# 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 partition and set covering in Google CP Solver.
Example from the Swedish book
Lundgren, Roennqvist, Vaebrand
'Optimeringslaera' (translation: 'Optimization theory'),
page 408.
* Set partition:
We want to minimize the cost of the alternatives which covers all the
objects, i.e. all objects must be choosen. The requirement is than an
object may be selected _exactly_ once.
Note: This is 1-based representation
Alternative Cost Object
1 19 1,6
2 16 2,6,8
3 18 1,4,7
4 13 2,3,5
5 15 2,5
6 19 2,3
7 15 2,3,4
8 17 4,5,8
9 16 3,6,8
10 15 1,6,7
The problem has a unique solution of z = 49 where alternatives
3, 5, and 9
is selected.
* Set covering:
If we, however, allow that an object is selected _more than one time_,
then the solution is z = 45 (i.e. less cost than the first problem),
and the alternatives
4, 8, and 10
is selected, where object 5 is selected twice (alt. 4 and 8).
It's an unique solution as well.
Compare with the following models:
* MiniZinc: http://www.hakank.org/minizinc/set_covering4.mzn
* Comet : http://www.hakank.org/comet/set_covering4.co
* ECLiPSe : http://www.hakank.org/eclipse/set_covering4.ecl
* SICStus : http://www.hakank.org/sicstus/set_covering4.pl
* Gecode : http://www.hakank.org/gecode/set_covering4.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(set_partition=1):
# Create the solver.
solver = pywrapcp.Solver("Set partition and set covering")
#
# data
#
num_alternatives = 10
num_objects = 8
# costs for the alternatives
costs = [19, 16, 18, 13, 15, 19, 15, 17, 16, 15]
# the alternatives, and their objects
a = [
# 1 2 3 4 5 6 7 8 the objects
[1, 0, 0, 0, 0, 1, 0, 0], # alternative 1
[0, 1, 0, 0, 0, 1, 0, 1], # alternative 2
[1, 0, 0, 1, 0, 0, 1, 0], # alternative 3
[0, 1, 1, 0, 1, 0, 0, 0], # alternative 4
[0, 1, 0, 0, 1, 0, 0, 0], # alternative 5
[0, 1, 1, 0, 0, 0, 0, 0], # alternative 6
[0, 1, 1, 1, 0, 0, 0, 0], # alternative 7
[0, 0, 0, 1, 1, 0, 0, 1], # alternative 8
[0, 0, 1, 0, 0, 1, 0, 1], # alternative 9
[1, 0, 0, 0, 0, 1, 1, 0] # alternative 10
]
#
# declare variables
#
x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(num_alternatives)]
#
# constraints
#
# sum the cost of the choosen alternative,
# to be minimized
z = solver.ScalProd(x, costs)
#
for j in range(num_objects):
if set_partition == 1:
solver.Add(
solver.SumGreaterOrEqual([x[i] * a[i][j]
for i in range(num_alternatives)],
1))
else:
solver.Add(
solver.SumGreaterOrEqual([x[i] * a[i][j]
for i in range(num_alternatives)],
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[i] for i in range(num_alternatives)],
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT),
[collector, objective])
print "z:", collector.ObjectiveValue(0)
print "selected alternatives:", [i + 1 for i in range(num_alternatives)
if collector.Value(0, x[i]) == 1]
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
if __name__ == "__main__":
print "Set partition:"
main(1)
print "\nSet covering:"
main(0)