86 lines
3.1 KiB
Python
86 lines
3.1 KiB
Python
#!/usr/bin/env python
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# This Python file uses the following encoding: utf-8
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# Copyright 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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from __future__ import print_function
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from ortools.linear_solver import pywraplp
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def main():
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"""Entry point of the program"""
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# Instantiate a Glop solver, naming it LinearExample.
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solver = pywraplp.Solver('LinearExample',
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pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
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# Create the two variables and let them take on any value.
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x = solver.NumVar(-solver.infinity(), solver.infinity(), 'x')
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y = solver.NumVar(-solver.infinity(), solver.infinity(), 'y')
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# Objective function: Maximize 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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# 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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print('Number of variables =', solver.NumVariables())
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print('Number of constraints =', solver.NumConstraints())
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# Solve the system.
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status = solver.Solve()
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# Check that the problem has an optimal solution.
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if status != pywraplp.Solver.OPTIMAL:
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print("The problem does not have an optimal solution!")
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exit(1)
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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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print('Optimal objective value =', objective.Value())
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print('')
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print('Advanced usage:')
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print('Problem solved in ', solver.wall_time(), ' milliseconds')
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print('Problem solved in ', solver.iterations(), ' iterations')
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print('x: reduced cost =', x.reduced_cost())
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print('y: reduced cost =', y.reduced_cost())
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activities = solver.ComputeConstraintActivities()
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print('constraint0: dual value =',
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constraint0.dual_value(), ' activities =',
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activities[constraint0.index()])
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print('constraint1: dual value =',
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constraint1.dual_value(), ' activities =',
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activities[constraint1.index()])
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print('constraint2: dual value =',
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constraint2.dual_value(), ' activities =',
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activities[constraint2.index()])
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if __name__ == '__main__':
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main()
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