max_flow_taha.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.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;

public class MaxFlowTaha
{
  /**
   *
   * Max flow problem.
   *
   * From Taha "Introduction to Operations Research", Example 6.4-2
   *
   * Translated from the AMPL code at
   * http://taha.ineg.uark.edu/maxflo.txt
   *
   * Also see http://www.hakank.org/or-tools/max_flow_taha.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("MaxFlowTaha");

    //
    // Data
    //
    int n     = 5;
    int start = 0;
    int end   = n-1;

    IEnumerable<int> NODES = Enumerable.Range(0, n);

    // cost matrix
    int[,] c = {
      {0, 20, 30, 10,  0},
      {0,  0, 40,  0, 30},
      {0,  0,  0, 10, 20},
      {0,  0,  5,  0, 20},
      {0,  0,  0,  0,  0}
    };



    //
    // Decision variables
    //
    IntVar[,] x = new IntVar[n,n];
    foreach(int i in NODES) {
      foreach(int j in NODES) {
        x[i,j] = solver.MakeIntVar(0, c[i,j], "x");
      }
    }

    IntVar[] x_flat = x.Flatten();

    IntVar[] out_flow = solver.MakeIntVarArray(n, 0, 1000, "out_flow");
    IntVar[] in_flow = solver.MakeIntVarArray(n, 0, 1000, "in_flow");
    IntVar total = solver.MakeIntVar(0, 10000, "total");

    //
    // Constraints
    //
    solver.Add( (from j in NODES
                 where c[start,j] > 0
                 select x[start,j]
                 ).ToArray().Sum() == total);

    foreach(int i in NODES) {

      var in_flow_sum = (from j in NODES
                         where c[j,i] > 0
                         select x[j,i]
                         );
      if (in_flow_sum.Count() > 0) {
        solver.Add(in_flow_sum.ToArray().Sum()  == in_flow[i]);
      }

      var out_flow_sum = (from j in NODES
                          where c[i,j] > 0
                          select x[i,j]
                          );
      if (out_flow_sum.Count() > 0) {
        solver.Add(out_flow_sum.ToArray().Sum()  == out_flow[i]);
      }

    }

    // in_flow == out_flow
    foreach(int i in NODES) {
      if (i != start && i != end) {
        solver.Add(out_flow[i] == in_flow[i]);
      }
    }

    var s1 = (from i in NODES where c[i,start] > 0 select x[i,start]);
    if (s1.Count() > 0) {
      solver.Add(s1.ToArray().Sum() == 0);
    }

    var s2 = (from j in NODES where c[end, j] > 0 select x[end,j]);
    if (s2.Count() > 0) {
      solver.Add(s2.ToArray().Sum() == 0);
    }


    //
    // Objective
    //
    OptimizeVar obj = total.Maximize(1);

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x_flat.Concat(in_flow).Concat(out_flow).ToArray(),
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.ASSIGN_MAX_VALUE);

    solver.NewSearch(db, obj);
    while (solver.NextSolution()) {
      Console.WriteLine("total: {0}",total.Value());
      Console.Write("in_flow : ");
      foreach(int i in NODES) {
        Console.Write(in_flow[i].Value() + " ");
      }
      Console.Write("\nout_flow: ");
      foreach(int i in NODES) {
        Console.Write(out_flow[i].Value() + " ");
      }
      Console.WriteLine();
      foreach(int i in NODES) {
        foreach(int j in NODES) {
          Console.Write("{0,2} ", x[i,j].Value());
        }
        Console.WriteLine();
      }
      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();
  }
}