set_covering.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.Linq;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;

public class SetCovering
{

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

    Solver solver = new Solver("SetCovering");

    //
    // data
    //

    // Placing of firestations, from Winston 'Operations Research',
    // page 486.
    int min_distance = 15;
    int num_cities = 6;

    int[,] distance = {{ 0,10,20,30,30,20},
                        {10, 0,25,35,20,10},
                        {20,25, 0,15,30,20},
                        {30,35,15, 0,15,25},
                        {30,20,30,15, 0,14},
                        {20,10,20,25,14, 0}};

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(num_cities, 0, 1, "x");
    IntVar z = x.Sum().Var();

    //
    // Constraints
    //

    // ensure that all cities are covered
    for(int i = 0; i < num_cities; i++) {
      IntVar[] b = (from j in Enumerable.Range(0, num_cities)
                 where distance[i,j] <= min_distance
                                 select x[j]).ToArray();
      solver.Add(b.Sum() >= 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 < num_cities; 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();
  }
}