examples/notebook/contrib/set_covering_deployment.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
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 following models:
This model was created by Hakan Kjellerstrand ([email protected]) 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], 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())
main()