set_covering_deployment.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 SetCoveringDeployment
{

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

    Solver solver = new Solver("SetCoveringDeployment");

    //
    // data
    //

    // From http://mathworld.wolfram.com/SetCoveringDeployment.html
    string[] countries = {"Alexandria",
                          "Asia Minor",
                          "Britain",
                          "Byzantium",
                          "Gaul",
                          "Iberia",
                          "Rome",
                          "Tunis"};

    int n = countries.Length;

    // the incidence matrix (neighbours)
    int[,] mat = {{0, 1, 0, 1, 0, 0, 1, 1},
                  {1, 0, 0, 1, 0, 0, 0, 0},
                  {0, 0, 0, 0, 1, 1, 0, 0},
                  {1, 1, 0, 0, 0, 0, 1, 0},
                  {0, 0, 1, 0, 0, 1, 1, 0},
                  {0, 0, 1, 0, 1, 0, 1, 1},
                  {1, 0, 0, 1, 1, 1, 0, 1},
                  {1, 0, 0, 0, 0, 1, 1, 0}};

    //
    // Decision variables
    //

    // First army
    IntVar[] x = solver.MakeIntVarArray(n, 0, 1, "x");

    // Second (reserve) army
    IntVar[] y = solver.MakeIntVarArray(n, 0, 1, "y");

    // total number of armies
    IntVar num_armies = (x.Sum() + y.Sum()).Var();


    //
    // Constraints
    //

    //
    //  Constraint 1: There is always an army in a city
    //                (+ maybe a backup)
    //                Or rather: Is there a backup, there
    //                must be an an army
    //
    for(int i = 0; i < n; i++) {
      solver.Add(x[i] >= y[i]);
    }

    //
    // Constraint 2: There should always be an backup
    //               army near every city
    //
    for(int i = 0; i < n; i++) {
      IntVar[] count_neighbours = (
                                   from j in Enumerable.Range(0, n)
                                   where mat[i,j] == 1
                                   select(y[j])).ToArray();

      solver.Add((x[i] + count_neighbours.Sum()) >= 1);

    }


    //
    // objective
    //
    OptimizeVar objective = num_armies.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("num_armies: " + num_armies.Value());
      for(int i = 0; i < n; i++) {
        if (x[i].Value() == 1) {
          Console.Write("Army: " + countries[i] + " ");
        }

        if (y[i].Value() == 1) {
          Console.WriteLine(" Reverse army: " + countries[i]);
        }
      }
      Console.WriteLine("\n");

    }

    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();
  }
}