87 lines
2.7 KiB
Python
87 lines
2.7 KiB
Python
# Copyright 2010-2018 Google LLC
|
|
# Licensed under the Apache License, Version 2.0 (the "License");
|
|
# you may not use this file except in compliance with the License.
|
|
# You may obtain a copy of the License at
|
|
#
|
|
# http://www.apache.org/licenses/LICENSE-2.0
|
|
#
|
|
# Unless required by applicable law or agreed to in writing, software
|
|
# distributed under the License is distributed on an "AS IS" BASIS,
|
|
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
# See the License for the specific language governing permissions and
|
|
# limitations under the License.
|
|
"""Linear optimization example."""
|
|
# [START program]
|
|
# [START import]
|
|
from ortools.linear_solver import pywraplp
|
|
# [END import]
|
|
|
|
|
|
def LinearProgrammingExample():
|
|
"""Linear programming sample."""
|
|
# Instantiate a Glop solver, naming it LinearExample.
|
|
# [START solver]
|
|
solver = pywraplp.Solver.CreateSolver('GLOP')
|
|
# [END solver]
|
|
|
|
# Create the two variables and let them take on any non-negative value.
|
|
# [START variables]
|
|
x = solver.NumVar(0, solver.infinity(), 'x')
|
|
y = solver.NumVar(0, solver.infinity(), 'y')
|
|
|
|
print('Number of variables =', solver.NumVariables())
|
|
# [END variables]
|
|
|
|
# [START constraints]
|
|
# 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)
|
|
|
|
print('Number of constraints =', solver.NumConstraints())
|
|
# [END constraints]
|
|
|
|
# [START objective]
|
|
# Objective function: 3x + 4y.
|
|
objective = solver.Objective()
|
|
objective.SetCoefficient(x, 3)
|
|
objective.SetCoefficient(y, 4)
|
|
objective.SetMaximization()
|
|
# [END objective]
|
|
|
|
# Solve the system.
|
|
# [START solve]
|
|
status = solver.Solve()
|
|
# [END solve]
|
|
|
|
# [START print_solution]
|
|
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.')
|
|
# [END print_solution]
|
|
|
|
# [START advanced]
|
|
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())
|
|
# [END advanced]
|
|
|
|
|
|
LinearProgrammingExample()
|
|
# [END program]
|