127 lines
3.6 KiB
Python
127 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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Set covering in Google CP Solver.
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Problem from
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Katta G. Murty: 'Optimization Models for Decision Making', page 302f
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http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
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10 senators making a committee, where there must at least be one
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representative from each group:
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group: senators:
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southern 1 2 3 4 5
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northern 6 7 8 9 10
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liberals 2 3 8 9 10
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conservative 1 5 6 7
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democrats 3 4 5 6 7 9
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republicans 1 2 8 10
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The objective is to minimize the number of senators.
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/set_covering3_model.mzn (model)
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http://www.hakank.org/minizinc/set_covering3.mzn (data)
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* Comet : http://www.hakank.org/comet/set_covering3.co
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* ECLiPSe : http://www.hakank.org/eclipse/set_covering3.ecl
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* SICStus : http://hakank.org/sicstus/set_covering3.pl
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* Gecode : http://hakank.org/gecode/set_covering3.cpp
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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:
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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(unused_argv):
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# Create the solver.
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solver = pywrapcp.Solver("Set covering")
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#
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# data
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#
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num_groups = 6
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num_senators = 10
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# which group does a senator belong to?
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belongs = [
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[1, 1, 1, 1, 1, 0, 0, 0, 0, 0], # 1 southern
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[0, 0, 0, 0, 0, 1, 1, 1, 1, 1], # 2 northern
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[0, 1, 1, 0, 0, 0, 0, 1, 1, 1], # 3 liberals
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[1, 0, 0, 0, 1, 1, 1, 0, 0, 0], # 4 conservative
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[0, 0, 1, 1, 1, 1, 1, 0, 1, 0], # 5 democrats
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[1, 1, 0, 0, 0, 0, 0, 1, 0, 1] # 6 republicans
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]
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#
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# declare variables
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#
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x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(num_senators)]
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#
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# constraints
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#
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# number of assigned senators (to minimize)
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z = solver.Sum(x)
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# ensure that each group is covered by at least
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# one senator
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for i in range(num_groups):
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solver.Add(
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solver.SumGreaterOrEqual([x[j] * belongs[i][j]
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for j in range(num_senators)],
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1))
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objective = solver.Minimize(z, 1)
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#
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# solution and search
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#
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solution = solver.Assignment()
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solution.Add(x)
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solution.AddObjective(z)
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collector = solver.LastSolutionCollector(solution)
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solver.Solve(solver.Phase(x,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT),
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[collector, objective])
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print "z:", collector.ObjectiveValue(0)
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print "x:", [collector.Value(0, x[i]) for i in range(num_senators)]
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for j in range(num_senators):
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if collector.Value(0, x[j]) == 1:
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print "Senator", j + 1, "belongs to these groups:",
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for i in range(num_groups):
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if belongs[i][j] == 1:
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print i + 1,
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print
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print
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print "failures:", solver.Failures()
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print "branches:", solver.Branches()
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print "WallTime:", solver.WallTime()
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if __name__ == "__main__":
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main("cp sample")
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