝐸−04 (1.4𝐸−03)
𝑓12	500	1.8𝐸−2 (1𝐸−4)	𝟒.𝟔𝐄−𝟏𝟕   (𝟏.𝟗𝐄−𝟏𝟔)	3.8𝐸−16 (8.3𝐸−16)
	1500	1.7𝐸−2 (4𝐸−4)	𝟏.𝟔𝐄−𝟑𝟐   (𝟓.𝟓𝐄−𝟒𝟖)	𝟏.𝟔𝐄−𝟑𝟐   (𝟓.𝟓𝐄−𝟒𝟖)
𝑓13	500	4.4𝐸−1 (2.1𝐸−2)	𝟐.𝟎𝐄−𝟏𝟔   (𝟔.𝟓𝐄−𝟏𝟔)	1.2𝐸−15 (2.8𝐸−15)
	1500	3.1𝐸−1 (1.6𝐸−2)	𝟏.𝟒𝐄−𝟑𝟐   (𝟏.𝟏𝐄−𝟒𝟕)	𝟏.𝟒𝐄−𝟑𝟐   (𝟏.𝟏𝐄−𝟒𝟕)