Motivation for the library

While the literature on the application of Bilevel Programming Problems (BPP) is extensive and diverse, there have been limited efforts in establishing a comprehensive test library for the evaluation of bilevel algorithms and their implementations. Thus, the primary goal of this library is to present an actively growing collection of bilevel test problems gathered from various sources devoted to bilevel programming.

Features

For each problem, this library provides:

• A problem statement
• Where feasible, a geometrical analysis of the problem
• The best know solutions and comments about literature inaccuracies
• Sources where the problem was used
• AMPL input files in the format, compatible with BASBL solver.
• Finally, convenient way to use it and contribute to it.

Contribution

We welcome contributions and corrections to this resource either way:

• common way - send us your comments, corrections or suggestions by email: remigijus.paulavicius@imperial.ac.uk
• modern way - fork this github repository, add new information & correct existing, then create a pull request and we gratefully incorporate your contribution!

Citation

If you use BASBLib, please cite the following source:

• Remigijus Paulavicius, & Claire S. Adjiman. (2017). BASBLib - a library of bilevel test problems, v2.2 [Data set]. Zenodo.

Problems classification

Since bilevel programming involves two optimization problems (the outer and the inner) our classification is based on the nature of these problems. At the moment, in our classification we distinguish the following classes (types) of bilevel programming problems:

Linear-Linear (LP-LP)

View a summary table of all LP-LP problems or click on a problem name for more information.

mb_2007_01	mb_2007_02	as_2013_01	cw_1988_01	lh_1994_01
sib_1997_02	sib_1997_02v	b_1984_01	aw_1990_01	b_1991_01
b_1991_01v	cw_1990_01	bf_1982_02	bf_1982_01	s_1989_01
ct_1982_01

Linear-Quadratic (LP-QP)

View a summary table of all LP-QP problems or click on a problem name for more information.

mb_2006_01	mb_2007_04	mb_2007_03	b_1991_02	as_1984_01

Quadratic-Quadratic (QP-QP)

View a summary table of all QP-QP problems or click on a problem name for more information.

b_1998_04	b_1998_05	lmp_1987_01	y_1996_02	d_1992_01
d_2000_01	cw_1990_02	tmh_2007_01	b_1988_01	sa_1981_01
sc_1998_01	b_1998_02	b_1998_03	b_1998_07	d_1978_01
fl_1995_01	sa_1981_02	b_1984_02	dd_2012_02	as_1981_01

Linear-Nonlinear (LP-NLP)

View a summary table of all LP-NLP problems or click on a problem name for more information.

mb_2007_05	mb_2007_06	mb_2007_10	mb_2007_11	mb_2007_13
mb_2007_13v	mb_2007_15	mb_2007_16	ka_2014_01	mb_2007_09
nwj_2017_01	gf_2001_01	cg_1999_01

Quadratic-Nonlinear (QP-NLP)

View a summary table of all QP-NLP problems or click on a problem name for more information.

mb_2007_12	mb_2007_14	mb_2007_17	mb_2007_18	mb_2007_18v
mb_2007_19	mb_2007_20	mb_2007_21	mb_2007_23	mb_2007_22
mb_2007_22v	dd_2012_01	sib_1997_01	yz_2010_01	mb_2007_08
c_2002_02	c_2002_04

Nonlinear-Nonlinear (NLP-NLP)

View a summary table of all NLP-NLP problems or click on a problem name for more information.

c_2002_01	c_2002_03	c_2002_05	fz_1998_01	mb_2007_24
nwj_2017_02	nwj_2017_04	nwj_2017_03	nwj_2017_05	ka_2014_02

Acknowledgment

This work was partially funded by a Grant (No. P-MIP-17-60) from the Research Council of Lithuania.

We also gratefully acknowledge funding from the EPSRC through a Leadership Fellowship [EP/J003840/1]