# 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 deployment in Google CP Solver
From http://mathworld.wolfram.com/SetCoveringDeployment.html
'''
Set covering deployment (sometimes written 'set-covering deployment'
and abbreviated SCDP for 'set covering deployment problem') seeks
an optimal stationing of troops in a set of regions so that a
relatively small number of troop units can control a large
geographic region. ReVelle and Rosing (2000) first described
this in a study of Emperor Constantine the Great's mobile field
army placements to secure the Roman Empire.
'''
Compare with the the following models:
* MiniZinc: http://www.hakank.org/minizinc/set_covering_deployment.mzn
* Comet : http://www.hakank.org/comet/set_covering_deployment.co
* Gecode : http://www.hakank.org/gecode/set_covering_deployment.cpp
* ECLiPSe : http://www.hakank.org/eclipse/set_covering_deployment.ecl
* SICStus : http://hakank.org/sicstus/set_covering_deployment.pl
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():
# Create the solver.
solver = pywrapcp.Solver("Set covering deployment")
#
# data
#
countries = ["Alexandria",
"Asia Minor",
"Britain",
"Byzantium",
"Gaul",
"Iberia",
"Rome",
"Tunis"]
n = len(countries)
# the incidence matrix (neighbours)
mat = [
[0, 1, 0, 1, 0, 0, 1, 1],
[1, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 0, 0],
[1, 1, 0, 0, 0, 0, 1, 0],
[0, 0, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 1, 0, 1, 1],
[1, 0, 0, 1, 1, 1, 0, 1],
[1, 0, 0, 0, 0, 1, 1, 0]
]
#
# declare variables
#
# First army
X = [solver.IntVar(0, 1, "X[%i]" % i) for i in range(n)]
# Second (reserv) army
Y = [solver.IntVar(0, 1, "Y[%i]" % i) for i in range(n)]
#
# constraints
#
# total number of armies
num_armies = solver.Sum([X[i] + Y[i] for i in range(n)])
#
# Constraint 1: There is always an army in a city
# (+ maybe a backup)
# Or rather: Is there a backup, there
# must be an an army
#
[solver.Add(X[i] >= Y[i]) for i in range(n)]
#
# Constraint 2: There should always be an backup army near every city
#
for i in range(n):
neighbors = solver.Sum([Y[j] for j in range(n) if mat[i][j] == 1])
solver.Add(X[i] + neighbors >= 1)
objective = solver.Minimize(num_armies, 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(X)
solution.Add(Y)
solution.Add(num_armies)
solution.AddObjective(num_armies)
collector = solver.LastSolutionCollector(solution)
solver.Solve(solver.Phase(X + Y,
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT),
[collector, objective])
print "num_armies:", collector.ObjectiveValue(0)
print "X:", [collector.Value(0, X[i]) for i in range(n)]
print "Y:", [collector.Value(0, Y[i]) for i in range(n)]
for i in range(n):
if collector.Value(0, X[i]) == 1:
print "army:", countries[i],
if collector.Value(0, Y[i]) == 1:
print "reserv army:", countries[i], " "
print
print
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
if __name__ == "__main__":
main()