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/*
* This example shows how to formulate and solve the following MIP problem:
*
* Maximize
* Objective: x1 + 2 x2 + 3 x3 + x4
* Subject to
* c1: - x1 + x2 + x3 + 10 x4 <= 20
* c2: x1 - 3 x2 + x3 <= 30
* c3: x2 - 3.5 x4 = 0
* Bounds
* 0 <= x1 <= 40
* 2 <= x4 <= 3
* General
* x4 is integer
*
* Expected results: x1=40; x2=10.5; x3=19.5; x4=3;
*/
#include <iostream>
#ifdef CGAL_USE_SCIP
#include <CGAL/SCIP_mixed_integer_program_traits.h>
typedef CGAL::SCIP_mixed_integer_program_traits<double> MIP_Solver;
#elif defined(CGAL_USE_GLPK)
#include <CGAL/GLPK_mixed_integer_program_traits.h>
typedef CGAL::GLPK_mixed_integer_program_traits<double> MIP_Solver;
#endif
typedef typename MIP_Solver::Variable Variable;
typedef typename MIP_Solver::Linear_objective Linear_objective;
typedef typename MIP_Solver::Linear_constraint Linear_constraint;
int main()
{
MIP_Solver solver;
// Variable x1
Variable* x1 = solver.create_variable(Variable::CONTINUOUS, 0, 40, "x1");
// Variable x2
// You can create first (using default parameters) and then assign values.
Variable* x2 = solver.create_variable();
x2->set_name("x2"); // This is optional (a default will be given)
// Variable x3
Variable* x3 = solver.create_variable(); // Uses all default parameters
x3->set_name("x3");
// Variable x4
Variable* x4 = solver.create_variable(Variable::INTEGER, 2, 3, "x4");
// Objective.
// Be careful this is "MAXIMIZE"
Linear_objective * obj = solver.create_objective(Linear_objective::MAXIMIZE);
obj->add_coefficient(x1, 1.0);
obj->add_coefficient(x2, 2.0);
obj->add_coefficient(x3, 3.0);
obj->add_coefficient(x4, 1.0);
// Constraint c1: -x1 + x2 + x3 + 10 x4 <= 20
Linear_constraint* c1 = solver.create_constraint(-Linear_constraint::infinity(), 20, "c1");
c1->add_coefficient(x1, -1);
c1->add_coefficient(x2, 1);
c1->add_coefficient(x3, 1);
c1->add_coefficient(x4, 10);
// Constraint c2: x1 - 3 x2 + x3 <= 30
Linear_constraint* c2 = solver.create_constraint(-Linear_constraint::infinity(), 30, "c2");
c2->add_coefficient(x1, 1);
c2->add_coefficient(x2, -3);
c2->add_coefficient(x3, 1);
// Constraint c3: x2 - 3.5 x4 = 0
Linear_constraint* c3 = solver.create_constraint(0, 0, "c3");
c3->add_coefficient(x2, 1);
c3->add_coefficient(x4, -3.5);
// Solve
if (solver.solve()) {
std::cout << "result: " << std::endl;
const std::vector<double>& results = solver.solution();
for (std::size_t i = 0; i < results.size(); ++i) {
std::cout << "\tx" << i + 1 << ": " << results[i] << std::endl;
}
return EXIT_SUCCESS;
}
else {
std::cerr << "solving problem failed" << std::endl;
return EXIT_FAILURE;
}
}
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