145 lines
4.0 KiB
Python
145 lines
4.0 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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Set covering deployment in Google CP Solver
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From http://mathworld.wolfram.com/SetCoveringDeployment.html
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'''
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Set covering deployment (sometimes written 'set-covering deployment'
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and abbreviated SCDP for 'set covering deployment problem') seeks
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an optimal stationing of troops in a set of regions so that a
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relatively small number of troop units can control a large
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geographic region. ReVelle and Rosing (2000) first described
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this in a study of Emperor Constantine the Great's mobile field
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army placements to secure the Roman Empire.
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'''
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Compare with the the following models:
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* MiniZinc: http://www.hakank.org/minizinc/set_covering_deployment.mzn
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* Comet : http://www.hakank.org/comet/set_covering_deployment.co
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* Gecode : http://www.hakank.org/gecode/set_covering_deployment.cpp
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* ECLiPSe : http://www.hakank.org/eclipse/set_covering_deployment.ecl
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* SICStus : http://hakank.org/sicstus/set_covering_deployment.pl
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models:
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http://www.hakank.org/google_or_tools/
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"""
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from ortools.constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver("Set covering deployment")
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#
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# data
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#
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countries = ["Alexandria",
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"Asia Minor",
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"Britain",
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"Byzantium",
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"Gaul",
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"Iberia",
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"Rome",
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"Tunis"]
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n = len(countries)
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# the incidence matrix (neighbours)
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mat = [
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[0, 1, 0, 1, 0, 0, 1, 1],
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[1, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 1, 0, 0],
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[1, 1, 0, 0, 0, 0, 1, 0],
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[0, 0, 1, 0, 0, 1, 1, 0],
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[0, 0, 1, 0, 1, 0, 1, 1],
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[1, 0, 0, 1, 1, 1, 0, 1],
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[1, 0, 0, 0, 0, 1, 1, 0]
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]
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#
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# declare variables
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#
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# First army
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X = [solver.IntVar(0, 1, "X[%i]" % i) for i in range(n)]
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# Second (reserv) army
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Y = [solver.IntVar(0, 1, "Y[%i]" % i) for i in range(n)]
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#
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# constraints
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#
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# total number of armies
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num_armies = solver.Sum([X[i] + Y[i] for i in range(n)])
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#
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# Constraint 1: There is always an army in a city
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# (+ maybe a backup)
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# Or rather: Is there a backup, there
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# must be an an army
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#
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[solver.Add(X[i] >= Y[i]) for i in range(n)]
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#
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# Constraint 2: There should always be an backup army near every city
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#
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for i in range(n):
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neighbors = solver.Sum([Y[j] for j in range(n) if mat[i][j] == 1])
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solver.Add(X[i] + neighbors >= 1)
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objective = solver.Minimize(num_armies, 1)
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#
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# solution and search
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#
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solution = solver.Assignment()
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solution.Add(X)
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solution.Add(Y)
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solution.Add(num_armies)
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solution.AddObjective(num_armies)
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collector = solver.LastSolutionCollector(solution)
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solver.Solve(solver.Phase(X + Y,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT),
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[collector, objective])
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print "num_armies:", collector.ObjectiveValue(0)
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print "X:", [collector.Value(0, X[i]) for i in range(n)]
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print "Y:", [collector.Value(0, Y[i]) for i in range(n)]
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for i in range(n):
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if collector.Value(0, X[i]) == 1:
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print "army:", countries[i],
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if collector.Value(0, Y[i]) == 1:
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print "reserv army:", countries[i], " "
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print
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print
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print "failures:", solver.Failures()
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print "branches:", solver.Branches()
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print "WallTime:", solver.WallTime()
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if __name__ == "__main__":
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main()
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