set_covering4.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 SetCovering4
{

  /**
   *
   * Solves a set covering problem.
   * See  See http://www.hakank.org/or-tools/set_covering4.py
   *
   */
  private static void Solve(int set_partition)
  {

    Solver solver = new Solver("SetCovering4");

    //
    // data
    //

    // Set partition and set covering problem from
    // Example from the Swedish book
    // Lundgren, Roennqvist, Vaebrand
    // 'Optimeringslaera' (translation: 'Optimization theory'),
    // page 408.
    int num_alternatives = 10;
    int num_objects = 8;

    // costs for the alternatives
    int[] costs = {19, 16, 18, 13, 15, 19, 15, 17, 16, 15};

    // the alternatives, and their objects
    int[,] a = {
      // 1 2 3 4 5 6 7 8    the objects
        {1,0,0,0,0,1,0,0},  // alternative 1
        {0,1,0,0,0,1,0,1},  // alternative 2
        {1,0,0,1,0,0,1,0},  // alternative 3
        {0,1,1,0,1,0,0,0},  // alternative 4
        {0,1,0,0,1,0,0,0},  // alternative 5
        {0,1,1,0,0,0,0,0},  // alternative 6
        {0,1,1,1,0,0,0,0},  // alternative 7
        {0,0,0,1,1,0,0,1},  // alternative 8
        {0,0,1,0,0,1,0,1},  // alternative 9
        {1,0,0,0,0,1,1,0}}; // alternative 10

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(num_alternatives, 0, 1, "x");
    // number of assigned senators, to be minimized
    IntVar z = x.ScalProd(costs).VarWithName("z");

    //
    // Constraints
    //


    for(int j = 0; j < num_objects; j++) {
      IntVar[] b = new IntVar[num_alternatives];
      for(int i = 0; i < num_alternatives; i++) {
        b[i] = (x[i] * a[i,j]).Var();
      }

      if (set_partition == 1) {
        solver.Add(b.Sum() >= 1);
      } else {
        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: " + z.Value());
      Console.Write("Selected alternatives: ");
      for(int i = 0; i < num_alternatives; i++) {
        if (x[i].Value() == 1) {
          Console.Write((i+1) + " ");
        }
      }
      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)
  {
    Console.WriteLine("Set partition:");
    Solve(1);
    Console.WriteLine("\nSet covering:");
    Solve(0);
  }
}