Models the well-known Moore and Bard (1990) example of a mixed-integer bilevel problem and solves it with the external solver MibS.

This example is taken from "The Mixed Integer Linear Bilevel Programming Problem" (Moore and Bard, 1990).

\[ \begin{align*} \min_{x,y} \quad & -x -10 y \\ \text{s.t.} \quad & x\in\mathbb{Z}_{\ge 0}, \\ & y\in S(x), \end{align*} \]

with \( S(x) \) being the set of optimal points to the lower level problem

\[ \begin{align*} \min_y \quad & y \\ \text{s.t.} \quad & -25 x + 20 y \le 30, \\ & x + 2 y \le 10, \\ & 2 x - y \le 15, \\ & 2 x + 10 y \ge 15, \\ & y\in\mathbb{Z}_{\ge 0} \\ \end{align*} \]

//
// Created by henri on 07.02.24.
//
#include <iostream>
#include "idol/modeling.h"
#include "idol/bilevel/optimizers/wrappers/MibS/MibS.h"
#include "idol/bilevel/modeling/Description.h"
 
using namespace idol;
 
int main(int t_argc, const char** t_argv) {
 
    /*
     This example is taken from "The Mixed Integer Linear Bilevel Programming Problem" (Moore and Bard, 1990).
 
        min -1 x + -10 y
        s.t.
 
        y in argmin { y :
            -25 x + 20 y <= 30,
            1 x + 2 y <= 10,
            2 x + -1 y <= 15,
            2 x + 10 y >= 15,
            y >= 0 and integer.
        }
        x >= 0 and integer.
 
     */
 
    Env env;
 
    // Define High Point Relaxation
    Model high_point_relaxation(env);
 
    auto x = high_point_relaxation.add_var(0, Inf, Integer, -1, "x");
    auto y = high_point_relaxation.add_var(0, Inf, Integer, -10, "y");
 
    auto follower_c1 = high_point_relaxation.add_ctr(-25 * x + 20 * y <= 30);
    auto follower_c2 = high_point_relaxation.add_ctr(x + 2 * y <= 10);
    auto follower_c3 = high_point_relaxation.add_ctr(2 * x - y <= 15);
    auto follower_c4 = high_point_relaxation.add_ctr(2 * x + 10 * y >= 15);
 
    // Prepare bilevel description
    Bilevel::Description description(env);
    description.set_lower_level_obj(y);
    description.make_lower_level(y);
    description.make_lower_level(follower_c1);
    description.make_lower_level(follower_c2);
    description.make_lower_level(follower_c3);
    description.make_lower_level(follower_c4);
 
    // Use coin-or/MibS as external solver
    high_point_relaxation.use(
                Bilevel::MibS(description)
                    .with_logs(true)
    );
 
    // Optimize and print solution
    high_point_relaxation.optimize();
 
    std::cout << save_primal(high_point_relaxation) << std::endl;
 
    return 0;
}