Solving an optimistic MILP-MILP bilevel problem with coin-or/MibS

Problem Definition

This example is taken from [10] and is a bilevel problem where the upper level is a mixed-integer linear program (MILP) and the lower level is a mixed-integer linear program (MILP).

The problem is formulated as follows:

\[\begin{split}\begin{align} \min_{x, y} \quad & -x + -10 y \\ \text{s.t.} \quad & x \in \mathbb Z_{\ge 0 },\\ & y\in \begin{array}[t]{rl} \displaystyle \underset{y}{\text{arg min}} \quad & y \\ \text{s.t.} \quad & -25 x + 20 y \leq 30, \\ & x + 2 y \leq 10, \\ & 2 x - y \leq 15, \\ & 2 x + 10 y \geq 15, \\ & y \geq 0, \\ & y \in \mathbb Z_{\ge 0}. \end{array} \end{align}\end{split}\]

Implementation