1# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
2#
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7#     http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14"""
15
16  Set covering in Google CP Solver.
17
18  Example 9.1-2, page 354ff, from
19  Taha 'Operations Research - An Introduction'
20  Minimize the number of security telephones in street
21  corners on a campus.
22
23  Compare with the following models:
24  * MiniZinc: http://www.hakank.org/minizinc/set_covering2.mzn
25  * Comet   : http://www.hakank.org/comet/set_covering2.co
26  * ECLiPSe : http://www.hakank.org/eclipse/set_covering2.ecl
27  * SICStus: http://hakank.org/sicstus/set_covering2.pl
28  * Gecode: http://hakank.org/gecode/set_covering2.cpp
29
30  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
31  Also see my other Google CP Solver models:
32  http://www.hakank.org/google_or_tools/
33
34"""
35from ortools.constraint_solver import pywrapcp
36
37
38def main(unused_argv):
39
40  # Create the solver.
41  solver = pywrapcp.Solver("Set covering")
42
43  #
44  # data
45  #
46  n = 8  # maximum number of corners
47  num_streets = 11  # number of connected streets
48
49  # corners of each street
50  # Note: 1-based (handled below)
51  corner = [[1, 2], [2, 3], [4, 5], [7, 8], [6, 7], [2, 6], [1, 6], [4, 7],
52            [2, 4], [5, 8], [3, 5]]
53
54  #
55  # declare variables
56  #
57  x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(n)]
58
59  #
60  # constraints
61  #
62
63  # number of telephones, to be minimized
64  z = solver.Sum(x)
65
66  # ensure that all corners are covered
67  for i in range(num_streets):
68    # also, convert to 0-based
69    solver.Add(solver.SumGreaterOrEqual([x[j - 1] for j in corner[i]], 1))
70
71  objective = solver.Minimize(z, 1)
72
73  #
74  # solution and search
75  #
76  solution = solver.Assignment()
77  solution.Add(x)
78  solution.AddObjective(z)
79
80  collector = solver.LastSolutionCollector(solution)
81  solver.Solve(
82      solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),
83      [collector, objective])
84
85  print("z:", collector.ObjectiveValue(0))
86  print("x:", [collector.Value(0, x[i]) for i in range(n)])
87
88  print("failures:", solver.Failures())
89  print("branches:", solver.Branches())
90  print("WallTime:", solver.WallTime())
91
92
93if __name__ == "__main__":
94  main("cp sample")
95