Model class
BOBILib contains bilevel optimization instances that are
all part of the class of MILP-MILP bilevel problems.
This means that both the upper- and the lower-level problem is a
mixed integer linear problem (MILP).
In particular, this includes the possibility that both the upper- and
the lower-level problem can be
- a continuous linear problem,
- a pure integer linear problem,
- a mixed integer linear problem.
Model statistics
The instances in the instance tables
(benchmark, collection)
can be sorted with respect to the following statistics of the instances.
Symbol | Explanation |
---|---|
\(n_x\) | Number of upper-level variables |
\(|I_u|\) | Number of upper-level integer variables |
\(|B_u|\) | Number of upper-level binary variables |
\(n_y\) | Number of lower-level variables |
\(|I_l|\) | Number of lower-level integer variables |
\(|B_l|\) | Number of lower-level binary variables |
\(n_\mathrm{Link}\) | Number of linking variables |
\(n_\mathrm{Link}^C\) | Number of continuous linking variables |
\(n_\mathrm{Link}^I\) | Number of integer linking variables |
\(n_\mathrm{Link}^B\) | Number of binary linking variables |
\(m_u\) | Number of upper-level constraints |
\(m_l\) | Number of lower-level constraints |
\(m_\mathrm{Coup}\) | Number of coupling constraints |
Input and solution file format
All instances in the BOBILib use
the (name-based) MibS input
file format and are thus given as pairs of mps and aux files.
For more information about the MPS file format, read the respective
MPS (format)
wikipedia page.
A detailed explanation with an example is given in section 4 of the BOBILib report.
There, you also find the definition and an example for the solution format.