# 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.
Example 9.1-2, page 354ff, from
Taha 'Operations Research - An Introduction'
Minimize the number of security telephones in street
corners on a campus.
Compare with the following models:
* MiniZinc: http://www.hakank.org/minizinc/set_covering2.mzn
* Comet : http://www.hakank.org/comet/set_covering2.co
* ECLiPSe : http://www.hakank.org/eclipse/set_covering2.ecl
* SICStus: http://hakank.org/sicstus/set_covering2.pl
* Gecode: http://hakank.org/gecode/set_covering2.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
#
n = 8 # maximum number of corners
num_streets = 11 # number of connected streets
# corners of each street
# Note: 1-based (handled below)
corner = [
[1, 2],
[2, 3],
[4, 5],
[7, 8],
[6, 7],
[2, 6],
[1, 6],
[4, 7],
[2, 4],
[5, 8],
[3, 5]
]
#
# declare variables
#
x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(n)]
#
# constraints
#
# number of telephones, to be minimized
z = solver.Sum(x)
# ensure that all corners are covered
for i in range(num_streets):
# also, convert to 0-based
solver.Add(solver.SumGreaterOrEqual([x[j - 1] for j in corner[i]], 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(n)]
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
if __name__ == "__main__":
main("cp sample")