An Evolutionary Algorithm for Solving Bilevel Programming Problems Using Duality Conditions

Table 3

Comparison of the results found by EADP and other algorithms in reference.

Prob.	EADP							Ref.-; 𝐹(𝑥^∗,𝑦^∗)
	𝐹(𝑥^∗,𝑦^∗)	𝐹mean	𝐹median	𝐹(𝑥,𝑦)	STD	CPU(s)	(𝑥^∗,𝑦^∗)
Example  1	−29.2	−29.2	−29.2	−29.2	0	0.6	(0,0.9,0,0.6,0.4)	−29.2
Example  2	6	6	6	6	0	0.5	(1,2,0)	6
Example  3	−8.7778	−8.7778	−8.7778	−8.7778	0	0.6	(2,0,0.7778)	−8.2230
Example  4	−85.0909	−85.0909	−85.0909	−85.0909	0	0.5	(17.4545,10.9091)	−85.0909
Example  5	1000	1000	1000	1000	0	0.4	(0,1,0)	1000
Example  6	0	0	0	0	0	0.4	(25,30,5,10)	0
Example  7	7.5	7.5	7.5	7.5	0	6.2	(0.5,0.5,0,0,0)	10.625