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 “static” collections of bilevel test problems:

• 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)

Thus, with the introduction of BASBLib, we present an actively growing online collection of 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: v2.1 - (2017-07-17)

- Added

• sib_1997_02v problem
• b_1991_01v problem
• mb_2007_13v problem
• mb_2007_18v problem

- Changed

• Fixed outer problem and solution point for mb_2007_18 problem

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