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#!/usr/bin/env python3
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# Copyright 2010-2025 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.
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"""Linear programming examples that show how to use the APIs."""
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from ortools.linear_solver import pywraplp
def Announce(solver, api_type):
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print(
"---- Linear programming example with " + solver + " (" + api_type + ") -----"
)
def RunLinearExampleNaturalLanguageAPI(optimization_problem_type):
"""Example of simple linear program with natural language API."""
solver = pywraplp.Solver.CreateSolver(optimization_problem_type)
if not solver:
return
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Announce(optimization_problem_type, "natural language API")
infinity = solver.infinity()
# x1, x2 and x3 are continuous non-negative variables.
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x1 = solver.NumVar(0.0, infinity, "x1")
x2 = solver.NumVar(0.0, infinity, "x2")
x3 = solver.NumVar(0.0, infinity, "x3")
solver.Maximize(10 * x1 + 6 * x2 + 4 * x3)
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c0 = solver.Add(10 * x1 + 4 * x2 + 5 * x3 <= 600, "ConstraintName0")
c1 = solver.Add(2 * x1 + 2 * x2 + 6 * x3 <= 300)
sum_of_vars = sum([x1, x2, x3])
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c2 = solver.Add(sum_of_vars <= 100.0, "OtherConstraintName")
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SolveAndPrint(
solver, [x1, x2, x3], [c0, c1, c2], optimization_problem_type != "PDLP"
)
# Print a linear expression's solution value.
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print("Sum of vars: %s = %s" % (sum_of_vars, sum_of_vars.solution_value()))
def RunLinearExampleCppStyleAPI(optimization_problem_type):
"""Example of simple linear program with the C++ style API."""
solver = pywraplp.Solver.CreateSolver(optimization_problem_type)
if not solver:
return
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Announce(optimization_problem_type, "C++ style API")
infinity = solver.infinity()
# x1, x2 and x3 are continuous non-negative variables.
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x1 = solver.NumVar(0.0, infinity, "x1")
x2 = solver.NumVar(0.0, infinity, "x2")
x3 = solver.NumVar(0.0, infinity, "x3")
# Maximize 10 * x1 + 6 * x2 + 4 * x3.
objective = solver.Objective()
objective.SetCoefficient(x1, 10)
objective.SetCoefficient(x2, 6)
objective.SetCoefficient(x3, 4)
objective.SetMaximization()
# x1 + x2 + x3 <= 100.
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c0 = solver.Constraint(-infinity, 100.0, "c0")
c0.SetCoefficient(x1, 1)
c0.SetCoefficient(x2, 1)
c0.SetCoefficient(x3, 1)
# 10 * x1 + 4 * x2 + 5 * x3 <= 600.
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c1 = solver.Constraint(-infinity, 600.0, "c1")
c1.SetCoefficient(x1, 10)
c1.SetCoefficient(x2, 4)
c1.SetCoefficient(x3, 5)
# 2 * x1 + 2 * x2 + 6 * x3 <= 300.
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c2 = solver.Constraint(-infinity, 300.0, "c2")
c2.SetCoefficient(x1, 2)
c2.SetCoefficient(x2, 2)
c2.SetCoefficient(x3, 6)
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SolveAndPrint(
solver, [x1, x2, x3], [c0, c1, c2], optimization_problem_type != "PDLP"
)
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def SolveAndPrint(solver, variable_list, constraint_list, is_precise):
"""Solve the problem and print the solution."""
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print("Number of variables = %d" % solver.NumVariables())
print("Number of constraints = %d" % solver.NumConstraints())
result_status = solver.Solve()
# The problem has an optimal solution.
assert result_status == pywraplp.Solver.OPTIMAL
# The solution looks legit (when using solvers others than
# GLOP_LINEAR_PROGRAMMING, verifying the solution is highly recommended!).
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if is_precise:
assert solver.VerifySolution(1e-7, True)
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print("Problem solved in %f milliseconds" % solver.wall_time())
# The objective value of the solution.
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print("Optimal objective value = %f" % solver.Objective().Value())
# The value of each variable in the solution.
for variable in variable_list:
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print("%s = %f" % (variable.name(), variable.solution_value()))
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print("Advanced usage:")
print("Problem solved in %d iterations" % solver.iterations())
for variable in variable_list:
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print("%s: reduced cost = %f" % (variable.name(), variable.reduced_cost()))
activities = solver.ComputeConstraintActivities()
for i, constraint in enumerate(constraint_list):
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print(
(
"constraint %d: dual value = %f\n activity = %f"
% (i, constraint.dual_value(), activities[constraint.index()])
)
)
def main():
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RunLinearExampleNaturalLanguageAPI("GLOP")
RunLinearExampleNaturalLanguageAPI("GLPK_LP")
RunLinearExampleNaturalLanguageAPI("CLP")
RunLinearExampleNaturalLanguageAPI("PDLP")
RunLinearExampleNaturalLanguageAPI("XPRESS_LP")
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RunLinearExampleCppStyleAPI("GLOP")
RunLinearExampleCppStyleAPI("GLPK_LP")
RunLinearExampleCppStyleAPI("CLP")
RunLinearExampleCppStyleAPI("PDLP")
RunLinearExampleCppStyleAPI("XPRESS_LP")
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if __name__ == "__main__":
main()