max_flow_winston1.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 MaxFlowWinston1
{
  /**
   *
   * Max flow problem.
   *
   * From Winston 'Operations Research', page 420f, 423f
   * Sunco Oil example.
   *
   *
   * Also see http://www.hakank.org/or-tools/max_flow_winston1.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("MaxFlowWinston1");

    //
    // Data
    //
    int n     = 5;
    IEnumerable<int> NODES = Enumerable.Range(0, n);

    // The arcs
    // Note:
    // This is 1-based to be compatible with other implementations.
    //
    int[,] arcs1 = {
      {1, 2},
      {1, 3},
      {2, 3},
      {2, 4},
      {3, 5},
      {4, 5},
      {5, 1}
    };

    // Capacities
    int [] cap = {2,3,3,4,2,1,100};

    // Convert arcs to 0-based
    int num_arcs = arcs1.GetLength(0);
    IEnumerable<int> ARCS = Enumerable.Range(0, num_arcs);
    int[,] arcs = new int[num_arcs, 2];
    foreach(int i in ARCS) {
      for(int j = 0; j < 2; j++) {
        arcs[i,j] = arcs1[i,j] - 1;
      }
    }

    // Convert arcs to matrix (for sanity checking below)
    int[,] mat = new int[num_arcs, num_arcs];
    foreach(int i in NODES) {
      foreach(int j in NODES) {
        int c = 0;
        foreach(int k in ARCS) {
          if (arcs[k,0] == i && arcs[k,1] == j) {
            c = 1;
          }
        }
        mat[i,j] = c;
      }
    }

    //
    // Decision variables
    //
    IntVar[,] flow = solver.MakeIntVarMatrix(n, n, 0, 200, "flow");
    IntVar z = flow[n-1, 0].VarWithName("z");

    //
    // Constraints
    //

    // capacity of arcs
    foreach(int i in ARCS) {
      solver.Add(flow[arcs[i,0], arcs[i,1]] <= cap[i]);
    }

    // inflows == outflows
    foreach(int i in NODES) {
      var s1 = (from k in ARCS
                where arcs[k,1] == i
                select flow[arcs[k,0], arcs[k,1]]
                ).ToArray().Sum();

      var s2 = (from k in ARCS
                where arcs[k,0] == i
                select flow[arcs[k,0], arcs[k,1]]
                ).ToArray().Sum();

      solver.Add(s1 == s2);

    }

    // Sanity check: just arcs with connections can have a flow.
    foreach(int i in NODES) {
      foreach(int j in NODES) {
        if (mat[i,j] == 0) {
          solver.Add(flow[i,j] == 0);
        }
      }
    }


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

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(flow.Flatten(),
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.ASSIGN_MAX_VALUE);
    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("z: {0}",z.Value());
      foreach(int i in NODES) {
        foreach(int j in NODES) {
          Console.Write(flow[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();
  }
}