or-tools工具使用教程

工具简介

• or-tools是用于解决组合优化问题的开源软件，旨在从众多的可能中寻找到最佳的解决方案，比如解决以下的问题：
  • 最优线路问题
  • 最佳计划问题
  • 装箱问题
• or-tools包括用于以下方面的求解器：
  • 约束优化问题
  • 线性和整数规划问题
  • 车辆路线问题
  • 图相关问题

代码仓库

• https://github.com/google/or-tools

安装

• pip install ortools

使用示例

线性优化问题

from __future__ import print_function
from ortools.linear_solver import pywraplp

def LinearProgrammingExample():
    """Linear programming sample."""
    # Instantiate a Glop solver, naming it LinearExample.
    solver = pywraplp.Solver('LinearProgrammingExample',
                             pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

    # Create the two variables and let them take on any non-negative value.
    x = solver.NumVar(0, solver.infinity(), 'x')
    y = solver.NumVar(0, solver.infinity(), 'y')

    # Constraint 0: x + 2y <= 14.
    constraint0 = solver.Constraint(-solver.infinity(), 14)
    constraint0.SetCoefficient(x, 1)
    constraint0.SetCoefficient(y, 2)

    # Constraint 1: 3x - y >= 0.
    constraint1 = solver.Constraint(0, solver.infinity())
    constraint1.SetCoefficient(x, 3)
    constraint1.SetCoefficient(y, -1)

    # Constraint 2: x - y <= 2.
    constraint2 = solver.Constraint(-solver.infinity(), 2)
    constraint2.SetCoefficient(x, 1)
    constraint2.SetCoefficient(y, -1)

    # Objective function: 3x + 4y.
    objective = solver.Objective()
    objective.SetCoefficient(x, 3)
    objective.SetCoefficient(y, 4)
    objective.SetMaximization()

    # Solve the system.
    solver.Solve()
    opt_solution = 3 * x.solution_value() + 4 * y.solution_value()
    print('Number of variables =', solver.NumVariables())
    print('Number of constraints =', solver.NumConstraints())
    # The value of each variable in the solution.
    print('Solution:')
    print('x = ', x.solution_value())
    print('y = ', y.solution_value())
    # The objective value of the solution.
    print('Optimal objective value =', opt_solution)


LinearProgrammingExample()

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from ortools.sat.python import cp_model

def SimpleSatProgram():
    """Minimal CP-SAT example to showcase calling the solver."""
    # Creates the model.
    model = cp_model.CpModel()
    # Creates the variables.
    num_vals = 3
    x = model.NewIntVar(0, num_vals - 1, 'x')
    y = model.NewIntVar(0, num_vals - 1, 'y')
    z = model.NewIntVar(0, num_vals - 1, 'z')
    # Creates the constraints.
    model.Add(x != y)
    # Creates a solver and solves the model.
    solver = cp_model.CpSolver()
    status = solver.Solve(model)
    if status == cp_model.FEASIBLE:
        print('x = %i' % solver.Value(x))
        print('y = %i' % solver.Value(y))
        print('z = %i' % solver.Value(z))

SimpleSatProgram()

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0

    def on_solution_callback(self):
        self.__solution_count += 1
        for v in self.__variables:
            print('%s=%i' % (v, self.Value(v)), end=' ')
        print()

    def solution_count(self):
        return self.__solution_count


def SearchForAllSolutionsSampleSat():
    """Showcases calling the solver to search for all solutions."""
    # Creates the model.
    model = cp_model.CpModel()

    # Creates the variables.
    num_vals = 3
    x = model.NewIntVar(0, num_vals - 1, 'x')
    y = model.NewIntVar(0, num_vals - 1, 'y')
    z = model.NewIntVar(0, num_vals - 1, 'z')

    # Create the constraints.
    model.Add(x != y)

    # Create a solver and solve.
    solver = cp_model.CpSolver()
    solution_printer = VarArraySolutionPrinter([x, y, z])
    status = solver.SearchForAllSolutions(model, solution_printer)

    print('Status = %s' % solver.StatusName(status))
    print('Number of solutions found: %i' % solution_printer.solution_count())

SearchForAllSolutionsSampleSat()

整数规划问题

from __future__ import print_function
from ortools.linear_solver import pywraplp


def main():
    # Create the mip solver with the CBC backend.
    solver = pywraplp.Solver('simple_mip_program',
                             pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)

    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()

from __future__ import print_function
from ortools.linear_solver import pywraplp
def create_data_model():
  """Stores the data for the problem."""
  data = {}
  data['constraint_coeffs'] = [
      [5, 7, 9, 2, 1],
      [18, 4, -9, 10, 12],
      [4, 7, 3, 8, 5],
      [5, 13, 16, 3, -7],
  ]
  data['bounds'] = [250, 285, 211, 315]
  data['obj_coeffs'] = [7, 8, 2, 9, 6]
  data['num_vars'] = 5
  data['num_constraints'] = 4
  return data


def main():
  data = create_data_model()
  # Create the mip solver with the CBC backend.
  solver = pywraplp.Solver('simple_mip_program',
                           pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
  infinity = solver.infinity()
  x = {}
  for j in range(data['num_vars']):
    x[j] = solver.IntVar(0, infinity, 'x[%i]' % j)
  print('Number of variables =', solver.NumVariables())

  for i in range(data['num_constraints']):
    constraint = solver.RowConstraint(0, data['bounds'][i], '')
    for j in range(data['num_vars']):
      constraint.SetCoefficient(x[j], data['constraint_coeffs'][i][j])
  print('Number of constraints =', solver.NumConstraints())
  # In Python, you can also set the constraints as follows.
  # for i in range(data['num_constraints']):
  #  constraint_expr = \
  # [data['constraint_coeffs'][i][j] * x[j] for j in range(data['num_vars'])]
  #  solver.Add(sum(constraint_expr) <= data['bounds'][i])

  objective = solver.Objective()
  for j in range(data['num_vars']):
    objective.SetCoefficient(x[j], data['obj_coeffs'][j])
  objective.SetMaximization()
  # In Python, you can also set the objective as follows.
  # obj_expr = [data['obj_coeffs'][j] * x[j] for j in range(data['num_vars'])]
  # solver.Maximize(solver.Sum(obj_expr))

  status = solver.Solve()

  if status == pywraplp.Solver.OPTIMAL:
    print('Objective value =', solver.Objective().Value())
    for j in range(data['num_vars']):
      print(x[j].name(), ' = ', x[j].solution_value())
    print()
    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())
  else:
    print('The problem does not have an optimal solution.')


if __name__ == '__main__':
  main()
 

其他(略)

• 参考文档