120 lines
3.3 KiB
Python
120 lines
3.3 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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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Max flow problem in Google CP Solver.
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From Taha 'Introduction to Operations Research', Example 6.4-2
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Translated from the AMPL code at
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http://taha.ineg.uark.edu/maxflo.txt
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Compare with the following model:
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* MiniZinc: http://www.hakank.org/minizinc/max_flow_taha.mzn
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This model was created by Hakan Kjellerstrand (hakank@gmail.com)
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Also see my other Google CP Solver models:
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http://www.hakank.org/google_or_tools/
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"""
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from ortools.constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('Max flow problem, Taha')
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#
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# data
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#
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n = 5
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start = 0
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end = n - 1
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nodes = list(range(n))
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# cost matrix
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c = [[0, 20, 30, 10, 0], [0, 0, 40, 0, 30], [0, 0, 0, 10, 20],
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[0, 0, 5, 0, 20], [0, 0, 0, 0, 0]]
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#
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# declare variables
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#
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x = {}
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for i in nodes:
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for j in nodes:
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x[i, j] = solver.IntVar(0, c[i][j], 'x[%i,%i]' % (i, j))
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x_flat = [x[i, j] for i in nodes for j in nodes]
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out_flow = [solver.IntVar(0, 10000, 'out_flow[%i]' % i) for i in nodes]
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in_flow = [solver.IntVar(0, 10000, 'in_flow[%i]' % i) for i in nodes]
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total = solver.IntVar(0, 10000, 'z')
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#
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# constraints
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#
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cost_sum = solver.Sum([x[start, j] for j in nodes if c[start][j] > 0])
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solver.Add(total == cost_sum)
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for i in nodes:
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in_flow_sum = solver.Sum([x[j, i] for j in nodes if c[j][i] > 0])
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solver.Add(in_flow[i] == in_flow_sum)
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out_flow_sum = solver.Sum([x[i, j] for j in nodes if c[i][j] > 0])
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solver.Add(out_flow[i] == out_flow_sum)
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# in_flow == out_flow
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for i in nodes:
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if i != start and i != end:
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solver.Add(out_flow[i] - in_flow[i] == 0)
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s1 = [x[i, start] for i in nodes if c[i][start] > 0]
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if len(s1) > 0:
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solver.Add(solver.Sum([x[i, start] for i in nodes if c[i][start] > 0] == 0))
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s2 = [x[end, j] for j in nodes if c[end][j] > 0]
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if len(s2) > 0:
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solver.Add(solver.Sum([x[end, j] for j in nodes if c[end][j] > 0]) == 0)
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# objective: maximize total cost
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objective = solver.Maximize(total, 1)
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#
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# solution and search
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#
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db = solver.Phase(x_flat, solver.INT_VAR_DEFAULT, solver.ASSIGN_MAX_VALUE)
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solver.NewSearch(db, [objective])
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num_solutions = 0
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while solver.NextSolution():
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num_solutions += 1
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print('total:', total.Value())
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print('in_flow:', [in_flow[i].Value() for i in nodes])
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print('out_flow:', [out_flow[i].Value() for i in nodes])
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for i in nodes:
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for j in nodes:
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print('%2i' % x[i, j].Value(), end=' ')
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print()
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print()
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print('num_solutions:', num_solutions)
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print('failures:', solver.Failures())
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print('branches:', solver.Branches())
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print('WallTime:', solver.WallTime(), 'ms')
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if __name__ == '__main__':
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main()
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