set_covering2.cs

//
// Copyright 2012 Hakan Kjellerstrand
//
// 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.

using System;
using System.Collections;
using System.IO;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;

public class SetCovering2
{

  /**
   *
   * Solves a set covering problem.
   * See  See http://www.hakank.org/or-tools/set_covering2.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("SetCovering2");

    //
    // data
    //

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

    int n = 8;            // maximum number of corners
    int num_streets = 11; // number of connected streets

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

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, 1, "x");
    // number of telephones, to be minimized
    IntVar z = x.Sum().Var();

    //
    // Constraints
    //

    // ensure that all streets are covered
    for(int i = 0; i < num_streets; i++) {
      solver.Add(x[corner[i,0] - 1] + x[corner[i,1] - 1]  >= 1);
    }

    //
    // objective
    //
    OptimizeVar objective = z.Minimize(1);

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db, objective);

    while (solver.NextSolution()) {
      Console.WriteLine("z: {0}", z.Value());
      Console.Write("x: ");
      for(int i = 0; i < n; i++) {
        Console.Write(x[i].Value() + " ");
      }
      Console.WriteLine();
    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());

    solver.EndSearch();

  }

  public static void Main(String[] args)
  {
    Solve();
  }
}