kp-highs

Models a simple binary knapsack problem and optimizes it with HiGHS. If the model is feasible, prints all solutions in the solution pool.

The knapsack problem instance is modeled as the mixed-integer optimization problem

\[ \begin{align*} \min_{x} \quad & -40x_1 - 50x_2 - 100x_3 - 95x_4 - 30x_5 \\ \text{s.t.} \quad & 2x_1 + 3.14x_2 + 1.98x_3 + 5x_4 + 3x_5 \le 10, \\ & x_i\in \{ 0,1 \}, \quad \text{for all } i=1,\dotsc,5. \end{align*} \]

#include <iostream>
#include "idol/modeling.h"
#include "idol/mixed-integer/optimizers/wrappers/HiGHS/HiGHS.h"
 
using namespace idol;
 
int main(int t_argc, const char** t_argv) {
 
    // Instance data
    const unsigned int n_items = 5;
    const std::vector<double> profit { 40., 50., 100., 95., 30., };
    const std::vector<double> weight { 2., 3.14, 1.98, 5., 3., };
    const double capacity = 10.;
 
    // Create optimization environment
    Env env;
 
    // Create model
    Model model(env);
 
    // Create decision variables
    auto x = model.add_vars(Dim<1>(n_items), 0, 1, Binary, 0., "x");
 
    // Create the knapsack constraint
    model.add_ctr(idol_Sum(j, Range(n_items), weight[j] * x[j]) <= capacity);
 
    // Set the objective function
    model.set_obj_expr(idol_Sum(j, Range(n_items), -profit[j] * x[j]));
 
    // Use HIGHS as the underlying MIP solver
    model.use(HiGHS());
 
    // Solve the problem
    model.optimize();
 
    // Analyze the solution status
    const auto status = model.get_status();
    const auto reason = model.get_reason();
 
    std::cout << "Solution status: " << status << std::endl;
    std::cout << "Reason: " << reason << std::endl;
 
    if (status == Optimal || status == Feasible) {
 
        // Get the number of solutions in the solution pool
        const auto n_solutions = model.get_n_solutions();
 
        std::cout << "Number of solutions: " << n_solutions << std::endl;
 
        // Print all solutions in the pool
        for (unsigned int i = 0 ; i < n_solutions ; ++i) {
            model.set_solution_index(i);
            std::cout << "Solution " << i << std::endl;
            std::cout << save_primal(model) << std::endl;
        }
 
    }
 
    return 0;
}