kpeter@1033: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@1033:  *
kpeter@1033:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@1033:  *
kpeter@1033:  * Copyright (C) 2003-2010
kpeter@1033:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@1033:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@1033:  *
kpeter@1033:  * Permission to use, modify and distribute this software is granted
kpeter@1033:  * provided that this copyright notice appears in all copies. For
kpeter@1033:  * precise terms see the accompanying LICENSE file.
kpeter@1033:  *
kpeter@1033:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@1033:  * express or implied, and with no claim as to its suitability for any
kpeter@1033:  * purpose.
kpeter@1033:  *
kpeter@1033:  */
kpeter@1033: 
f4c3@1031: #ifndef LEMON_OPT2_TSP_H
f4c3@1031: #define LEMON_OPT2_TSP_H
f4c3@1031: 
kpeter@1033: /// \ingroup tsp
kpeter@1033: /// \file
kpeter@1034: /// \brief 2-opt algorithm for symmetric TSP.
kpeter@1033: 
f4c3@1031: #include <vector>
f4c3@1031: #include <lemon/full_graph.h>
f4c3@1031: 
f4c3@1031: namespace lemon {
kpeter@1033: 
kpeter@1034:   /// \ingroup tsp
kpeter@1034:   ///
kpeter@1033:   /// \brief 2-opt algorithm for symmetric TSP.
kpeter@1033:   ///
kpeter@1033:   /// Opt2Tsp implements the 2-opt heuristic for solving
kpeter@1033:   /// symmetric \ref tsp "TSP".
kpeter@1033:   ///
kpeter@1033:   /// This algorithm starts with an initial tour and iteratively improves it.
kpeter@1033:   /// At each step, it removes two edges and the reconnects the created two
kpeter@1033:   /// paths in the other way if the resulting tour is shorter.
kpeter@1033:   /// The algorithm finishes when no such 2-opt move can be applied, and so
kpeter@1033:   /// the tour is 2-optimal.
kpeter@1033:   ///
kpeter@1033:   /// If no starting tour is given to the \ref run() function, then the
kpeter@1033:   /// algorithm uses the node sequence determined by the node IDs.
kpeter@1033:   /// Oherwise, it starts with the given tour.
kpeter@1033:   ///
kpeter@1036:   /// This is a rather slow but effective method.
kpeter@1036:   /// Its typical usage is the improvement of the result of a fast tour
kpeter@1036:   /// construction heuristic (e.g. the InsertionTsp algorithm).
kpeter@1033:   ///
kpeter@1033:   /// \tparam CM Type of the cost map.
f4c3@1031:   template <typename CM>
kpeter@1033:   class Opt2Tsp
kpeter@1033:   {
kpeter@1033:     public:
kpeter@1033: 
kpeter@1033:       /// Type of the cost map
kpeter@1033:       typedef CM CostMap;
kpeter@1033:       /// Type of the edge costs
kpeter@1033:       typedef typename CM::Value Cost;
kpeter@1033: 
f4c3@1031:     private:
kpeter@1033: 
f4c3@1031:       GRAPH_TYPEDEFS(FullGraph);
f4c3@1031: 
kpeter@1033:       const FullGraph &_gr;
kpeter@1033:       const CostMap &_cost;
kpeter@1033:       Cost _sum;
kpeter@1033:       std::vector<int> _plist;
kpeter@1033:       std::vector<Node> _path;
kpeter@1033: 
f4c3@1031:     public:
kpeter@1033: 
kpeter@1033:       /// \brief Constructor
kpeter@1033:       ///
kpeter@1033:       /// Constructor.
kpeter@1033:       /// \param gr The \ref FullGraph "full graph" the algorithm runs on.
kpeter@1033:       /// \param cost The cost map.
kpeter@1033:       Opt2Tsp(const FullGraph &gr, const CostMap &cost)
kpeter@1033:         : _gr(gr), _cost(cost) {}
kpeter@1033: 
kpeter@1033:       /// \name Execution Control
kpeter@1033:       /// @{
kpeter@1033: 
kpeter@1033:       /// \brief Runs the algorithm from scratch.
kpeter@1033:       ///
kpeter@1033:       /// This function runs the algorithm starting from the tour that is
kpeter@1033:       /// determined by the node ID sequence.
kpeter@1033:       ///
kpeter@1033:       /// \return The total cost of the found tour.
kpeter@1033:       Cost run() {
kpeter@1033:         _path.clear();
kpeter@1033: 
kpeter@1033:         if (_gr.nodeNum() == 0) return _sum = 0;
kpeter@1033:         else if (_gr.nodeNum() == 1) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           return _sum = 0;
f4c3@1031:         }
kpeter@1033:         else if (_gr.nodeNum() == 2) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           _path.push_back(_gr(1));
kpeter@1033:           return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
kpeter@1033:         }
f4c3@1031: 
kpeter@1033:         _plist.resize(2*_gr.nodeNum());
kpeter@1033:         for (int i = 1; i < _gr.nodeNum()-1; ++i) {
kpeter@1033:           _plist[2*i] = i-1;
kpeter@1033:           _plist[2*i+1] = i+1;
f4c3@1031:         }
kpeter@1033:         _plist[0] = _gr.nodeNum()-1;
kpeter@1033:         _plist[1] = 1;
kpeter@1033:         _plist[2*_gr.nodeNum()-2] = _gr.nodeNum()-2;
kpeter@1033:         _plist[2*_gr.nodeNum()-1] = 0;
kpeter@1033: 
kpeter@1033:         return start();
f4c3@1031:       }
f4c3@1031: 
kpeter@1034:       /// \brief Runs the algorithm starting from the given tour.
kpeter@1033:       ///
kpeter@1033:       /// This function runs the algorithm starting from the given tour.
kpeter@1033:       ///
kpeter@1033:       /// \param tour The tour as a path structure. It must be a
kpeter@1033:       /// \ref checkPath() "valid path" containing excactly n arcs.
kpeter@1033:       ///
kpeter@1033:       /// \return The total cost of the found tour.
kpeter@1033:       template <typename Path>
kpeter@1033:       Cost run(const Path& tour) {
kpeter@1033:         _path.clear();
kpeter@1033: 
kpeter@1033:         if (_gr.nodeNum() == 0) return _sum = 0;
kpeter@1033:         else if (_gr.nodeNum() == 1) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           return _sum = 0;
kpeter@1033:         }
kpeter@1033:         else if (_gr.nodeNum() == 2) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           _path.push_back(_gr(1));
kpeter@1033:           return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
kpeter@1033:         }
kpeter@1033: 
kpeter@1033:         _plist.resize(2*_gr.nodeNum());
kpeter@1033:         typename Path::ArcIt it(tour);
kpeter@1033:         int first = _gr.id(_gr.source(it)),
kpeter@1033:             prev = first,
kpeter@1033:             curr = _gr.id(_gr.target(it)),
kpeter@1033:             next = -1;
kpeter@1033:         _plist[2*first+1] = curr;
kpeter@1033:         for (++it; it != INVALID; ++it) {
kpeter@1033:           next = _gr.id(_gr.target(it));
kpeter@1033:           _plist[2*curr] = prev;
kpeter@1033:           _plist[2*curr+1] = next;
kpeter@1033:           prev = curr;
kpeter@1033:           curr = next;
kpeter@1033:         }
kpeter@1033:         _plist[2*first] = prev;
kpeter@1033: 
kpeter@1033:         return start();
kpeter@1033:       }
kpeter@1033: 
kpeter@1034:       /// \brief Runs the algorithm starting from the given tour.
kpeter@1033:       ///
kpeter@1034:       /// This function runs the algorithm starting from the given tour
kpeter@1034:       /// (node sequence).
kpeter@1033:       ///
kpeter@1034:       /// \param tour A vector that stores all <tt>Node</tt>s of the graph
kpeter@1034:       /// in the desired order.
kpeter@1033:       ///
kpeter@1033:       /// \return The total cost of the found tour.
kpeter@1034:       Cost run(const std::vector<Node>& tour) {
kpeter@1033:         _path.clear();
kpeter@1033: 
kpeter@1033:         if (_gr.nodeNum() == 0) return _sum = 0;
kpeter@1033:         else if (_gr.nodeNum() == 1) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           return _sum = 0;
kpeter@1033:         }
kpeter@1033:         else if (_gr.nodeNum() == 2) {
kpeter@1033:           _path.push_back(_gr(0));
kpeter@1033:           _path.push_back(_gr(1));
kpeter@1033:           return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];
kpeter@1033:         }
kpeter@1033: 
kpeter@1033:         _plist.resize(2*_gr.nodeNum());
kpeter@1034:         typename std::vector<Node>::const_iterator it = tour.begin();
kpeter@1033:         int first = _gr.id(*it),
kpeter@1033:             prev = first,
kpeter@1033:             curr = _gr.id(*(++it)),
kpeter@1033:             next = -1;
kpeter@1033:         _plist[2*first+1] = curr;
kpeter@1033:         for (++it; it != tour.end(); ++it) {
kpeter@1033:           next = _gr.id(*it);
kpeter@1033:           _plist[2*curr] = prev;
kpeter@1033:           _plist[2*curr+1] = next;
kpeter@1033:           prev = curr;
kpeter@1033:           curr = next;
kpeter@1033:         }
kpeter@1033:         _plist[2*first] = curr;
kpeter@1033:         _plist[2*curr] = prev;
kpeter@1033:         _plist[2*curr+1] = first;
kpeter@1033: 
kpeter@1033:         return start();
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       /// @}
kpeter@1033: 
kpeter@1033:       /// \name Query Functions
kpeter@1033:       /// @{
kpeter@1033: 
kpeter@1033:       /// \brief The total cost of the found tour.
kpeter@1033:       ///
kpeter@1033:       /// This function returns the total cost of the found tour.
kpeter@1033:       ///
kpeter@1033:       /// \pre run() must be called before using this function.
kpeter@1033:       Cost tourCost() const {
kpeter@1033:         return _sum;
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       /// \brief Returns a const reference to the node sequence of the
kpeter@1033:       /// found tour.
kpeter@1033:       ///
kpeter@1034:       /// This function returns a const reference to a vector
kpeter@1033:       /// that stores the node sequence of the found tour.
kpeter@1033:       ///
kpeter@1033:       /// \pre run() must be called before using this function.
kpeter@1033:       const std::vector<Node>& tourNodes() const {
kpeter@1033:         return _path;
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       /// \brief Gives back the node sequence of the found tour.
kpeter@1033:       ///
kpeter@1033:       /// This function copies the node sequence of the found tour into
kpeter@1037:       /// an STL container through the given output iterator. The
kpeter@1037:       /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>.
kpeter@1037:       /// For example,
kpeter@1037:       /// \code
kpeter@1037:       /// std::vector<FullGraph::Node> nodes(countNodes(graph));
kpeter@1037:       /// tsp.tourNodes(nodes.begin());
kpeter@1037:       /// \endcode
kpeter@1037:       /// or
kpeter@1037:       /// \code
kpeter@1037:       /// std::list<FullGraph::Node> nodes;
kpeter@1037:       /// tsp.tourNodes(std::back_inserter(nodes));
kpeter@1037:       /// \endcode
kpeter@1033:       ///
kpeter@1033:       /// \pre run() must be called before using this function.
kpeter@1037:       template <typename Iterator>
kpeter@1037:       void tourNodes(Iterator out) const {
kpeter@1037:         std::copy(_path.begin(), _path.end(), out);
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       /// \brief Gives back the found tour as a path.
kpeter@1033:       ///
kpeter@1033:       /// This function copies the found tour as a list of arcs/edges into
kpeter@1033:       /// the given \ref concept::Path "path structure".
kpeter@1033:       ///
kpeter@1033:       /// \pre run() must be called before using this function.
kpeter@1033:       template <typename Path>
kpeter@1033:       void tour(Path &path) const {
kpeter@1033:         path.clear();
kpeter@1033:         for (int i = 0; i < int(_path.size()) - 1; ++i) {
kpeter@1033:           path.addBack(_gr.arc(_path[i], _path[i+1]));
kpeter@1033:         }
kpeter@1033:         if (int(_path.size()) >= 2) {
kpeter@1033:           path.addBack(_gr.arc(_path.back(), _path.front()));
kpeter@1033:         }
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       /// @}
kpeter@1033: 
f4c3@1031:     private:
kpeter@1033: 
kpeter@1033:       // Iterator class for the linked list storage of the tour
kpeter@1033:       class PathListIt {
f4c3@1031:         public:
kpeter@1033:           PathListIt(const std::vector<int> &pl, int i=0)
kpeter@1033:             : plist(&pl), act(i), last(pl[2*act]) {}
kpeter@1033:           PathListIt(const std::vector<int> &pl, int i, int l)
kpeter@1033:             : plist(&pl), act(i), last(l) {}
f4c3@1031: 
kpeter@1033:           int nextIndex() const {
kpeter@1033:             return (*plist)[2*act] == last ? 2*act+1 : 2*act;
f4c3@1031:           }
kpeter@1033: 
kpeter@1033:           int prevIndex() const {
kpeter@1033:             return (*plist)[2*act] == last ? 2*act : 2*act+1;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:           int next() const {
kpeter@1033:             int x = (*plist)[2*act];
kpeter@1033:             return x == last ? (*plist)[2*act+1] : x;
f4c3@1031:           }
f4c3@1031: 
f4c3@1031:           int prev() const {
kpeter@1033:             return last;
f4c3@1031:           }
kpeter@1033: 
kpeter@1033:           PathListIt& operator++() {
f4c3@1031:             int tmp = act;
f4c3@1031:             act = next();
f4c3@1031:             last = tmp;
f4c3@1031:             return *this;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:           operator int() const {
f4c3@1031:             return act;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:         private:
kpeter@1033:           const std::vector<int> *plist;
f4c3@1031:           int act;
f4c3@1031:           int last;
f4c3@1031:       };
f4c3@1031: 
kpeter@1033:       // Checks and applies 2-opt move (if it improves the tour)
kpeter@1033:       bool checkOpt2(const PathListIt& i, const PathListIt& j) {
kpeter@1033:         Node u  = _gr.nodeFromId(i),
kpeter@1033:              un = _gr.nodeFromId(i.next()),
kpeter@1033:              v  = _gr.nodeFromId(j),
kpeter@1033:              vn = _gr.nodeFromId(j.next());
f4c3@1031: 
kpeter@1033:         if (_cost[_gr.edge(u, un)] + _cost[_gr.edge(v, vn)] >
kpeter@1033:             _cost[_gr.edge(u, v)] + _cost[_gr.edge(un, vn)])
kpeter@1033:         {
kpeter@1033:           _plist[PathListIt(_plist, i.next(), i).prevIndex()] = j.next();
kpeter@1033:           _plist[PathListIt(_plist, j.next(), j).prevIndex()] = i.next();
f4c3@1031: 
kpeter@1033:           _plist[i.nextIndex()] = j;
kpeter@1033:           _plist[j.nextIndex()] = i;
f4c3@1031: 
kpeter@1033:           return true;
f4c3@1031:         }
kpeter@1033: 
f4c3@1031:         return false;
kpeter@1033:      }
f4c3@1031: 
kpeter@1033:       // Executes the algorithm from the initial tour
kpeter@1033:       Cost start() {
f4c3@1031: 
kpeter@1033:       restart_search:
kpeter@1033:         for (PathListIt i(_plist); true; ++i) {
kpeter@1033:           PathListIt j = i;
kpeter@1033:           if (++j == 0 || ++j == 0) break;
kpeter@1033:           for (; j != 0 && j != i.prev(); ++j) {
kpeter@1033:             if (checkOpt2(i, j))
kpeter@1033:               goto restart_search;
f4c3@1031:           }
f4c3@1031:         }
f4c3@1031: 
kpeter@1033:         PathListIt i(_plist);
kpeter@1033:         _path.push_back(_gr.nodeFromId(i));
kpeter@1033:         for (++i; i != 0; ++i)
kpeter@1033:           _path.push_back(_gr.nodeFromId(i));
f4c3@1031: 
kpeter@1033:         _sum = _cost[_gr.edge(_path.back(), _path.front())];
kpeter@1033:         for (int i = 0; i < int(_path.size())-1; ++i) {
kpeter@1033:           _sum += _cost[_gr.edge(_path[i], _path[i+1])];
kpeter@1033:         }
f4c3@1031: 
f4c3@1031:         return _sum;
f4c3@1031:       }
f4c3@1031: 
f4c3@1031:   };
f4c3@1031: 
f4c3@1031: }; // namespace lemon
f4c3@1031: 
f4c3@1031: #endif