A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems

Table 2

The results found by EDA with EDA-NM.

Number	𝐹(𝑥,𝑦)				𝑓(𝑥,𝑦)		EDA-NM
	𝐹(𝑥^∗,𝑦^∗)	𝐹(𝑥,𝑦)	Avg.	Std.	𝑓(𝑥^∗,𝑦^∗)	𝑓(𝑥,𝑦)	𝐹(𝑥^∗,𝑦^∗)	𝐹(𝑥,𝑦)
1^∗	85.090908	85.071393	85.088957	6.2𝑒−3	−50.181818	−50.175008	85.090909	85.090908
2^∗	11.0	10.956557	10.956557	3.4𝑒−5	−10.999999	−10.999268	11.0	10.999999
3^∗	15.999999	15.915111	15.199612	2.8𝑒−5	−4.0	−3.999974	16.0	15.999999
4^∗	25.999997	25.999126	25.999458	2.1𝑒−7	−3.199999	−3.198546	26.0	25.999999
5	22.5	22.500000	22.500001	2.8𝑒−7	−4.500064	−4.499873	22.5	22.500001
6^∗	469.142857	469.142856	469.142857	2.1𝑒−7	8.856955	8.857432	469.142857	469.142856
7	0.000000	0.000001	0.000000	2.0𝑒−7	−54.999969	−54.998378	0.000000	0.000001
8	251.999999	252.000001	251.998745	4.5𝑒−7	−8.0	−8.0	252.0	252.000001
9	7.500000	7.571070	7.500001	2.2𝑒−2	−0.000000	−0.000032	7.500000	7.500001
10^∗	32.468750	32.393623	32.150867	1.9𝑒−2	62.999976	62.999996	32.468750	32.468748
11	0.000000	0.000000	0.000000	2.8𝑒−7	0.791998	1.008143	0.000000	0.000000
12	0.000000	0.000000	0.000000	3.4𝑒−7	0.851285	1.119564	0.000000	0.000000
13	−469.142857	−469.142846	−469.142857	2.1𝑒−6	−0.794871	−0.795079	−469.142857	−469.142856
14	−1.688889	−1.688847	−1.687668	3.4𝑒−5	4.333312	4.325765	−1.688887	−1.688148