lemon/opt2_tsp.h
changeset 1184 3c00344f49c9
parent 1074 97d978243703
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/opt2_tsp.h	Wed Oct 17 19:14:07 2018 +0200
     1.3 @@ -0,0 +1,367 @@
     1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library.
     1.7 + *
     1.8 + * Copyright (C) 2003-2013
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_OPT2_TSP_H
    1.23 +#define LEMON_OPT2_TSP_H
    1.24 +
    1.25 +/// \ingroup tsp
    1.26 +/// \file
    1.27 +/// \brief 2-opt algorithm for symmetric TSP.
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <lemon/full_graph.h>
    1.31 +
    1.32 +namespace lemon {
    1.33 +
    1.34 +  /// \ingroup tsp
    1.35 +  ///
    1.36 +  /// \brief 2-opt algorithm for symmetric TSP.
    1.37 +  ///
    1.38 +  /// Opt2Tsp implements the 2-opt heuristic for solving
    1.39 +  /// symmetric \ref tsp "TSP".
    1.40 +  ///
    1.41 +  /// This algorithm starts with an initial tour and iteratively improves it.
    1.42 +  /// At each step, it removes two edges and the reconnects the created two
    1.43 +  /// paths in the other way if the resulting tour is shorter.
    1.44 +  /// The algorithm finishes when no such 2-opt move can be applied, and so
    1.45 +  /// the tour is 2-optimal.
    1.46 +  ///
    1.47 +  /// If no starting tour is given to the \ref run() function, then the
    1.48 +  /// algorithm uses the node sequence determined by the node IDs.
    1.49 +  /// Oherwise, it starts with the given tour.
    1.50 +  ///
    1.51 +  /// This is a rather slow but effective method.
    1.52 +  /// Its typical usage is the improvement of the result of a fast tour
    1.53 +  /// construction heuristic (e.g. the InsertionTsp algorithm).
    1.54 +  ///
    1.55 +  /// \tparam CM Type of the cost map.
    1.56 +  template <typename CM>
    1.57 +  class Opt2Tsp
    1.58 +  {
    1.59 +    public:
    1.60 +
    1.61 +      /// Type of the cost map
    1.62 +      typedef CM CostMap;
    1.63 +      /// Type of the edge costs
    1.64 +      typedef typename CM::Value Cost;
    1.65 +
    1.66 +    private:
    1.67 +
    1.68 +      GRAPH_TYPEDEFS(FullGraph);
    1.69 +
    1.70 +      const FullGraph &_gr;
    1.71 +      const CostMap &_cost;
    1.72 +      Cost _sum;
    1.73 +      std::vector<int> _plist;
    1.74 +      std::vector<Node> _path;
    1.75 +
    1.76 +    public:
    1.77 +
    1.78 +      /// \brief Constructor
    1.79 +      ///
    1.80 +      /// Constructor.
    1.81 +      /// \param gr The \ref FullGraph "full graph" the algorithm runs on.
    1.82 +      /// \param cost The cost map.
    1.83 +      Opt2Tsp(const FullGraph &gr, const CostMap &cost)
    1.84 +        : _gr(gr), _cost(cost) {}
    1.85 +
    1.86 +      /// \name Execution Control
    1.87 +      /// @{
    1.88 +
    1.89 +      /// \brief Runs the algorithm from scratch.
    1.90 +      ///
    1.91 +      /// This function runs the algorithm starting from the tour that is
    1.92 +      /// determined by the node ID sequence.
    1.93 +      ///
    1.94 +      /// \return The total cost of the found tour.
    1.95 +      Cost run() {
    1.96 +        _path.clear();
    1.97 +
    1.98 +        if (_gr.nodeNum() == 0) return _sum = 0;
    1.99 +        else if (_gr.nodeNum() == 1) {
   1.100 +          _path.push_back(_gr(0));
   1.101 +          return _sum = 0;
   1.102 +        }
   1.103 +        else if (_gr.nodeNum() == 2) {
   1.104 +          _path.push_back(_gr(0));
   1.105 +          _path.push_back(_gr(1));
   1.106 +          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
   1.107 +        }
   1.108 +
   1.109 +        _plist.resize(2*_gr.nodeNum());
   1.110 +        for (int i = 1; i < _gr.nodeNum()-1; ++i) {
   1.111 +          _plist[2*i] = i-1;
   1.112 +          _plist[2*i+1] = i+1;
   1.113 +        }
   1.114 +        _plist[0] = _gr.nodeNum()-1;
   1.115 +        _plist[1] = 1;
   1.116 +        _plist[2*_gr.nodeNum()-2] = _gr.nodeNum()-2;
   1.117 +        _plist[2*_gr.nodeNum()-1] = 0;
   1.118 +
   1.119 +        return start();
   1.120 +      }
   1.121 +
   1.122 +      /// \brief Runs the algorithm starting from the given tour.
   1.123 +      ///
   1.124 +      /// This function runs the algorithm starting from the given tour.
   1.125 +      ///
   1.126 +      /// \param tour The tour as a path structure. It must be a
   1.127 +      /// \ref checkPath() "valid path" containing excactly n arcs.
   1.128 +      ///
   1.129 +      /// \return The total cost of the found tour.
   1.130 +      template <typename Path>
   1.131 +      Cost run(const Path& tour) {
   1.132 +        _path.clear();
   1.133 +
   1.134 +        if (_gr.nodeNum() == 0) return _sum = 0;
   1.135 +        else if (_gr.nodeNum() == 1) {
   1.136 +          _path.push_back(_gr(0));
   1.137 +          return _sum = 0;
   1.138 +        }
   1.139 +        else if (_gr.nodeNum() == 2) {
   1.140 +          _path.push_back(_gr(0));
   1.141 +          _path.push_back(_gr(1));
   1.142 +          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
   1.143 +        }
   1.144 +
   1.145 +        _plist.resize(2*_gr.nodeNum());
   1.146 +        typename Path::ArcIt it(tour);
   1.147 +        int first = _gr.id(_gr.source(it)),
   1.148 +            prev = first,
   1.149 +            curr = _gr.id(_gr.target(it)),
   1.150 +            next = -1;
   1.151 +        _plist[2*first+1] = curr;
   1.152 +        for (++it; it != INVALID; ++it) {
   1.153 +          next = _gr.id(_gr.target(it));
   1.154 +          _plist[2*curr] = prev;
   1.155 +          _plist[2*curr+1] = next;
   1.156 +          prev = curr;
   1.157 +          curr = next;
   1.158 +        }
   1.159 +        _plist[2*first] = prev;
   1.160 +
   1.161 +        return start();
   1.162 +      }
   1.163 +
   1.164 +      /// \brief Runs the algorithm starting from the given tour.
   1.165 +      ///
   1.166 +      /// This function runs the algorithm starting from the given tour
   1.167 +      /// (node sequence).
   1.168 +      ///
   1.169 +      /// \param tour A vector that stores all <tt>Node</tt>s of the graph
   1.170 +      /// in the desired order.
   1.171 +      ///
   1.172 +      /// \return The total cost of the found tour.
   1.173 +      Cost run(const std::vector<Node>& tour) {
   1.174 +        _path.clear();
   1.175 +
   1.176 +        if (_gr.nodeNum() == 0) return _sum = 0;
   1.177 +        else if (_gr.nodeNum() == 1) {
   1.178 +          _path.push_back(_gr(0));
   1.179 +          return _sum = 0;
   1.180 +        }
   1.181 +        else if (_gr.nodeNum() == 2) {
   1.182 +          _path.push_back(_gr(0));
   1.183 +          _path.push_back(_gr(1));
   1.184 +          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
   1.185 +        }
   1.186 +
   1.187 +        _plist.resize(2*_gr.nodeNum());
   1.188 +        typename std::vector<Node>::const_iterator it = tour.begin();
   1.189 +        int first = _gr.id(*it),
   1.190 +            prev = first,
   1.191 +            curr = _gr.id(*(++it)),
   1.192 +            next = -1;
   1.193 +        _plist[2*first+1] = curr;
   1.194 +        for (++it; it != tour.end(); ++it) {
   1.195 +          next = _gr.id(*it);
   1.196 +          _plist[2*curr] = prev;
   1.197 +          _plist[2*curr+1] = next;
   1.198 +          prev = curr;
   1.199 +          curr = next;
   1.200 +        }
   1.201 +        _plist[2*first] = curr;
   1.202 +        _plist[2*curr] = prev;
   1.203 +        _plist[2*curr+1] = first;
   1.204 +
   1.205 +        return start();
   1.206 +      }
   1.207 +
   1.208 +      /// @}
   1.209 +
   1.210 +      /// \name Query Functions
   1.211 +      /// @{
   1.212 +
   1.213 +      /// \brief The total cost of the found tour.
   1.214 +      ///
   1.215 +      /// This function returns the total cost of the found tour.
   1.216 +      ///
   1.217 +      /// \pre run() must be called before using this function.
   1.218 +      Cost tourCost() const {
   1.219 +        return _sum;
   1.220 +      }
   1.221 +
   1.222 +      /// \brief Returns a const reference to the node sequence of the
   1.223 +      /// found tour.
   1.224 +      ///
   1.225 +      /// This function returns a const reference to a vector
   1.226 +      /// that stores the node sequence of the found tour.
   1.227 +      ///
   1.228 +      /// \pre run() must be called before using this function.
   1.229 +      const std::vector<Node>& tourNodes() const {
   1.230 +        return _path;
   1.231 +      }
   1.232 +
   1.233 +      /// \brief Gives back the node sequence of the found tour.
   1.234 +      ///
   1.235 +      /// This function copies the node sequence of the found tour into
   1.236 +      /// an STL container through the given output iterator. The
   1.237 +      /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>.
   1.238 +      /// For example,
   1.239 +      /// \code
   1.240 +      /// std::vector<FullGraph::Node> nodes(countNodes(graph));
   1.241 +      /// tsp.tourNodes(nodes.begin());
   1.242 +      /// \endcode
   1.243 +      /// or
   1.244 +      /// \code
   1.245 +      /// std::list<FullGraph::Node> nodes;
   1.246 +      /// tsp.tourNodes(std::back_inserter(nodes));
   1.247 +      /// \endcode
   1.248 +      ///
   1.249 +      /// \pre run() must be called before using this function.
   1.250 +      template <typename Iterator>
   1.251 +      void tourNodes(Iterator out) const {
   1.252 +        std::copy(_path.begin(), _path.end(), out);
   1.253 +      }
   1.254 +
   1.255 +      /// \brief Gives back the found tour as a path.
   1.256 +      ///
   1.257 +      /// This function copies the found tour as a list of arcs/edges into
   1.258 +      /// the given \ref lemon::concepts::Path "path structure".
   1.259 +      ///
   1.260 +      /// \pre run() must be called before using this function.
   1.261 +      template <typename Path>
   1.262 +      void tour(Path &path) const {
   1.263 +        path.clear();
   1.264 +        for (int i = 0; i < int(_path.size()) - 1; ++i) {
   1.265 +          path.addBack(_gr.arc(_path[i], _path[i+1]));
   1.266 +        }
   1.267 +        if (int(_path.size()) >= 2) {
   1.268 +          path.addBack(_gr.arc(_path.back(), _path.front()));
   1.269 +        }
   1.270 +      }
   1.271 +
   1.272 +      /// @}
   1.273 +
   1.274 +    private:
   1.275 +
   1.276 +      // Iterator class for the linked list storage of the tour
   1.277 +      class PathListIt {
   1.278 +        public:
   1.279 +          PathListIt(const std::vector<int> &pl, int i=0)
   1.280 +            : plist(&pl), act(i), last(pl[2*act]) {}
   1.281 +          PathListIt(const std::vector<int> &pl, int i, int l)
   1.282 +            : plist(&pl), act(i), last(l) {}
   1.283 +
   1.284 +          int nextIndex() const {
   1.285 +            return (*plist)[2*act] == last ? 2*act+1 : 2*act;
   1.286 +          }
   1.287 +
   1.288 +          int prevIndex() const {
   1.289 +            return (*plist)[2*act] == last ? 2*act : 2*act+1;
   1.290 +          }
   1.291 +
   1.292 +          int next() const {
   1.293 +            int x = (*plist)[2*act];
   1.294 +            return x == last ? (*plist)[2*act+1] : x;
   1.295 +          }
   1.296 +
   1.297 +          int prev() const {
   1.298 +            return last;
   1.299 +          }
   1.300 +
   1.301 +          PathListIt& operator++() {
   1.302 +            int tmp = act;
   1.303 +            act = next();
   1.304 +            last = tmp;
   1.305 +            return *this;
   1.306 +          }
   1.307 +
   1.308 +          operator int() const {
   1.309 +            return act;
   1.310 +          }
   1.311 +
   1.312 +        private:
   1.313 +          const std::vector<int> *plist;
   1.314 +          int act;
   1.315 +          int last;
   1.316 +      };
   1.317 +
   1.318 +      // Checks and applies 2-opt move (if it improves the tour)
   1.319 +      bool checkOpt2(const PathListIt& i, const PathListIt& j) {
   1.320 +        Node u  = _gr.nodeFromId(i),
   1.321 +             un = _gr.nodeFromId(i.next()),
   1.322 +             v  = _gr.nodeFromId(j),
   1.323 +             vn = _gr.nodeFromId(j.next());
   1.324 +
   1.325 +        if (_cost[_gr.edge(u, un)] + _cost[_gr.edge(v, vn)] >
   1.326 +            _cost[_gr.edge(u, v)] + _cost[_gr.edge(un, vn)])
   1.327 +        {
   1.328 +          _plist[PathListIt(_plist, i.next(), i).prevIndex()] = j.next();
   1.329 +          _plist[PathListIt(_plist, j.next(), j).prevIndex()] = i.next();
   1.330 +
   1.331 +          _plist[i.nextIndex()] = j;
   1.332 +          _plist[j.nextIndex()] = i;
   1.333 +
   1.334 +          return true;
   1.335 +        }
   1.336 +
   1.337 +        return false;
   1.338 +     }
   1.339 +
   1.340 +      // Executes the algorithm from the initial tour
   1.341 +      Cost start() {
   1.342 +
   1.343 +      restart_search:
   1.344 +        for (PathListIt i(_plist); true; ++i) {
   1.345 +          PathListIt j = i;
   1.346 +          if (++j == 0 || ++j == 0) break;
   1.347 +          for (; j != 0 && j != i.prev(); ++j) {
   1.348 +            if (checkOpt2(i, j))
   1.349 +              goto restart_search;
   1.350 +          }
   1.351 +        }
   1.352 +
   1.353 +        PathListIt i(_plist);
   1.354 +        _path.push_back(_gr.nodeFromId(i));
   1.355 +        for (++i; i != 0; ++i)
   1.356 +          _path.push_back(_gr.nodeFromId(i));
   1.357 +
   1.358 +        _sum = _cost[_gr.edge(_path.back(), _path.front())];
   1.359 +        for (int i = 0; i < int(_path.size())-1; ++i) {
   1.360 +          _sum += _cost[_gr.edge(_path[i], _path[i+1])];
   1.361 +        }
   1.362 +
   1.363 +        return _sum;
   1.364 +      }
   1.365 +
   1.366 +  };
   1.367 +
   1.368 +}; // namespace lemon
   1.369 +
   1.370 +#endif