155 lines
4.5 KiB
Python
155 lines
4.5 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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 partition and set covering in Google CP Solver.
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Example from the Swedish book
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Lundgren, Roennqvist, Vaebrand
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'Optimeringslaera' (translation: 'Optimization theory'),
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page 408.
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* Set partition:
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We want to minimize the cost of the alternatives which covers all the
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objects, i.e. all objects must be choosen. The requirement is than an
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object may be selected _exactly_ once.
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Note: This is 1-based representation
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Alternative Cost Object
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1 19 1,6
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2 16 2,6,8
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3 18 1,4,7
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4 13 2,3,5
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5 15 2,5
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6 19 2,3
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7 15 2,3,4
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8 17 4,5,8
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9 16 3,6,8
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10 15 1,6,7
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The problem has a unique solution of z = 49 where alternatives
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3, 5, and 9
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is selected.
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* Set covering:
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If we, however, allow that an object is selected _more than one time_,
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then the solution is z = 45 (i.e. less cost than the first problem),
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and the alternatives
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4, 8, and 10
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is selected, where object 5 is selected twice (alt. 4 and 8).
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It's an unique solution as well.
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/set_covering4.mzn
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* Comet : http://www.hakank.org/comet/set_covering4.co
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* ECLiPSe : http://www.hakank.org/eclipse/set_covering4.ecl
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* SICStus : http://www.hakank.org/sicstus/set_covering4.pl
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* Gecode : http://www.hakank.org/gecode/set_covering4.cpp
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This model was created by Hakan Kjellerstrand (hakank@gmail.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(set_partition=1):
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# Create the solver.
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solver = pywrapcp.Solver("Set partition and set covering")
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#
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# data
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#
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num_alternatives = 10
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num_objects = 8
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# costs for the alternatives
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costs = [19, 16, 18, 13, 15, 19, 15, 17, 16, 15]
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# the alternatives, and their objects
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a = [
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# 1 2 3 4 5 6 7 8 the objects
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[1, 0, 0, 0, 0, 1, 0, 0], # alternative 1
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[0, 1, 0, 0, 0, 1, 0, 1], # alternative 2
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[1, 0, 0, 1, 0, 0, 1, 0], # alternative 3
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[0, 1, 1, 0, 1, 0, 0, 0], # alternative 4
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[0, 1, 0, 0, 1, 0, 0, 0], # alternative 5
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[0, 1, 1, 0, 0, 0, 0, 0], # alternative 6
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[0, 1, 1, 1, 0, 0, 0, 0], # alternative 7
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[0, 0, 0, 1, 1, 0, 0, 1], # alternative 8
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[0, 0, 1, 0, 0, 1, 0, 1], # alternative 9
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[1, 0, 0, 0, 0, 1, 1, 0] # alternative 10
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]
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#
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# declare variables
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#
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x = [solver.IntVar(0, 1, "x[%i]" % i) for i in range(num_alternatives)]
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#
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# constraints
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#
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# sum the cost of the choosen alternative,
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# to be minimized
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z = solver.ScalProd(x, costs)
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#
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for j in range(num_objects):
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if set_partition == 1:
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solver.Add(
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solver.SumEquality([x[i] * a[i][j] for i in range(num_alternatives)],
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1))
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else:
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solver.Add(
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solver.SumGreaterOrEqual(
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[x[i] * a[i][j] for i in range(num_alternatives)], 1))
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objective = solver.Minimize(z, 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.AddObjective(z)
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collector = solver.LastSolutionCollector(solution)
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solver.Solve(
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solver.Phase([x[i] for i in range(num_alternatives)],
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solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),
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[collector, objective])
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print("z:", collector.ObjectiveValue(0))
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print(
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"selected alternatives:",
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[i + 1 for i in range(num_alternatives) if collector.Value(0, x[i]) == 1])
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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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print("Set partition:")
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main(1)
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print("\nSet covering:")
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main(0)
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