examples/notebook/contrib/set_covering3.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Set covering in Google CP Solver.
Problem from Katta G. Murty: 'Optimization Models for Decision Making', page 302f http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
10 senators making a committee, where there must at least be one representative from each group: group: senators: southern 1 2 3 4 5 northern 6 7 8 9 10 liberals 2 3 8 9 10 conservative 1 5 6 7 democrats 3 4 5 6 7 9 republicans 1 2 8 10
The objective is to minimize the number of senators.
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(unused_argv):
# Create the solver.
solver = pywrapcp.Solver("Set covering")
#
# data
#
num_groups = 6
num_senators = 10
# which group does a senator belong to?
belongs = [
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0], # 1 southern
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1], # 2 northern
[0, 1, 1, 0, 0, 0, 0, 1, 1, 1], # 3 liberals
[1, 0, 0, 0, 1, 1, 1, 0, 0, 0], # 4 conservative
[0, 0, 1, 1, 1, 1, 1, 0, 1, 0], # 5 democrats
[1, 1, 0, 0, 0, 0, 0, 1, 0, 1] # 6 republicans
]
#
# declare variables
#
x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(num_senators)]
#
# constraints
#
# number of assigned senators (to minimize)
z = solver.Sum(x)
# ensure that each group is covered by at least
# one senator
for i in range(num_groups):
solver.Add(
solver.SumGreaterOrEqual(
[x[j] * belongs[i][j] for j in range(num_senators)], 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, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),
[collector, objective])
print("z:", collector.ObjectiveValue(0))
print("x:", [collector.Value(0, x[i]) for i in range(num_senators)])
for j in range(num_senators):
if collector.Value(0, x[j]) == 1:
print("Senator", j + 1, "belongs to these groups:", end=" ")
for i in range(num_groups):
if belongs[i][j] == 1:
print(i + 1, end=" ")
print()
print()
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
main("cp sample")