100 lines
2.5 KiB
Python
100 lines
2.5 KiB
Python
# Copyright 2011 Hakan Kjellerstrand hakank@bonetmail.com
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#
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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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"""
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Least square optimization problem in Google or-tools.
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Solving a fourth grade least square equation.
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From the Swedish book 'Optimeringslara' [Optimization Theory],
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page 286f.
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
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"""
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import sys
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from linear_solver import pywraplp
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def main(sol = 'GLPK'):
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# Create the solver.
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# using GLPK
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if sol == 'GLPK':
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solver = pywraplp.Solver('CoinsGridGLPK',
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pywraplp.Solver.GLPK_LINEAR_PROGRAMMING)
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else:
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# Using CLP
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solver = pywraplp.Solver('CoinsGridCLP',
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pywraplp.Solver.CLP_LINEAR_PROGRAMMING)
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# data
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# number of points
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num = 14
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# temperature
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t = [20, 30, 80,125,175,225,275,325,360,420,495,540,630,700]
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# percentage gas
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F = [0.0,5.8,14.7,31.6,43.2,58.3,78.4,89.4,96.4,99.1,99.5,99.9,100.0,100.0]
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p = 4
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#
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# declare variables
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#
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a = [solver.NumVar(-100, 100, 'a[%i]' % i ) for i in range(p + 1)]
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# to minimize
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z = solver.Sum([(F[i] -
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(sum([a[j]*t[i]**j for j in range(p+1)])))
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for i in range(num)])
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#
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# constraints
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#
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solver.Add(solver.Sum([20**i*a[i] for i in range(p+1)]) == 0)
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solver.Add( (a[0] + sum([700.0**j*a[j]
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for j in range(1,p+1)])) == 100.0)
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for i in range(num):
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solver.Add(solver.Sum([j*a[j]*t[i]**(j-1)
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for j in range(p+1)]) >= 0)
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objective = solver.Minimize(z)
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solver.Solve()
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print
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print 'z = ', solver.objective_value()
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for i in range(p + 1):
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print a[i].solution_value(),
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print
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if __name__ == '__main__':
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sol = 'GLPK'
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if len(sys.argv) > 1:
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sol = sys.argv[1]
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if sol != 'GLPK' and sol != 'CBC':
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print 'Solver must be either GLPK or CBC'
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sys.exit(1)
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main(sol)
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