79 lines
2.5 KiB
Python
79 lines
2.5 KiB
Python
# Copyright 2010-2018 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Linear optimization example."""
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# [START program]
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from __future__ import print_function
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# [START import]
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from ortools.linear_solver import pywraplp
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# [END import]
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def LinearProgrammingExample():
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"""Linear programming sample."""
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# Instantiate a Glop solver, naming it LinearExample.
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# [START solver]
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solver = pywraplp.Solver.CreateSolver('linear_programming_examples', 'glop')
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# [END solver]
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# Create the two variables and let them take on any non-negative value.
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# [START variables]
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x = solver.NumVar(0, solver.infinity(), 'x')
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y = solver.NumVar(0, solver.infinity(), 'y')
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# [END variables]
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# [START constraints]
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# Constraint 0: x + 2y <= 14.
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constraint0 = solver.Constraint(-solver.infinity(), 14)
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constraint0.SetCoefficient(x, 1)
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constraint0.SetCoefficient(y, 2)
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# Constraint 1: 3x - y >= 0.
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constraint1 = solver.Constraint(0, solver.infinity())
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constraint1.SetCoefficient(x, 3)
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constraint1.SetCoefficient(y, -1)
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# Constraint 2: x - y <= 2.
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constraint2 = solver.Constraint(-solver.infinity(), 2)
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constraint2.SetCoefficient(x, 1)
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constraint2.SetCoefficient(y, -1)
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# [END constraints]
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# [START objective]
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# Objective function: 3x + 4y.
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objective = solver.Objective()
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objective.SetCoefficient(x, 3)
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objective.SetCoefficient(y, 4)
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objective.SetMaximization()
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# [END objective]
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# Solve the system.
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# [START solve]
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solver.Solve()
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# [END solve]
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# [START print_solution]
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opt_solution = 3 * x.solution_value() + 4 * y.solution_value()
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print('Number of variables =', solver.NumVariables())
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print('Number of constraints =', solver.NumConstraints())
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# The value of each variable in the solution.
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print('Solution:')
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print('x = ', x.solution_value())
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print('y = ', y.solution_value())
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# The objective value of the solution.
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print('Optimal objective value =', opt_solution)
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# [END print_solution]
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LinearProgrammingExample()
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# [END program]
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