BASBLib - a library of bilevel test problems

BASBLib - A Library of Bilevel Test Problems

While the literature on the application of bilevel programming problems is extensive and diverse (see
e.g., [1, 6, 7, 11] and references therein), there have been limited efforts to establish a systematic test library for the evaluation of the bilevel algorithms and their implementations. While there exist generators of bilevel test problems [2, 3, 4], they are limited to linear and quadratic problems. There already exist several collections of bilevel test problems, however, again, limited to special subclasses:

• Chapter 9 in [9] contains linear and quadratic problems (19 problems in total)
• The GAMS EMP Library [8] contains mainly linear and quadratic problems (33 problems in total)
• The test set included with BIPA [5] contains convex inner problems (22 problems in total)
• A test set for bilevel problems [10] containing either nonconvex inner problems or problems with a structure that causes convergence issues for algorithms (36 problems in total)
• MIPLIB [12] containing bilevel problems with only binary variables (57 problems in total)
• Bilevel optimization problem library, version 0.1 [13] containing binary bilevel problems (315 problems in total)

Thus, with the introduction of BASBLib, we present an actively growing online collection of general bilevel test problems, gathered from the various sources and devoted to bilevel programming. The library is designed as an open resource to which other
researchers in the bilevel programming community can easily contribute. An in-depth description of BASBLib is provided in an online resource: http://basblsolver.github.io/BASBLib/. It includes problem statements, a geometrical analysis of the problems, the best-known solutions, comments on inaccuracies in the literature, sources where the problem was used, AMPL input files in the BASBL format, and finally instructions on how to use it and contribute to it. We welcome contributions and corrections to this resource either
by email: remigijus.paulavicius@imperial.ac.uk or by forking the Github repository http://basblsolver.github.io/BASBLib/: which makes to possible to add and/or correct existing information, and then create a pull request to include new contributions.

Changelog: v2.2 - (2017-09-20)

- Added

• mb_2007_22v problem, variant of problem mb_2007_22

- Changed

Renamed the following problems:

• nwj_2016_01 to nwj_2017_01
• nwj_2016_02 to nwj_2017_02
• nwj_2016_03 to nwj_2017_03
• nwj_2016_04 to nwj_2017_04
• nwj_2016_05 to nwj_2017_05

References

1. J. F. Bard, Practical Bilevel Optimization, vol. 30 of Nonconvex Optimization and Its Applications, Springer US, 1998, doi:10.1007/978-1-4757-2836-1.
2. P. H. Calamai and L. N. Vicente, Generating linear and linear-quadratic bilevel programming problems, SIAM Journal on Scientific Computing, 14 (1993), pp. 770–782, doi:10.1137/0914049.
3. P. H. Calamai and L. N. Vicente, Generating quadratic bilevel programming test problems, ACM Transactions on Mathematical Software (TOMS), 20 (1994), pp. 103–119, doi:10.1145/174603.174411.
4. P. H. Calamai, L. N. Vicente, and J. J. Júdice, A new technique for generating quadratic programming test problems, Mathematical Programming, 61 (1993), pp. 215–231, doi:10.1007/BF01582148.
5. B. Colson, BIPA (BIlevel Programming with Approximation Methods)(software guide and test problems), Cahiers du GERAD, (2002).
6. S. Dempe, Foundations of Bilevel Programming, vol. 61 of Nonconvex Optimization and Its Applications, Kluwer Academic Publishers, Boston, 2002, doi:10.1007/b101970.
7. S. Dempe, V. Kalashnikov, G. A. Pérez-Valdés, and N. Kalashnykova, Bilevel programming problems, Energy Systems, Springer Berlin Heidelberg, Berlin, Heidelberg, 2015, doi:10.1007/978-3-662-45827-3.
8. EMPlib Library. https://www.gams.com/emplib/libhtml/alfindx.htm. Accessed: 2017-04-21.
9. C. A. Floudas, P. M. Pardalos, C. S. Adjiman, W. R. Esposito, Z. H. Gümüs, S. T. Harding, J. L. Klepeis, C. A. Meyer, and C. A. Schweiger, Handbook of test problems in local and global optimization, Springer Science & Business Media, 1999, doi:10.1007/978-1-4757-3040-1.
10. A. Mitsos and P. I. Barton, A test set for bilevel programs. http://www.researchgate.net/publication/228455291, 2007. [Last updated September 19, 2007].
11. K. Shimizu, Y. Ishizuka, and J. F. Bard, Nondifferentiable and two-level mathematical programming, vol. 102, Kluwer Academic Publishers, Boston, 1997, doi:10.1016/S0377-2217(97)00228-2
12. M. Fischetti, I. Ljubić, M. Monaci, and M. Sinnl, Intersection Cuts for Bilevel Optimization, Springer International Publishing, 2016, pp. 77–88, doi:10.1007/978-3-319-33461-5_7
13. T. Ralphs and E. Adams, Bilevel instance library, 2016, http://coral.ise.lehigh.edu/data-sets/bilevel-instances/