126 lines
2.7 KiB
Python
126 lines
2.7 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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Game theory in Google or-tools.
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2 player zero sum game.
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From Taha, Operations Research (8'th edition), page 528.
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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 ortools.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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rows = 3
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cols = 3
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game = [[3.0, -1.0, -3.0],
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[-2.0, 4.0, -1.0],
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[-5.0, -6.0, 2.0]
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]
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#
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# declare variables
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#
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#
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# row player
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#
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x1 = [solver.NumVar(0, 1, 'x1[%i]' % i )
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for i in range(rows)]
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v = solver.NumVar(-2, 2, 'v')
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for i in range(rows):
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solver.Add(v - solver.Sum([x1[j]*game[j][i] for j in range(cols)]) <= 0)
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solver.Add(solver.Sum(x1) == 1)
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objective = solver.Maximize(v)
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solver.Solve()
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print
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print 'row player:';
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print 'v = ', solver.Objective().Value()
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print 'Strategies: '
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for i in range(rows):
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print x1[i].SolutionValue(),
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print
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print
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#
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# For column player:
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#
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x2 = [solver.NumVar(0, 1, 'x2[%i]' % i )
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for i in range(cols)]
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v2 = solver.NumVar(-2, 2, 'v2')
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for i in range(cols):
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solver.Add(v2 - solver.Sum([x2[j]*game[i][j] for j in range(rows)]) >= 0)
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solver.Add(solver.Sum(x2) == 1)
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objective = solver.Minimize(v2)
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solver.Solve()
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print
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print 'column player:';
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print 'v2 = ', solver.Objective().Value()
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print 'Strategies: '
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for i in range(rows):
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print x2[i].SolutionValue(),
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print
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print
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print 'walltime :', solver.WallTime(), 'ms'
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print 'iterations:', solver.Iterations()
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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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