# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Set covering in Google CP Solver.
Problem from
Katta G. Murty: 'Optimization Models for Decision Making', page 302f
http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
10 senators making a committee, where there must at least be one
representative from each group:
group: senators:
southern 1 2 3 4 5
northern 6 7 8 9 10
liberals 2 3 8 9 10
conservative 1 5 6 7
democrats 3 4 5 6 7 9
republicans 1 2 8 10
The objective is to minimize the number of senators.
Compare with the following models:
* MiniZinc: http://www.hakank.org/minizinc/set_covering3_model.mzn (model)
http://www.hakank.org/minizinc/set_covering3.mzn (data)
* Comet : http://www.hakank.org/comet/set_covering3.co
* ECLiPSe : http://www.hakank.org/eclipse/set_covering3.ecl
* SICStus : http://hakank.org/sicstus/set_covering3.pl
* Gecode : http://hakank.org/gecode/set_covering3.cpp
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
from ortools.constraint_solver import pywrapcp
def main(unused_argv):
# Create the solver.
solver = pywrapcp.Solver("Set covering")
#
# data
#
num_groups = 6
num_senators = 10
# which group does a senator belong to?
belongs = [
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0], # 1 southern
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1], # 2 northern
[0, 1, 1, 0, 0, 0, 0, 1, 1, 1], # 3 liberals
[1, 0, 0, 0, 1, 1, 1, 0, 0, 0], # 4 conservative
[0, 0, 1, 1, 1, 1, 1, 0, 1, 0], # 5 democrats
[1, 1, 0, 0, 0, 0, 0, 1, 0, 1] # 6 republicans
]
#
# declare variables
#
x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(num_senators)]
#
# constraints
#
# number of assigned senators (to minimize)
z = solver.Sum(x)
# ensure that each group is covered by at least
# one senator
for i in range(num_groups):
solver.Add(
solver.SumGreaterOrEqual([x[j] * belongs[i][j]
for j in range(num_senators)],
1))
objective = solver.Minimize(z, 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x)
solution.AddObjective(z)
collector = solver.LastSolutionCollector(solution)
solver.Solve(solver.Phase(x,
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT),
[collector, objective])
print "z:", collector.ObjectiveValue(0)
print "x:", [collector.Value(0, x[i]) for i in range(num_senators)]
for j in range(num_senators):
if collector.Value(0, x[j]) == 1:
print "Senator", j + 1, "belongs to these groups:",
for i in range(num_groups):
if belongs[i][j] == 1:
print i + 1,
print
print
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
if __name__ == "__main__":
main("cp sample")