132 lines
3.5 KiB
C#
132 lines
3.5 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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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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using System;
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using System.Collections;
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using System.IO;
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using System.Text.RegularExpressions;
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using Google.OrTools.ConstraintSolver;
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public class SetCovering3
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{
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/**
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*
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* Solves a set covering problem.
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* See See http://www.hakank.org/or-tools/set_covering3.py
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*
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*/
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private static void Solve()
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{
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Solver solver = new Solver("SetCovering3");
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//
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// data
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//
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// Set covering problem from
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// Katta G. Murty: 'Optimization Models for Decision Making',
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// page 302f
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// http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
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int num_groups = 6;
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int num_senators = 10;
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// which group does a senator belong to?
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int[,] belongs = {{1, 1, 1, 1, 1, 0, 0, 0, 0, 0}, // 1 southern
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{0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, // 2 northern
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{0, 1, 1, 0, 0, 0, 0, 1, 1, 1}, // 3 liberals
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{1, 0, 0, 0, 1, 1, 1, 0, 0, 0}, // 4 conservative
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{0, 0, 1, 1, 1, 1, 1, 0, 1, 0}, // 5 democrats
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{1, 1, 0, 0, 0, 0, 0, 1, 0, 1}}; // 6 republicans
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//
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// Decision variables
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//
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IntVar[] x = solver.MakeIntVarArray(num_senators, 0, 1, "x");
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// number of assigned senators, to be minimized
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IntVar z = x.Sum().Var();
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//
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// Constraints
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//
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// ensure that each group is covered by at least
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// one senator
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for(int i = 0; i < num_groups; i++) {
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IntVar[] b = new IntVar[num_senators];
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for(int j = 0; j < num_senators; j++) {
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b[j] = (x[j]*belongs[i,j]).Var();
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}
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solver.Add(b.Sum() >= 1);
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}
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//
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// objective
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//
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OptimizeVar objective = z.Minimize(1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(x,
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Solver.INT_VAR_DEFAULT,
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Solver.INT_VALUE_DEFAULT);
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solver.NewSearch(db, objective);
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while (solver.NextSolution()) {
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Console.WriteLine("z: " + z.Value());
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Console.Write("x: ");
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for(int j = 0; j < num_senators; j++) {
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Console.Write(x[j].Value() + " ");
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}
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Console.WriteLine();
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// More details
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for(int j = 0; j < num_senators; j++) {
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if (x[j].Value() == 1) {
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Console.Write("Senator " + (1 + j) +
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" belongs to these groups: ");
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for(int i = 0; i < num_groups; i++) {
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if (belongs[i,j] == 1) {
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Console.Write((1 + i) + " ");
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}
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}
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Console.WriteLine();
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}
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}
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}
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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solver.EndSearch();
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}
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public static void Main(String[] args)
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{
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Solve();
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}
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}
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