如何使用OR-Tools获得双重问题，并使用solver.Add()添加约束

Question

我遵循本教程解决了使用或-tools：https://developers.google.com/optimization/mip/integer_opt的MIP。

以下是代码：

from ortools.linear_solver import pywraplp


def main():
    # Create the mip solver with the SCIP backend.
    solver = pywraplp.Solver.CreateSolver('SCIP')

    infinity = solver.infinity()
    # x and y are integer non-negative variables.
    x = solver.IntVar(0.0, infinity, 'x')
    y = solver.IntVar(0.0, infinity, 'y')

    print('Number of variables =', solver.NumVariables())

    # x + 7 * y <= 17.5.
    solver.Add(x + 7 * y <= 17.5)

    # x <= 3.5.
    solver.Add(x <= 3.5)

    print('Number of constraints =', solver.NumConstraints())

    # Maximize x + 10 * y.
    solver.Maximize(x + 10 * y)

    status = solver.Solve()

    if status == pywraplp.Solver.OPTIMAL:
        print('Solution:')
        print('Objective value =', solver.Objective().Value())
        print('x =', x.solution_value())
        print('y =', y.solution_value())
    else:
        print('The problem does not have an optimal solution.')

    print('\nAdvanced usage:')
    print('Problem solved in %f milliseconds' % solver.wall_time())
    print('Problem solved in %d iterations' % solver.iterations())
    print('Problem solved in %d branch-and-bound nodes' % solver.nodes())


if __name__ == '__main__':
    main()

现在我的问题是得到对偶问题，或者至少是对偶变量的值。我已经找到了这段代码https://github.com/google/or-tools/issues/419，但它们没有以相同的方式实现约束，而且我不希望重写整个代码(现在的代码相当长)。

Answer 1

双变量不公开。我甚至不确定它们是被创造出来的。此外，双值仅适用于纯LP，而不适用于MIP。