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

Table 3

The best solution found by EDA-NM, EDA, and compared algorithms in the corresponding references.

Number	EDA-NM	EDA	Reference
1^∗	(17.454545, 10.909091)	(17.454545, 10.909091)	(17.4545, 10.9091)
2^∗	(16.0, 11.0)	(15.999999, 11.0)	(16, 11)
3^∗	(4.0, 4.000000)	(3.999999, 4.000000)	(4, 4)
4^∗	(0, 0.9, 0, 0.6, 0.4)	(0, 0.899999, 0, 0.599999, 0.4)	(0, 0.8992, 0, 0.5994, 0.3978)
5	(4.499992, 1.500025)	(1.500021, 4.499981)	(4.492188, 1.523438)
6^∗	(11.142856, 8.857143)	(11.142642, 8.857358)	(11.14286, 8.85714)
7	(25.000177, 29.999830, 5.999823, 9.999915)	(24.999974, 30.000326, 6.000026, 10.000163)	(25, 30, 5, 10)
8	(4.000000, 8.000000)	(4.000000, 7.999999)	(4, 8)
9	(0.500000, 0.500000, 0.000000, 0, 0.000000)	(0.500000, 0.500000, 0.0000000, 0, 0.000000)	(0, 0.75, 0, 0.5, 0); (0, 0.75, 0, 0.5, 0)
10^∗	(0.000081, 0.625000, 0.375000, 0.000192, 10.0, 5.0, 0, 10.0, 0, 0, 5.000000, 3.0)	(0.006095, 0.625000, 0.375000, 0.000223, 10.0, 5.0, 0, 10.0, 0, 0, 5.0, 3.0)	(0, 0.625, 0.375, 0, 10, 5, 0,; 10, 0, 0, 5, 3)
11	(0.402746, 0.211323, 0, 0, 0)	(0.340452, 0.335910, 0, 0, 0)	(0.3298, 0.3571, 0, 0, 0)
12	(0.429411, 0.157992, 0, 0, 0)	(0.322653, 0.371508, 0, 0, 0)	(0.3255, 0.3659, 0, 0, 0)
13	(11.142768, 8.857233)	(11.14286, 8.857140)	(11.14, 8.86)
14	(8.666667, 4.333333)	(8.666656, 4.333312)	(8.6667, 4.3333)