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set_covering2

examples/notebook/contrib/set_covering2.ipynb

2016-063.2 KB
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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

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set_covering2

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/set_covering2.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/set_covering2.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python
%pip install ortools

Set covering in Google CP Solver.

Example 9.1-2, page 354ff, from Taha 'Operations Research - An Introduction' Minimize the number of security telephones in street corners on a campus.

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/

python
from ortools.constraint_solver import pywrapcp


def main(unused_argv):

  # Create the solver.
  solver = pywrapcp.Solver("Set covering")

  #
  # data
  #
  n = 8  # maximum number of corners
  num_streets = 11  # number of connected streets

  # corners of each street
  # Note: 1-based (handled below)
  corner = [[1, 2], [2, 3], [4, 5], [7, 8], [6, 7], [2, 6], [1, 6], [4, 7],
            [2, 4], [5, 8], [3, 5]]

  #
  # declare variables
  #
  x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(n)]

  #
  # constraints
  #

  # number of telephones, to be minimized
  z = solver.Sum(x)

  # ensure that all corners are covered
  for i in range(num_streets):
    # also, convert to 0-based
    solver.Add(solver.SumGreaterOrEqual([x[j - 1] for j in corner[i]], 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(n)])

  print("failures:", solver.Failures())
  print("branches:", solver.Branches())
  print("WallTime:", solver.WallTime())


main("cp sample")