Summary of LP-LP bilevel problems
Description of the Linear-Linear bilevel test problems: data and references
| Label | Source | n | m | F* | f* | x* | y* |
|---|---|---|---|---|---|---|---|
| mb_2007_01 | (Mitsos & Barton, 2007) | 0 | 1 | 1.000 | -1.000 | - | 1.000 |
| mb_2007_02 | (Mitsos & Barton, 2007) | 0 | 1 | Infeas. | Infeas. | - | - |
| as_2013_01 | (Allende & Still, 2013) | 1 | 1 | 0.000 | 0.000 | 0.000 | 0.000 |
| cw_1988_01 | (Clark & Westerberg, 1988) | 1 | 1 | -37.000 | 14.000 | 19.000 | 14.000 |
| lh_1994_01 | (Liu & Hart, 1994) | 1 | 1 | -16.000 | 4.000 | 4.000 | 4.000 |
| sib_1997_02 | (Shimizu et al., 1997) | 1 | 1 | -2.000 | 1.000 | 2.000 | 1.000 |
| sib_1997_02v | [(Paulavicius et al., 2017b)][Paulavicius et al., 2017b] | 1 | 1 | -12.000 | 4.000 | 4.000 | 4.000 |
| b_1984_01 | (Bard, 1984) | 1 | 1 | 3.111 | -6.667 | 0.889 | 2.222 |
| aw_1990_01 | (Anandalingam & White, 1990) | 1 | 1 | -49.00 | 17.000 | 16.000 | 11.000 |
| b_1991_01 | (Bard, 1991) | 1 | 2 | -1.000 | 0.000 | 1.000 | (0.000, 0.000) |
| b_1991_01v | [(Paulavicius et al., 2017b)][Paulavicius et al., 2017b] | 1 | 2 | -2.000 | -1.000 | 0.000 | (0.000, 1.000) |
| cw_1990_01 | (Clark & Westerberg, 1990) | 1 | 2 | -13.00 | -4.000 | 5.000 | (4.000, 2.000) |
| bf_1982_02 | (Bard & Falk, 1982) | 2 | 2 | -3.250 | -4.000 | (2.000, 0.000) | (1.500, 0.000) |
| bf_1982_01 | (Bard & Falk, 1982) | 2 | 3 | -26.000 | 3.200 | (0.000, 0.900) | (0.000, 0.600, 0.400) |
| s_1989_01 | (Savard, 1989) | 2 | 3 | -14.600 | 0.300 | (0.000, 0.650) | (0.000, 0.300, 0.000) |
| ct_1982_01 | (Candler & Townsley, 1982) | 2 | 6 | -29.200 | 3.200 | (0.000, 0.900) | (0.0, 0.6, 0.4, 0.0, 0.0, 0.0) |
References
- G. B. Allende and G. Still, Solving bilevel programs with the KKT-approach, Mathematical programming, 138 (2013), pp. 309–332
- G. Anandalingam and D. White, A solution method for the linear static stackelberg problem using penalty functions, IEEE Transactions on Automatic Control, 35 (1990), pp. 1170– 1173
- J. F. Bard, Optimality conditions for the bilevel programming problem, Naval research logistics quarterly, 31 (1984), pp. 13–26
- J. F. Bard, Some properties of the bilevel programming problem, Journal of optimization theory and applications, 68 (1991), pp. 371–378
- J. F. Bard and J. E. Falk, An explicit solution to the multi-level programming problem, Computers & Operations Research, 9 (1982), pp. 77–100
- W. Candler and R. Townsley, A linear two-level programming problem, Computers & Operations Research, 9 (1982), pp. 59–76
- P. Clark and A. Westerberg, A note on the optimality conditions for the bilevel programming problem, Naval Research Logistics (NRL), 35 (1988), pp. 413–418
- P. A. Clark and A. W. Westerberg, Bilevel programming for steady-state chemical process design-I. fundamentals and algorithms, Computers & Chemical Engineering, 14 (1990), pp. 87–97
- Y.-H. Liu and S. M. Hart, Characterizing an optimal solution to the linear bilevel programming problem, European Journal of Operational Research, 73 (1994), pp. 164–166
- A. Mitsos and P. I. Barton, A Test Set for Bilevel Programs, 2007. Last updated September 19, 2007
- R. Paulavičius, P.M. Kleniati, and C. S. Adjiman, BASBL: Branch-And-Sandwich BiLevel solver. II. Implementation and computational study with the BASBLib test set, (2017). Submitted.
- G. Savard, Contribution à la programmation mathématique à deux niveaux, phd thesis, Ecole Polytechnique de Montréal, Université de Montréal, 1989
- K. Shimizu, Y. Ishizuka, and J. F. Bard, Nondifferentiable and Two-Level Mathematical Programming, vol. 102, Kluwer Academic Publishers, Boston, 1997
