A Differential Evolution with Two Mutation Strategies and a Selection Based on an Improved Constraint-Handling Technique for Bilevel Programming Problems

Table 2

Best results obtained by the proposed algorithm for linear BLPPs.

Problem	(𝑥^∗,𝑦^∗)	𝐹(𝑥^∗,𝑦^∗)	𝑓(𝑥^∗,𝑦^∗)
A.1	(19.00, 14.00)	−37.00	14.00
A.2	(16.00, 11.00)	−49.00	17.00
A.3	(17.45, 10.91)	−85.09	50.18
A.4	(0.00, 0.90, 0, 0.60, 0.40)	−29.20	3.20
A.5	(1.00, 9.00, 0.00)	−19.00	−9.00
A.6	(2.00, 0.00, 1.50, 0.00)	−3.25	−6.00
A.7	(0.50, 0.80, 0, 0.20, 0.80)	−18.40	1.80
A.8	(1.55, 0.78, 0.16, 2.21, 1.89, 0)	14.99	−16.99
A.9	(0.00, 2.44, 10.00, 0.00, 10.00, 8.74, 5.25, 10.00, 0.00, 10.00, 3.73, 10.00, 10.00, 10.00, 0.00, 0.00)	−453.61	−68.81