134 lines
4.0 KiB
Python
134 lines
4.0 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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@gmail.com)
|
|
Also see my other Google CP Solver models:
|
|
http://www.hakank.org/google_or_tools/
|
|
|
|
"""
|
|
from __future__ import print_function
|
|
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], end=" ")
|
|
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()
|