test/min_cost_flow_test.cc
author Peter Kovacs <kpeter@inf.elte.hu>
Tue, 12 May 2009 12:08:06 +0200
changeset 711 cc61d09f053b
parent 689 111698359429
child 716 4faca85d40e6
permissions -rw-r--r--
Extend min cost flow test file + check dual costs (#291)
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#include <iostream>
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#include <fstream>
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#include <limits>
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#include <lemon/list_graph.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/network_simplex.h>
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#include <lemon/concepts/digraph.h>
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#include <lemon/concept_check.h>
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#include "test_tools.h"
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using namespace lemon;
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char test_lgf[] =
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  "@nodes\n"
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  "label  sup1 sup2 sup3 sup4 sup5 sup6\n"
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  "    1    20   27    0   30   20   30\n"
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  "    2    -4    0    0    0   -8   -3\n"
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  "    3     0    0    0    0    0    0\n"
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  "    4     0    0    0    0    0    0\n"
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  "    5     9    0    0    0    6   11\n"
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  "    6    -6    0    0    0   -5   -6\n"
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  "    7     0    0    0    0    0    0\n"
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  "    8     0    0    0    0    0    3\n"
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  "    9     3    0    0    0    0    0\n"
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  "   10    -2    0    0    0   -7   -2\n"
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  "   11     0    0    0    0  -10    0\n"
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  "   12   -20  -27    0  -30  -30  -20\n"
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  "\n"                
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  "@arcs\n"
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  "       cost  cap low1 low2 low3\n"
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  " 1  2    70   11    0    8    8\n"
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  " 1  3   150    3    0    1    0\n"
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  " 1  4    80   15    0    2    2\n"
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  " 2  8    80   12    0    0    0\n"
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  " 3  5   140    5    0    3    1\n"
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  " 4  6    60   10    0    1    0\n"
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  " 4  7    80    2    0    0    0\n"
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  " 4  8   110    3    0    0    0\n"
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  " 5  7    60   14    0    0    0\n"
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  " 5 11   120   12    0    0    0\n"
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  " 6  3     0    3    0    0    0\n"
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  " 6  9   140    4    0    0    0\n"
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  " 6 10    90    8    0    0    0\n"
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  " 7  1    30    5    0    0   -5\n"
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  " 8 12    60   16    0    4    3\n"
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  " 9 12    50    6    0    0    0\n"
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  "10 12    70   13    0    5    2\n"
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  "10  2   100    7    0    0    0\n"
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  "10  7    60   10    0    0   -3\n"
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  "11 10    20   14    0    6  -20\n"
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  "12 11    30   10    0    0  -10\n"
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  "\n"
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  "@attributes\n"
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  "source 1\n"
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  "target 12\n";
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enum SupplyType {
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  EQ,
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  GEQ,
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  LEQ
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};
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// Check the interface of an MCF algorithm
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template <typename GR, typename Value, typename Cost>
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class McfClassConcept
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{
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public:
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  template <typename MCF>
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  struct Constraints {
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    void constraints() {
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      checkConcept<concepts::Digraph, GR>();
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      MCF mcf(g);
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      const MCF& const_mcf = mcf;
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      b = mcf.reset()
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             .lowerMap(lower)
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             .upperMap(upper)
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             .costMap(cost)
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             .supplyMap(sup)
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             .stSupply(n, n, k)
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             .run();
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      c = const_mcf.totalCost();
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      x = const_mcf.template totalCost<double>();
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      v = const_mcf.flow(a);
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      c = const_mcf.potential(n);
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      const_mcf.flowMap(fm);
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      const_mcf.potentialMap(pm);
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    }
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    typedef typename GR::Node Node;
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    typedef typename GR::Arc Arc;
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    typedef concepts::ReadMap<Node, Value> NM;
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    typedef concepts::ReadMap<Arc, Value> VAM;
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    typedef concepts::ReadMap<Arc, Cost> CAM;
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    typedef concepts::WriteMap<Arc, Value> FlowMap;
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    typedef concepts::WriteMap<Node, Cost> PotMap;
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    const GR &g;
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    const VAM &lower;
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    const VAM &upper;
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    const CAM &cost;
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    const NM &sup;
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    const Node &n;
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    const Arc &a;
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    const Value &k;
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    FlowMap fm;
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    PotMap pm;
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    bool b;
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    double x;
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    typename MCF::Value v;
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    typename MCF::Cost c;
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  };
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};
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// Check the feasibility of the given flow (primal soluiton)
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template < typename GR, typename LM, typename UM,
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           typename SM, typename FM >
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bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
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                const SM& supply, const FM& flow,
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                SupplyType type = EQ )
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{
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  TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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  for (ArcIt e(gr); e != INVALID; ++e) {
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    if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
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  }
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  for (NodeIt n(gr); n != INVALID; ++n) {
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    typename SM::Value sum = 0;
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    for (OutArcIt e(gr, n); e != INVALID; ++e)
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      sum += flow[e];
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    for (InArcIt e(gr, n); e != INVALID; ++e)
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      sum -= flow[e];
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    bool b = (type ==  EQ && sum == supply[n]) ||
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             (type == GEQ && sum >= supply[n]) ||
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             (type == LEQ && sum <= supply[n]);
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    if (!b) return false;
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  }
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  return true;
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}
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// Check the feasibility of the given potentials (dual soluiton)
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// using the "Complementary Slackness" optimality condition
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template < typename GR, typename LM, typename UM,
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           typename CM, typename SM, typename FM, typename PM >
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bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
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                     const CM& cost, const SM& supply, const FM& flow, 
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                     const PM& pi, SupplyType type )
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{
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  TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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  bool opt = true;
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  for (ArcIt e(gr); opt && e != INVALID; ++e) {
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    typename CM::Value red_cost =
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      cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
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    opt = red_cost == 0 ||
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          (red_cost > 0 && flow[e] == lower[e]) ||
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          (red_cost < 0 && flow[e] == upper[e]);
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  }
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  for (NodeIt n(gr); opt && n != INVALID; ++n) {
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    typename SM::Value sum = 0;
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    for (OutArcIt e(gr, n); e != INVALID; ++e)
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      sum += flow[e];
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    for (InArcIt e(gr, n); e != INVALID; ++e)
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      sum -= flow[e];
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    if (type != LEQ) {
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      opt = (pi[n] <= 0) && (sum == supply[n] || pi[n] == 0);
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    } else {
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      opt = (pi[n] >= 0) && (sum == supply[n] || pi[n] == 0);
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    }
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  }
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  return opt;
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}
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// Check whether the dual cost is equal to the primal cost
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template < typename GR, typename LM, typename UM,
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           typename CM, typename SM, typename PM >
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bool checkDualCost( const GR& gr, const LM& lower, const UM& upper,
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                    const CM& cost, const SM& supply, const PM& pi,
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                    typename CM::Value total )
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{
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  TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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  typename CM::Value dual_cost = 0;
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  SM red_supply(gr);
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  for (NodeIt n(gr); n != INVALID; ++n) {
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    red_supply[n] = supply[n];
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  }
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  for (ArcIt a(gr); a != INVALID; ++a) {
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    if (lower[a] != 0) {
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      dual_cost += lower[a] * cost[a];
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      red_supply[gr.source(a)] -= lower[a];
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      red_supply[gr.target(a)] += lower[a];
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    }
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  }
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  for (NodeIt n(gr); n != INVALID; ++n) {
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    dual_cost -= red_supply[n] * pi[n];
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  }
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  for (ArcIt a(gr); a != INVALID; ++a) {
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    typename CM::Value red_cost =
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      cost[a] + pi[gr.source(a)] - pi[gr.target(a)];
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    dual_cost -= (upper[a] - lower[a]) * std::max(-red_cost, 0);
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  }
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  return dual_cost == total;
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}
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// Run a minimum cost flow algorithm and check the results
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template < typename MCF, typename GR,
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           typename LM, typename UM,
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           typename CM, typename SM,
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           typename PT >
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void checkMcf( const MCF& mcf, PT mcf_result,
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               const GR& gr, const LM& lower, const UM& upper,
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               const CM& cost, const SM& supply,
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               PT result, bool optimal, typename CM::Value total,
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               const std::string &test_id = "",
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               SupplyType type = EQ )
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{
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  check(mcf_result == result, "Wrong result " + test_id);
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  if (optimal) {
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    typename GR::template ArcMap<typename SM::Value> flow(gr);
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    typename GR::template NodeMap<typename CM::Value> pi(gr);
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    mcf.flowMap(flow);
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    mcf.potentialMap(pi);
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    check(checkFlow(gr, lower, upper, supply, flow, type),
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          "The flow is not feasible " + test_id);
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    check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
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    check(checkPotential(gr, lower, upper, cost, supply, flow, pi, type),
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          "Wrong potentials " + test_id);
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    check(checkDualCost(gr, lower, upper, cost, supply, pi, total),
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          "Wrong dual cost " + test_id);
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  }
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}
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int main()
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{
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  // Check the interfaces
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  {
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    typedef concepts::Digraph GR;
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    checkConcept< McfClassConcept<GR, int, int>,
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                  NetworkSimplex<GR> >();
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    checkConcept< McfClassConcept<GR, double, double>,
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                  NetworkSimplex<GR, double> >();
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    checkConcept< McfClassConcept<GR, int, double>,
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                  NetworkSimplex<GR, int, double> >();
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  }
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  // Run various MCF tests
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  typedef ListDigraph Digraph;
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  DIGRAPH_TYPEDEFS(ListDigraph);
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  // Read the test digraph
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  Digraph gr;
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  Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), l3(gr), u(gr);
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  Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr), s6(gr);
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  ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());
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  Node v, w;
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  std::istringstream input(test_lgf);
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  DigraphReader<Digraph>(gr, input)
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    .arcMap("cost", c)
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    .arcMap("cap", u)
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    .arcMap("low1", l1)
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    .arcMap("low2", l2)
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    .arcMap("low3", l3)
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    .nodeMap("sup1", s1)
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    .nodeMap("sup2", s2)
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    .nodeMap("sup3", s3)
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    .nodeMap("sup4", s4)
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    .nodeMap("sup5", s5)
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    .nodeMap("sup6", s6)
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    .node("source", v)
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    .node("target", w)
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    .run();
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  // Build test digraphs with negative costs
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  Digraph neg_gr;
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  Node n1 = neg_gr.addNode();
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  Node n2 = neg_gr.addNode();
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  Node n3 = neg_gr.addNode();
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  Node n4 = neg_gr.addNode();
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  Node n5 = neg_gr.addNode();
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  Node n6 = neg_gr.addNode();
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  Node n7 = neg_gr.addNode();
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  Arc a1 = neg_gr.addArc(n1, n2);
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  Arc a2 = neg_gr.addArc(n1, n3);
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  Arc a3 = neg_gr.addArc(n2, n4);
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  Arc a4 = neg_gr.addArc(n3, n4);
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  Arc a5 = neg_gr.addArc(n3, n2);
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  Arc a6 = neg_gr.addArc(n5, n3);
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  Arc a7 = neg_gr.addArc(n5, n6);
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  Arc a8 = neg_gr.addArc(n6, n7);
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  Arc a9 = neg_gr.addArc(n7, n5);
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  Digraph::ArcMap<int> neg_c(neg_gr), neg_l1(neg_gr, 0), neg_l2(neg_gr, 0);
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  ConstMap<Arc, int> neg_u1(std::numeric_limits<int>::max()), neg_u2(5000);
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  Digraph::NodeMap<int> neg_s(neg_gr, 0);
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  neg_l2[a7] =  1000;
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  neg_l2[a8] = -1000;
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  neg_s[n1] =  100;
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  neg_s[n4] = -100;
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  neg_c[a1] =  100;
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  neg_c[a2] =   30;
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  neg_c[a3] =   20;
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  neg_c[a4] =   80;
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  neg_c[a5] =   50;
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  neg_c[a6] =   10;
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  neg_c[a7] =   80;
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  neg_c[a8] =   30;
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  neg_c[a9] = -120;
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  Digraph negs_gr;
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  Digraph::NodeMap<int> negs_s(negs_gr);
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  Digraph::ArcMap<int> negs_c(negs_gr);
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  ConstMap<Arc, int> negs_l(0), negs_u(1000);
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  n1 = negs_gr.addNode();
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  n2 = negs_gr.addNode();
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  negs_s[n1] = 100;
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  negs_s[n2] = -300;
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  negs_c[negs_gr.addArc(n1, n2)] = -1;
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  // A. Test NetworkSimplex with the default pivot rule
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  {
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    NetworkSimplex<Digraph> mcf(gr);
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    // Check the equality form
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   365
    mcf.upperMap(u).costMap(c);
kpeter@653
   366
    checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687
   367
             gr, l1, u, c, s1, mcf.OPTIMAL, true,   5240, "#A1");
kpeter@653
   368
    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
kpeter@687
   369
             gr, l1, u, c, s2, mcf.OPTIMAL, true,   7620, "#A2");
kpeter@653
   370
    mcf.lowerMap(l2);
kpeter@653
   371
    checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687
   372
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#A3");
kpeter@653
   373
    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
kpeter@687
   374
             gr, l2, u, c, s2, mcf.OPTIMAL, true,   8010, "#A4");
kpeter@653
   375
    mcf.reset();
kpeter@653
   376
    checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687
   377
             gr, l1, cu, cc, s1, mcf.OPTIMAL, true,   74, "#A5");
kpeter@653
   378
    checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(),
kpeter@687
   379
             gr, l2, cu, cc, s2, mcf.OPTIMAL, true,   94, "#A6");
kpeter@653
   380
    mcf.reset();
kpeter@653
   381
    checkMcf(mcf, mcf.run(),
kpeter@687
   382
             gr, l1, cu, cc, s3, mcf.OPTIMAL, true,    0, "#A7");
kpeter@687
   383
    checkMcf(mcf, mcf.lowerMap(l2).upperMap(u).run(),
kpeter@687
   384
             gr, l2, u, cc, s3, mcf.INFEASIBLE, false, 0, "#A8");
kpeter@687
   385
    mcf.reset().lowerMap(l3).upperMap(u).costMap(c).supplyMap(s4);
kpeter@687
   386
    checkMcf(mcf, mcf.run(),
kpeter@687
   387
             gr, l3, u, c, s4, mcf.OPTIMAL, true,   6360, "#A9");
kpeter@656
   388
kpeter@656
   389
    // Check the GEQ form
kpeter@687
   390
    mcf.reset().upperMap(u).costMap(c).supplyMap(s5);
kpeter@656
   391
    checkMcf(mcf, mcf.run(),
kpeter@687
   392
             gr, l1, u, c, s5, mcf.OPTIMAL, true,   3530, "#A10", GEQ);
kpeter@687
   393
    mcf.supplyType(mcf.GEQ);
kpeter@656
   394
    checkMcf(mcf, mcf.lowerMap(l2).run(),
kpeter@687
   395
             gr, l2, u, c, s5, mcf.OPTIMAL, true,   4540, "#A11", GEQ);
kpeter@711
   396
    mcf.supplyMap(s6);
kpeter@656
   397
    checkMcf(mcf, mcf.run(),
kpeter@687
   398
             gr, l2, u, c, s6, mcf.INFEASIBLE, false,  0, "#A12", GEQ);
kpeter@656
   399
kpeter@656
   400
    // Check the LEQ form
kpeter@687
   401
    mcf.reset().supplyType(mcf.LEQ);
kpeter@687
   402
    mcf.upperMap(u).costMap(c).supplyMap(s6);
kpeter@656
   403
    checkMcf(mcf, mcf.run(),
kpeter@687
   404
             gr, l1, u, c, s6, mcf.OPTIMAL, true,   5080, "#A13", LEQ);
kpeter@656
   405
    checkMcf(mcf, mcf.lowerMap(l2).run(),
kpeter@687
   406
             gr, l2, u, c, s6, mcf.OPTIMAL, true,   5930, "#A14", LEQ);
kpeter@711
   407
    mcf.supplyMap(s5);
kpeter@656
   408
    checkMcf(mcf, mcf.run(),
kpeter@687
   409
             gr, l2, u, c, s5, mcf.INFEASIBLE, false,  0, "#A15", LEQ);
kpeter@687
   410
kpeter@687
   411
    // Check negative costs
kpeter@711
   412
    NetworkSimplex<Digraph> neg_mcf(neg_gr);
kpeter@711
   413
    neg_mcf.lowerMap(neg_l1).costMap(neg_c).supplyMap(neg_s);
kpeter@711
   414
    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u1,
kpeter@711
   415
      neg_c, neg_s, neg_mcf.UNBOUNDED, false,    0, "#A16");
kpeter@711
   416
    neg_mcf.upperMap(neg_u2);
kpeter@711
   417
    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u2,
kpeter@711
   418
      neg_c, neg_s, neg_mcf.OPTIMAL, true,  -40000, "#A17");
kpeter@711
   419
    neg_mcf.reset().lowerMap(neg_l2).costMap(neg_c).supplyMap(neg_s);
kpeter@711
   420
    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l2, neg_u1,
kpeter@711
   421
      neg_c, neg_s, neg_mcf.UNBOUNDED, false,    0, "#A18");
kpeter@711
   422
      
kpeter@711
   423
    NetworkSimplex<Digraph> negs_mcf(negs_gr);
kpeter@711
   424
    negs_mcf.costMap(negs_c).supplyMap(negs_s);
kpeter@711
   425
    checkMcf(negs_mcf, negs_mcf.run(), negs_gr, negs_l, negs_u,
kpeter@711
   426
      negs_c, negs_s, negs_mcf.OPTIMAL, true, -300, "#A19", GEQ);
kpeter@648
   427
  }
kpeter@648
   428
kpeter@652
   429
  // B. Test NetworkSimplex with each pivot rule
kpeter@648
   430
  {
kpeter@653
   431
    NetworkSimplex<Digraph> mcf(gr);
kpeter@687
   432
    mcf.supplyMap(s1).costMap(c).upperMap(u).lowerMap(l2);
kpeter@648
   433
kpeter@653
   434
    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::FIRST_ELIGIBLE),
kpeter@687
   435
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B1");
kpeter@653
   436
    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BEST_ELIGIBLE),
kpeter@687
   437
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B2");
kpeter@653
   438
    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BLOCK_SEARCH),
kpeter@687
   439
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B3");
kpeter@653
   440
    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::CANDIDATE_LIST),
kpeter@687
   441
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B4");
kpeter@653
   442
    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::ALTERING_LIST),
kpeter@687
   443
             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B5");
kpeter@648
   444
  }
kpeter@648
   445
kpeter@648
   446
  return 0;
kpeter@648
   447
}