assignment.py

# 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.
"""

  Assignment problem in Google CP Solver.

  Winston 'Operations Research', Assignment Problems, page 393f
  (generalized version with added test column)

  Compare with the following models:
  * Comet   : http://www.hakank.org/comet/assignment.co
  * ECLiPSE : http://www.hakank.org/eclipse/assignment.ecl
  * Gecode  : http://www.hakank.org/gecode/assignment.cpp
  * MiniZinc: http://www.hakank.org/minizinc/assignment.mzn
  * Tailor/Essence': http://www.hakank.org/tailor/assignment.eprime
  * SICStus: http://hakank.org/sicstus/assignment.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 ortools.constraint_solver import pywrapcp


def main(cost, rows, cols):
  # Create the solver.
  solver = pywrapcp.Solver("n-queens")

  #
  # data
  #

  # declare variables
  total_cost = solver.IntVar(0, 100, "total_cost")
  x = []
  for i in range(rows):
    t = []
    for j in range(cols):
      t.append(solver.IntVar(0, 1, "x[%i,%i]" % (i, j)))
    x.append(t)
  x_flat = [x[i][j] for i in range(rows) for j in range(cols)]

  #
  # constraints
  #

  # total_cost
  solver.Add(total_cost == solver.Sum(
      [solver.ScalProd(x_row, cost_row) for (x_row, cost_row) in zip(x, cost)]))

  # exacly one assignment per row, all rows must be assigned
  [
      solver.Add(solver.Sum([x[row][j]
                             for j in range(cols)]) == 1)
      for row in range(rows)
  ]

  # zero or one assignments per column
  [
      solver.Add(solver.Sum([x[i][col]
                             for i in range(rows)]) <= 1)
      for col in range(cols)
  ]

  objective = solver.Minimize(total_cost, 1)

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add(x_flat)
  solution.Add(total_cost)

  # db: DecisionBuilder
  db = solver.Phase(x_flat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)

  solver.NewSearch(db, [objective])
  num_solutions = 0
  while solver.NextSolution():
    print("total_cost:", total_cost.Value())
    for i in range(rows):
      for j in range(cols):
        print(x[i][j].Value(), end=" ")
      print()
    print()

    for i in range(rows):
      print("Task:", i, end=" ")
      for j in range(cols):
        if x[i][j].Value() == 1:
          print(" is done by ", j)
    print()

    num_solutions += 1
  solver.EndSearch()

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


# Problem instance
# hakank: I added the fifth column to make it more
#         interesting
rows = 4
cols = 5
cost = [[14, 5, 8, 7, 15], [2, 12, 6, 5, 3], [7, 8, 3, 9, 7], [2, 4, 6, 10, 1]]

if __name__ == "__main__":
  main(cost, rows, cols)