149 lines
3.6 KiB
Python
149 lines
3.6 KiB
Python
# Copyright 2010 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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Max flow problem in Google CP Solver.
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From Winston 'Operations Research', page 420f, 423f
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Sunco Oil example.
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/max_flow_winston1.mzn
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* Comet: http://hakank.org/comet/max_flow_winston1.co
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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 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, Winston')
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#
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# data
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#
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n = 5
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nodes = range(n)
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# the arcs
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# Note:
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# This is 1-based to be compatible with other
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# implementations.
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arcs1 = [
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[1, 2],
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[1, 3],
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[2, 3],
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[2, 4],
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[3, 5],
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[4, 5],
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[5, 1]
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]
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# convert arcs to 0-based
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arcs = []
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for (a_from, a_to) in arcs1:
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a_from -= 1
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a_to -= 1
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arcs.append([a_from, a_to])
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num_arcs = len(arcs)
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# capacities
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cap = [2,3,3,4,2,1,100]
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# convert arcs to matrix
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# for sanity checking below
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mat = {}
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for i in nodes:
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for j in nodes:
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c = 0;
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for k in range(num_arcs):
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if arcs[k][0] == i and arcs[k][1] == j:
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c = 1
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mat[i,j] = c
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#
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# declare variables
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#
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flow = {}
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for i in nodes:
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for j in nodes:
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flow[i,j] = solver.IntVar(0, 200, 'flow %i %i' % (i, j))
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flow_flat = [flow[i,j] for i in nodes for j in nodes]
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z = solver.IntVar(0, 10000, 'z')
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#
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# constraints
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#
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solver.Add(z == flow[n-1, 0])
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# capacity of arcs
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for i in range(num_arcs):
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solver.Add(flow[arcs[i][0], arcs[i][1]] <= cap[i])
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# inflows == outflows
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for i in nodes:
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s1 = solver.Sum([flow[arcs[k][0], arcs[k][1]]
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for k in range(num_arcs) if arcs[k][1] == i])
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s2 = solver.Sum([flow[arcs[k][0], arcs[k][1]]
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for k in range(num_arcs) if arcs[k][0] == i])
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solver.Add(s1 == s2)
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# sanity: just arcs with connections can have a flow
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for i in nodes:
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for j in nodes:
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if mat[i,j] == 0:
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solver.Add(flow[i,j] == 0)
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# objective: maximize z
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objective = solver.Maximize(z, 1)
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#
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# solution and search
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#
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db = solver.Phase(flow_flat,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT)
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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 "z:", z.Value()
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for i in nodes:
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for j in nodes:
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print flow[i,j].Value(),
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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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