kpeter@648: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@648:  *
kpeter@648:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@648:  *
kpeter@648:  * Copyright (C) 2003-2009
kpeter@648:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@648:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@648:  *
kpeter@648:  * Permission to use, modify and distribute this software is granted
kpeter@648:  * provided that this copyright notice appears in all copies. For
kpeter@648:  * precise terms see the accompanying LICENSE file.
kpeter@648:  *
kpeter@648:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@648:  * express or implied, and with no claim as to its suitability for any
kpeter@648:  * purpose.
kpeter@648:  *
kpeter@648:  */
kpeter@648: 
kpeter@648: #include <iostream>
kpeter@648: #include <fstream>
kpeter@687: #include <limits>
kpeter@648: 
kpeter@648: #include <lemon/list_graph.h>
kpeter@648: #include <lemon/lgf_reader.h>
kpeter@648: 
kpeter@648: #include <lemon/network_simplex.h>
kpeter@648: 
kpeter@648: #include <lemon/concepts/digraph.h>
kpeter@648: #include <lemon/concept_check.h>
kpeter@648: 
kpeter@648: #include "test_tools.h"
kpeter@648: 
kpeter@648: using namespace lemon;
kpeter@648: 
kpeter@648: char test_lgf[] =
kpeter@648:   "@nodes\n"
kpeter@687:   "label  sup1 sup2 sup3 sup4 sup5 sup6\n"
kpeter@687:   "    1    20   27    0   30   20   30\n"
kpeter@687:   "    2    -4    0    0    0   -8   -3\n"
kpeter@687:   "    3     0    0    0    0    0    0\n"
kpeter@687:   "    4     0    0    0    0    0    0\n"
kpeter@687:   "    5     9    0    0    0    6   11\n"
kpeter@687:   "    6    -6    0    0    0   -5   -6\n"
kpeter@687:   "    7     0    0    0    0    0    0\n"
kpeter@687:   "    8     0    0    0    0    0    3\n"
kpeter@687:   "    9     3    0    0    0    0    0\n"
kpeter@687:   "   10    -2    0    0    0   -7   -2\n"
kpeter@687:   "   11     0    0    0    0  -10    0\n"
kpeter@687:   "   12   -20  -27    0  -30  -30  -20\n"
kpeter@687:   "\n"                
kpeter@648:   "@arcs\n"
kpeter@687:   "       cost  cap low1 low2 low3\n"
kpeter@687:   " 1  2    70   11    0    8    8\n"
kpeter@687:   " 1  3   150    3    0    1    0\n"
kpeter@687:   " 1  4    80   15    0    2    2\n"
kpeter@687:   " 2  8    80   12    0    0    0\n"
kpeter@687:   " 3  5   140    5    0    3    1\n"
kpeter@687:   " 4  6    60   10    0    1    0\n"
kpeter@687:   " 4  7    80    2    0    0    0\n"
kpeter@687:   " 4  8   110    3    0    0    0\n"
kpeter@687:   " 5  7    60   14    0    0    0\n"
kpeter@687:   " 5 11   120   12    0    0    0\n"
kpeter@687:   " 6  3     0    3    0    0    0\n"
kpeter@687:   " 6  9   140    4    0    0    0\n"
kpeter@687:   " 6 10    90    8    0    0    0\n"
kpeter@687:   " 7  1    30    5    0    0   -5\n"
kpeter@687:   " 8 12    60   16    0    4    3\n"
kpeter@687:   " 9 12    50    6    0    0    0\n"
kpeter@687:   "10 12    70   13    0    5    2\n"
kpeter@687:   "10  2   100    7    0    0    0\n"
kpeter@687:   "10  7    60   10    0    0   -3\n"
kpeter@687:   "11 10    20   14    0    6  -20\n"
kpeter@687:   "12 11    30   10    0    0  -10\n"
kpeter@648:   "\n"
kpeter@648:   "@attributes\n"
kpeter@648:   "source 1\n"
kpeter@648:   "target 12\n";
kpeter@648: 
kpeter@648: 
kpeter@687: enum SupplyType {
kpeter@656:   EQ,
kpeter@656:   GEQ,
kpeter@656:   LEQ
kpeter@656: };
kpeter@656: 
kpeter@648: // Check the interface of an MCF algorithm
kpeter@689: template <typename GR, typename Value, typename Cost>
kpeter@648: class McfClassConcept
kpeter@648: {
kpeter@648: public:
kpeter@648: 
kpeter@648:   template <typename MCF>
kpeter@648:   struct Constraints {
kpeter@648:     void constraints() {
kpeter@648:       checkConcept<concepts::Digraph, GR>();
kpeter@648: 
kpeter@652:       MCF mcf(g);
kpeter@689:       const MCF& const_mcf = mcf;
kpeter@648: 
kpeter@653:       b = mcf.reset()
kpeter@653:              .lowerMap(lower)
kpeter@652:              .upperMap(upper)
kpeter@652:              .costMap(cost)
kpeter@652:              .supplyMap(sup)
kpeter@652:              .stSupply(n, n, k)
kpeter@652:              .run();
kpeter@652: 
kpeter@687:       c = const_mcf.totalCost();
kpeter@689:       x = const_mcf.template totalCost<double>();
kpeter@656:       v = const_mcf.flow(a);
kpeter@687:       c = const_mcf.potential(n);
kpeter@689:       const_mcf.flowMap(fm);
kpeter@689:       const_mcf.potentialMap(pm);
kpeter@648:     }
kpeter@648: 
kpeter@648:     typedef typename GR::Node Node;
kpeter@648:     typedef typename GR::Arc Arc;
kpeter@689:     typedef concepts::ReadMap<Node, Value> NM;
kpeter@689:     typedef concepts::ReadMap<Arc, Value> VAM;
kpeter@654:     typedef concepts::ReadMap<Arc, Cost> CAM;
kpeter@689:     typedef concepts::WriteMap<Arc, Value> FlowMap;
kpeter@689:     typedef concepts::WriteMap<Node, Cost> PotMap;
kpeter@648: 
kpeter@648:     const GR &g;
kpeter@689:     const VAM &lower;
kpeter@689:     const VAM &upper;
kpeter@654:     const CAM &cost;
kpeter@648:     const NM &sup;
kpeter@648:     const Node &n;
kpeter@648:     const Arc &a;
kpeter@689:     const Value &k;
kpeter@689:     FlowMap fm;
kpeter@689:     PotMap pm;
kpeter@652:     bool b;
kpeter@689:     double x;
kpeter@689:     typename MCF::Value v;
kpeter@689:     typename MCF::Cost c;
kpeter@648:   };
kpeter@648: 
kpeter@648: };
kpeter@648: 
kpeter@648: 
kpeter@648: // Check the feasibility of the given flow (primal soluiton)
kpeter@648: template < typename GR, typename LM, typename UM,
kpeter@648:            typename SM, typename FM >
kpeter@648: bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
kpeter@656:                 const SM& supply, const FM& flow,
kpeter@687:                 SupplyType type = EQ )
kpeter@648: {
kpeter@648:   TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@648: 
kpeter@648:   for (ArcIt e(gr); e != INVALID; ++e) {
kpeter@648:     if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
kpeter@648:   }
kpeter@648: 
kpeter@648:   for (NodeIt n(gr); n != INVALID; ++n) {
kpeter@648:     typename SM::Value sum = 0;
kpeter@648:     for (OutArcIt e(gr, n); e != INVALID; ++e)
kpeter@648:       sum += flow[e];
kpeter@648:     for (InArcIt e(gr, n); e != INVALID; ++e)
kpeter@648:       sum -= flow[e];
kpeter@656:     bool b = (type ==  EQ && sum == supply[n]) ||
kpeter@656:              (type == GEQ && sum >= supply[n]) ||
kpeter@656:              (type == LEQ && sum <= supply[n]);
kpeter@656:     if (!b) return false;
kpeter@648:   }
kpeter@648: 
kpeter@648:   return true;
kpeter@648: }
kpeter@648: 
kpeter@648: // Check the feasibility of the given potentials (dual soluiton)
kpeter@652: // using the "Complementary Slackness" optimality condition
kpeter@648: template < typename GR, typename LM, typename UM,
kpeter@656:            typename CM, typename SM, typename FM, typename PM >
kpeter@648: bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
kpeter@656:                      const CM& cost, const SM& supply, const FM& flow, 
kpeter@656:                      const PM& pi )
kpeter@648: {
kpeter@648:   TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@648: 
kpeter@648:   bool opt = true;
kpeter@648:   for (ArcIt e(gr); opt && e != INVALID; ++e) {
kpeter@648:     typename CM::Value red_cost =
kpeter@648:       cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
kpeter@648:     opt = red_cost == 0 ||
kpeter@648:           (red_cost > 0 && flow[e] == lower[e]) ||
kpeter@648:           (red_cost < 0 && flow[e] == upper[e]);
kpeter@648:   }
kpeter@656:   
kpeter@656:   for (NodeIt n(gr); opt && n != INVALID; ++n) {
kpeter@656:     typename SM::Value sum = 0;
kpeter@656:     for (OutArcIt e(gr, n); e != INVALID; ++e)
kpeter@656:       sum += flow[e];
kpeter@656:     for (InArcIt e(gr, n); e != INVALID; ++e)
kpeter@656:       sum -= flow[e];
kpeter@656:     opt = (sum == supply[n]) || (pi[n] == 0);
kpeter@656:   }
kpeter@656:   
kpeter@648:   return opt;
kpeter@648: }
kpeter@648: 
kpeter@648: // Run a minimum cost flow algorithm and check the results
kpeter@648: template < typename MCF, typename GR,
kpeter@648:            typename LM, typename UM,
kpeter@687:            typename CM, typename SM,
kpeter@687:            typename PT >
kpeter@687: void checkMcf( const MCF& mcf, PT mcf_result,
kpeter@648:                const GR& gr, const LM& lower, const UM& upper,
kpeter@648:                const CM& cost, const SM& supply,
kpeter@687:                PT result, bool optimal, typename CM::Value total,
kpeter@656:                const std::string &test_id = "",
kpeter@687:                SupplyType type = EQ )
kpeter@648: {
kpeter@648:   check(mcf_result == result, "Wrong result " + test_id);
kpeter@687:   if (optimal) {
kpeter@689:     typename GR::template ArcMap<typename SM::Value> flow(gr);
kpeter@689:     typename GR::template NodeMap<typename CM::Value> pi(gr);
kpeter@689:     mcf.flowMap(flow);
kpeter@689:     mcf.potentialMap(pi);
kpeter@689:     check(checkFlow(gr, lower, upper, supply, flow, type),
kpeter@648:           "The flow is not feasible " + test_id);
kpeter@648:     check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
kpeter@689:     check(checkPotential(gr, lower, upper, cost, supply, flow, pi),
kpeter@648:           "Wrong potentials " + test_id);
kpeter@648:   }
kpeter@648: }
kpeter@648: 
kpeter@648: int main()
kpeter@648: {
kpeter@648:   // Check the interfaces
kpeter@648:   {
kpeter@662:     typedef concepts::Digraph GR;
kpeter@689:     checkConcept< McfClassConcept<GR, int, int>,
kpeter@689:                   NetworkSimplex<GR> >();
kpeter@689:     checkConcept< McfClassConcept<GR, double, double>,
kpeter@689:                   NetworkSimplex<GR, double> >();
kpeter@689:     checkConcept< McfClassConcept<GR, int, double>,
kpeter@689:                   NetworkSimplex<GR, int, double> >();
kpeter@648:   }
kpeter@648: 
kpeter@648:   // Run various MCF tests
kpeter@648:   typedef ListDigraph Digraph;
kpeter@648:   DIGRAPH_TYPEDEFS(ListDigraph);
kpeter@648: 
kpeter@648:   // Read the test digraph
kpeter@648:   Digraph gr;
kpeter@687:   Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), l3(gr), u(gr);
kpeter@687:   Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr), s6(gr);
kpeter@652:   ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());
kpeter@648:   Node v, w;
kpeter@648: 
kpeter@648:   std::istringstream input(test_lgf);
kpeter@648:   DigraphReader<Digraph>(gr, input)
kpeter@648:     .arcMap("cost", c)
kpeter@648:     .arcMap("cap", u)
kpeter@648:     .arcMap("low1", l1)
kpeter@648:     .arcMap("low2", l2)
kpeter@687:     .arcMap("low3", l3)
kpeter@648:     .nodeMap("sup1", s1)
kpeter@648:     .nodeMap("sup2", s2)
kpeter@648:     .nodeMap("sup3", s3)
kpeter@656:     .nodeMap("sup4", s4)
kpeter@656:     .nodeMap("sup5", s5)
kpeter@687:     .nodeMap("sup6", s6)
kpeter@648:     .node("source", v)
kpeter@648:     .node("target", w)
kpeter@648:     .run();
kpeter@687:   
kpeter@687:   // Build a test digraph for testing negative costs
kpeter@687:   Digraph ngr;
kpeter@687:   Node n1 = ngr.addNode();
kpeter@687:   Node n2 = ngr.addNode();
kpeter@687:   Node n3 = ngr.addNode();
kpeter@687:   Node n4 = ngr.addNode();
kpeter@687:   Node n5 = ngr.addNode();
kpeter@687:   Node n6 = ngr.addNode();
kpeter@687:   Node n7 = ngr.addNode();
kpeter@687:   
kpeter@687:   Arc a1 = ngr.addArc(n1, n2);
kpeter@687:   Arc a2 = ngr.addArc(n1, n3);
kpeter@687:   Arc a3 = ngr.addArc(n2, n4);
kpeter@687:   Arc a4 = ngr.addArc(n3, n4);
kpeter@687:   Arc a5 = ngr.addArc(n3, n2);
kpeter@687:   Arc a6 = ngr.addArc(n5, n3);
kpeter@687:   Arc a7 = ngr.addArc(n5, n6);
kpeter@687:   Arc a8 = ngr.addArc(n6, n7);
kpeter@687:   Arc a9 = ngr.addArc(n7, n5);
kpeter@687:   
kpeter@687:   Digraph::ArcMap<int> nc(ngr), nl1(ngr, 0), nl2(ngr, 0);
kpeter@687:   ConstMap<Arc, int> nu1(std::numeric_limits<int>::max()), nu2(5000);
kpeter@687:   Digraph::NodeMap<int> ns(ngr, 0);
kpeter@687:   
kpeter@687:   nl2[a7] =  1000;
kpeter@687:   nl2[a8] = -1000;
kpeter@687:   
kpeter@687:   ns[n1] =  100;
kpeter@687:   ns[n4] = -100;
kpeter@687:   
kpeter@687:   nc[a1] =  100;
kpeter@687:   nc[a2] =   30;
kpeter@687:   nc[a3] =   20;
kpeter@687:   nc[a4] =   80;
kpeter@687:   nc[a5] =   50;
kpeter@687:   nc[a6] =   10;
kpeter@687:   nc[a7] =   80;
kpeter@687:   nc[a8] =   30;
kpeter@687:   nc[a9] = -120;
kpeter@648: 
kpeter@652:   // A. Test NetworkSimplex with the default pivot rule
kpeter@648:   {
kpeter@653:     NetworkSimplex<Digraph> mcf(gr);
kpeter@648: 
kpeter@656:     // Check the equality form
kpeter@653:     mcf.upperMap(u).costMap(c);
kpeter@653:     checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687:              gr, l1, u, c, s1, mcf.OPTIMAL, true,   5240, "#A1");
kpeter@653:     checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
kpeter@687:              gr, l1, u, c, s2, mcf.OPTIMAL, true,   7620, "#A2");
kpeter@653:     mcf.lowerMap(l2);
kpeter@653:     checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#A3");
kpeter@653:     checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
kpeter@687:              gr, l2, u, c, s2, mcf.OPTIMAL, true,   8010, "#A4");
kpeter@653:     mcf.reset();
kpeter@653:     checkMcf(mcf, mcf.supplyMap(s1).run(),
kpeter@687:              gr, l1, cu, cc, s1, mcf.OPTIMAL, true,   74, "#A5");
kpeter@653:     checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(),
kpeter@687:              gr, l2, cu, cc, s2, mcf.OPTIMAL, true,   94, "#A6");
kpeter@653:     mcf.reset();
kpeter@653:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l1, cu, cc, s3, mcf.OPTIMAL, true,    0, "#A7");
kpeter@687:     checkMcf(mcf, mcf.lowerMap(l2).upperMap(u).run(),
kpeter@687:              gr, l2, u, cc, s3, mcf.INFEASIBLE, false, 0, "#A8");
kpeter@687:     mcf.reset().lowerMap(l3).upperMap(u).costMap(c).supplyMap(s4);
kpeter@687:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l3, u, c, s4, mcf.OPTIMAL, true,   6360, "#A9");
kpeter@656: 
kpeter@656:     // Check the GEQ form
kpeter@687:     mcf.reset().upperMap(u).costMap(c).supplyMap(s5);
kpeter@656:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l1, u, c, s5, mcf.OPTIMAL, true,   3530, "#A10", GEQ);
kpeter@687:     mcf.supplyType(mcf.GEQ);
kpeter@656:     checkMcf(mcf, mcf.lowerMap(l2).run(),
kpeter@687:              gr, l2, u, c, s5, mcf.OPTIMAL, true,   4540, "#A11", GEQ);
kpeter@687:     mcf.supplyType(mcf.CARRY_SUPPLIES).supplyMap(s6);
kpeter@656:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l2, u, c, s6, mcf.INFEASIBLE, false,  0, "#A12", GEQ);
kpeter@656: 
kpeter@656:     // Check the LEQ form
kpeter@687:     mcf.reset().supplyType(mcf.LEQ);
kpeter@687:     mcf.upperMap(u).costMap(c).supplyMap(s6);
kpeter@656:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l1, u, c, s6, mcf.OPTIMAL, true,   5080, "#A13", LEQ);
kpeter@656:     checkMcf(mcf, mcf.lowerMap(l2).run(),
kpeter@687:              gr, l2, u, c, s6, mcf.OPTIMAL, true,   5930, "#A14", LEQ);
kpeter@687:     mcf.supplyType(mcf.SATISFY_DEMANDS).supplyMap(s5);
kpeter@656:     checkMcf(mcf, mcf.run(),
kpeter@687:              gr, l2, u, c, s5, mcf.INFEASIBLE, false,  0, "#A15", LEQ);
kpeter@687: 
kpeter@687:     // Check negative costs
kpeter@687:     NetworkSimplex<Digraph> nmcf(ngr);
kpeter@687:     nmcf.lowerMap(nl1).costMap(nc).supplyMap(ns);
kpeter@687:     checkMcf(nmcf, nmcf.run(),
kpeter@687:       ngr, nl1, nu1, nc, ns, nmcf.UNBOUNDED, false,    0, "#A16");
kpeter@687:     checkMcf(nmcf, nmcf.upperMap(nu2).run(),
kpeter@687:       ngr, nl1, nu2, nc, ns, nmcf.OPTIMAL, true,  -40000, "#A17");
kpeter@687:     nmcf.reset().lowerMap(nl2).costMap(nc).supplyMap(ns);
kpeter@687:     checkMcf(nmcf, nmcf.run(),
kpeter@687:       ngr, nl2, nu1, nc, ns, nmcf.UNBOUNDED, false,    0, "#A18");
kpeter@648:   }
kpeter@648: 
kpeter@652:   // B. Test NetworkSimplex with each pivot rule
kpeter@648:   {
kpeter@653:     NetworkSimplex<Digraph> mcf(gr);
kpeter@687:     mcf.supplyMap(s1).costMap(c).upperMap(u).lowerMap(l2);
kpeter@648: 
kpeter@653:     checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::FIRST_ELIGIBLE),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B1");
kpeter@653:     checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BEST_ELIGIBLE),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B2");
kpeter@653:     checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BLOCK_SEARCH),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B3");
kpeter@653:     checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::CANDIDATE_LIST),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B4");
kpeter@653:     checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::ALTERING_LIST),
kpeter@687:              gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B5");
kpeter@648:   }
kpeter@648: 
kpeter@648:   return 0;
kpeter@648: }