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_INSERTION_TSP_H
f4c3@1031: #define LEMON_INSERTION_TSP_H
f4c3@1031: 
kpeter@1033: /// \ingroup tsp
kpeter@1033: /// \file
kpeter@1033: /// \brief Insertion algorithm for symmetric TSP
kpeter@1033: 
kpeter@1033: #include <vector>
f4c3@1031: #include <lemon/full_graph.h>
f4c3@1031: #include <lemon/maps.h>
f4c3@1031: #include <lemon/random.h>
f4c3@1031: 
f4c3@1031: namespace lemon {
f4c3@1031: 
kpeter@1034:   /// \ingroup tsp
kpeter@1034:   ///
kpeter@1033:   /// \brief Insertion algorithm for symmetric TSP.
kpeter@1033:   ///
kpeter@1033:   /// InsertionTsp implements the insertion heuristic for solving
kpeter@1033:   /// symmetric \ref tsp "TSP".
kpeter@1033:   ///
kpeter@1033:   /// This is a basic TSP heuristic that has many variants.
kpeter@1033:   /// It starts with a subtour containing a few nodes of the graph and it
kpeter@1033:   /// iteratively inserts the other nodes into this subtour according to a
kpeter@1033:   /// certain node selection rule.
kpeter@1033:   ///
kpeter@1033:   /// This implementation provides four different node selection rules,
kpeter@1033:   /// from which the most powerful one is used by default.
kpeter@1033:   /// For more information, see \ref SelectionRule.
kpeter@1033:   ///
kpeter@1033:   /// \tparam CM Type of the cost map.
kpeter@1033:   template <typename CM>
kpeter@1033:   class InsertionTsp
kpeter@1033:   {
kpeter@1033:     public:
f4c3@1031: 
kpeter@1033:       /// Type of the cost map
f4c3@1031:       typedef CM CostMap;
kpeter@1033:       /// Type of the edge costs
f4c3@1031:       typedef typename CM::Value Cost;
f4c3@1031: 
f4c3@1031:     private:
f4c3@1031: 
kpeter@1033:       GRAPH_TYPEDEFS(FullGraph);
kpeter@1033: 
kpeter@1033:       const FullGraph &_gr;
kpeter@1033:       const CostMap &_cost;
kpeter@1033:       std::vector<Node> _notused;
kpeter@1033:       std::vector<Node> _path;
kpeter@1033:       Cost _sum;
kpeter@1033: 
kpeter@1033:     public:
kpeter@1033: 
kpeter@1033:       /// \brief Constants for specifying the node selection rule.
kpeter@1033:       ///
kpeter@1033:       /// Enum type containing constants for specifying the node selection
kpeter@1033:       /// rule for the \ref run() function.
kpeter@1033:       ///
kpeter@1033:       /// During the algorithm, nodes are selected for addition to the current
kpeter@1033:       /// subtour according to the applied rule.
kpeter@1034:       /// In general, the FARTHEST method yields the best tours, thus it is the
kpeter@1034:       /// default option. The RANDOM rule usually gives somewhat worse results,
kpeter@1034:       /// but it is much faster than the others and it is the most robust.
kpeter@1033:       ///
kpeter@1033:       /// The desired selection rule can be specified as a parameter of the
kpeter@1033:       /// \ref run() function.
kpeter@1033:       enum SelectionRule {
kpeter@1033: 
kpeter@1033:         /// An unvisited node having minimum distance from the current
kpeter@1033:         /// subtour is selected at each step.
kpeter@1033:         /// The algorithm runs in O(n<sup>3</sup>) time using this
kpeter@1033:         /// selection rule.
kpeter@1033:         NEAREST,
kpeter@1033: 
kpeter@1033:         /// An unvisited node having maximum distance from the current
kpeter@1033:         /// subtour is selected at each step.
kpeter@1033:         /// The algorithm runs in O(n<sup>3</sup>) time using this
kpeter@1033:         /// selection rule.
kpeter@1033:         FARTHEST,
kpeter@1033: 
kpeter@1033:         /// An unvisited node whose insertion results in the least
kpeter@1033:         /// increase of the subtour's total cost is selected at each step.
kpeter@1033:         /// The algorithm runs in O(n<sup>3</sup>) time using this
kpeter@1033:         /// selection rule.
kpeter@1033:         CHEAPEST,
kpeter@1033: 
kpeter@1033:         /// An unvisited node is selected randomly without any evaluation
kpeter@1033:         /// at each step.
kpeter@1033:         /// The global \ref rnd "random number generator instance" is used.
kpeter@1033:         /// You can seed it before executing the algorithm, if you
kpeter@1033:         /// would like to.
kpeter@1033:         /// The algorithm runs in O(n<sup>2</sup>) time using this
kpeter@1033:         /// selection rule.
kpeter@1033:         RANDOM
kpeter@1033:       };
kpeter@1033: 
kpeter@1033:     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:       InsertionTsp(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.
kpeter@1033:       ///
kpeter@1033:       /// This function runs the algorithm.
kpeter@1033:       ///
kpeter@1033:       /// \param rule The node selection rule. For more information, see
kpeter@1033:       /// \ref SelectionRule.
kpeter@1033:       ///
kpeter@1033:       /// \return The total cost of the found tour.
kpeter@1033:       Cost run(SelectionRule rule = FARTHEST) {
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: 
kpeter@1033:         switch (rule) {
kpeter@1033:           case NEAREST:
kpeter@1033:             init(true);
kpeter@1033:             start<NearestSelection, DefaultInsertion>();
kpeter@1033:             break;
kpeter@1033:           case FARTHEST:
kpeter@1033:             init(false);
kpeter@1033:             start<FarthestSelection, DefaultInsertion>();
kpeter@1033:             break;
kpeter@1033:           case CHEAPEST:
kpeter@1033:             init(true);
kpeter@1033:             start<CheapestSelection, CheapestInsertion>();
kpeter@1033:             break;
kpeter@1033:           case RANDOM:
kpeter@1033:             init(true);
kpeter@1033:             start<RandomSelection, DefaultInsertion>();
kpeter@1033:             break;
kpeter@1033:         }
kpeter@1033:         return _sum;
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@1033:       /// the given standard container.
kpeter@1033:       ///
kpeter@1033:       /// \pre run() must be called before using this function.
kpeter@1033:       template <typename Container>
kpeter@1033:       void tourNodes(Container &container) const {
kpeter@1033:         container.assign(_path.begin(), _path.end());
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: 
kpeter@1033:     private:
kpeter@1033: 
kpeter@1033:       // Initializes the algorithm
kpeter@1033:       void init(bool min) {
kpeter@1033:         Edge min_edge = min ? mapMin(_gr, _cost) : mapMax(_gr, _cost);
kpeter@1033: 
kpeter@1033:         _path.clear();
kpeter@1033:         _path.push_back(_gr.u(min_edge));
kpeter@1033:         _path.push_back(_gr.v(min_edge));
kpeter@1033: 
kpeter@1033:         _notused.clear();
kpeter@1033:         for (NodeIt n(_gr); n!=INVALID; ++n) {
kpeter@1033:           if (n != _gr.u(min_edge) && n != _gr.v(min_edge)) {
kpeter@1033:             _notused.push_back(n);
kpeter@1033:           }
kpeter@1033:         }
kpeter@1033: 
kpeter@1033:         _sum = _cost[min_edge] * 2;
kpeter@1033:       }
kpeter@1033: 
kpeter@1033:       // Executes the algorithm
kpeter@1033:       template <class SelectionFunctor, class InsertionFunctor>
kpeter@1033:       void start() {
kpeter@1033:         SelectionFunctor selectNode(_gr, _cost, _path, _notused);
kpeter@1033:         InsertionFunctor insertNode(_gr, _cost, _path, _sum);
kpeter@1033: 
kpeter@1033:         for (int i=0; i<_gr.nodeNum()-2; ++i) {
kpeter@1033:           insertNode.insert(selectNode.select());
kpeter@1033:         }
kpeter@1033: 
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:         }
kpeter@1033:       }
kpeter@1033: 
kpeter@1033: 
kpeter@1033:       // Implementation of the nearest selection rule
kpeter@1033:       class NearestSelection {
f4c3@1031:         public:
kpeter@1033:           NearestSelection(const FullGraph &gr, const CostMap &cost,
kpeter@1033:                            std::vector<Node> &path, std::vector<Node> &notused)
kpeter@1033:             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}
f4c3@1031: 
kpeter@1033:           Node select() const {
kpeter@1033:             Cost insert_val = 0;
kpeter@1033:             int insert_node = -1;
kpeter@1033: 
kpeter@1033:             for (unsigned int i=0; i<_notused.size(); ++i) {
kpeter@1033:               Cost min_val = _cost[_gr.edge(_notused[i], _path[0])];
kpeter@1033:               int min_node = 0;
kpeter@1033: 
kpeter@1033:               for (unsigned int j=1; j<_path.size(); ++j) {
kpeter@1033:                 Cost curr = _cost[_gr.edge(_notused[i], _path[j])];
kpeter@1033:                 if (min_val > curr) {
kpeter@1033:                     min_val = curr;
kpeter@1033:                     min_node = j;
kpeter@1033:                 }
kpeter@1033:               }
kpeter@1033: 
kpeter@1033:               if (insert_val > min_val || insert_node == -1) {
kpeter@1033:                 insert_val = min_val;
kpeter@1033:                 insert_node = i;
f4c3@1031:               }
f4c3@1031:             }
kpeter@1033: 
kpeter@1033:             Node n = _notused[insert_node];
kpeter@1033:             _notused.erase(_notused.begin()+insert_node);
kpeter@1033: 
kpeter@1033:             return n;
f4c3@1031:           }
f4c3@1031: 
f4c3@1031:         private:
f4c3@1031:           const FullGraph &_gr;
f4c3@1031:           const CostMap &_cost;
kpeter@1033:           std::vector<Node> &_path;
f4c3@1031:           std::vector<Node> &_notused;
f4c3@1031:       };
f4c3@1031: 
kpeter@1033: 
kpeter@1033:       // Implementation of the farthest selection rule
f4c3@1031:       class FarthestSelection {
f4c3@1031:         public:
f4c3@1031:           FarthestSelection(const FullGraph &gr, const CostMap &cost,
kpeter@1033:                             std::vector<Node> &path, std::vector<Node> &notused)
kpeter@1033:             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}
kpeter@1033: 
f4c3@1031:           Node select() const {
kpeter@1033:             Cost insert_val = 0;
kpeter@1033:             int insert_node = -1;
f4c3@1031: 
f4c3@1031:             for (unsigned int i=0; i<_notused.size(); ++i) {
kpeter@1033:               Cost min_val = _cost[_gr.edge(_notused[i], _path[0])];
f4c3@1031:               int min_node = 0;
kpeter@1033: 
kpeter@1033:               for (unsigned int j=1; j<_path.size(); ++j) {
kpeter@1033:                 Cost curr = _cost[_gr.edge(_notused[i], _path[j])];
kpeter@1033:                 if (min_val > curr) {
kpeter@1033:                   min_val = curr;
f4c3@1031:                   min_node = j;
f4c3@1031:                 }
f4c3@1031:               }
kpeter@1033: 
f4c3@1031:               if (insert_val < min_val || insert_node == -1) {
f4c3@1031:                 insert_val = min_val;
f4c3@1031:                 insert_node = i;
f4c3@1031:               }
f4c3@1031:             }
kpeter@1033: 
f4c3@1031:             Node n = _notused[insert_node];
f4c3@1031:             _notused.erase(_notused.begin()+insert_node);
kpeter@1033: 
f4c3@1031:             return n;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:         private:
f4c3@1031:           const FullGraph &_gr;
f4c3@1031:           const CostMap &_cost;
kpeter@1033:           std::vector<Node> &_path;
f4c3@1031:           std::vector<Node> &_notused;
f4c3@1031:       };
f4c3@1031: 
f4c3@1031: 
kpeter@1033:       // Implementation of the cheapest selection rule
f4c3@1031:       class CheapestSelection {
f4c3@1031:         private:
f4c3@1031:           Cost costDiff(Node u, Node v, Node w) const {
kpeter@1033:             return
f4c3@1031:               _cost[_gr.edge(u, w)] +
f4c3@1031:               _cost[_gr.edge(v, w)] -
f4c3@1031:               _cost[_gr.edge(u, v)];
f4c3@1031:           }
f4c3@1031: 
f4c3@1031:         public:
f4c3@1031:           CheapestSelection(const FullGraph &gr, const CostMap &cost,
kpeter@1033:                             std::vector<Node> &path, std::vector<Node> &notused)
kpeter@1033:             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}
kpeter@1033: 
f4c3@1031:           Cost select() const {
f4c3@1031:             int insert_notused = -1;
f4c3@1031:             int best_insert_index = -1;
kpeter@1033:             Cost insert_val = 0;
kpeter@1033: 
f4c3@1031:             for (unsigned int i=0; i<_notused.size(); ++i) {
f4c3@1031:               int min = i;
f4c3@1031:               int best_insert_tmp = 0;
f4c3@1031:               Cost min_val =
kpeter@1033:                 costDiff(_path.front(), _path.back(), _notused[i]);
kpeter@1033: 
kpeter@1033:               for (unsigned int j=1; j<_path.size(); ++j) {
f4c3@1031:                 Cost tmp =
kpeter@1033:                   costDiff(_path[j-1], _path[j], _notused[i]);
f4c3@1031: 
f4c3@1031:                 if (min_val > tmp) {
f4c3@1031:                   min = i;
f4c3@1031:                   min_val = tmp;
f4c3@1031:                   best_insert_tmp = j;
f4c3@1031:                 }
f4c3@1031:               }
f4c3@1031: 
kpeter@1033:               if (insert_val > min_val || insert_notused == -1) {
f4c3@1031:                 insert_notused = min;
f4c3@1031:                 insert_val = min_val;
f4c3@1031:                 best_insert_index = best_insert_tmp;
f4c3@1031:               }
f4c3@1031:             }
f4c3@1031: 
kpeter@1033:             _path.insert(_path.begin()+best_insert_index,
kpeter@1033:                          _notused[insert_notused]);
f4c3@1031:             _notused.erase(_notused.begin()+insert_notused);
f4c3@1031: 
f4c3@1031:             return insert_val;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:         private:
f4c3@1031:           const FullGraph &_gr;
f4c3@1031:           const CostMap &_cost;
kpeter@1033:           std::vector<Node> &_path;
f4c3@1031:           std::vector<Node> &_notused;
f4c3@1031:       };
f4c3@1031: 
kpeter@1033:       // Implementation of the random selection rule
f4c3@1031:       class RandomSelection {
f4c3@1031:         public:
f4c3@1031:           RandomSelection(const FullGraph &, const CostMap &,
kpeter@1033:                           std::vector<Node> &, std::vector<Node> &notused)
kpeter@1033:             : _notused(notused) {}
kpeter@1033: 
f4c3@1031:           Node select() const {
f4c3@1031:             const int index = rnd[_notused.size()];
f4c3@1031:             Node n = _notused[index];
f4c3@1031:             _notused.erase(_notused.begin()+index);
f4c3@1031:             return n;
f4c3@1031:           }
f4c3@1031:         private:
f4c3@1031:           std::vector<Node> &_notused;
f4c3@1031:       };
f4c3@1031: 
f4c3@1031: 
kpeter@1033:       // Implementation of the default insertion method
kpeter@1033:       class DefaultInsertion {
f4c3@1031:         private:
f4c3@1031:           Cost costDiff(Node u, Node v, Node w) const {
kpeter@1033:             return
f4c3@1031:               _cost[_gr.edge(u, w)] +
f4c3@1031:               _cost[_gr.edge(v, w)] -
f4c3@1031:               _cost[_gr.edge(u, v)];
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:         public:
kpeter@1033:           DefaultInsertion(const FullGraph &gr, const CostMap &cost,
kpeter@1033:                            std::vector<Node> &path, Cost &total_cost) :
kpeter@1033:             _gr(gr), _cost(cost), _path(path), _total(total_cost) {}
kpeter@1033: 
f4c3@1031:           void insert(Node n) const {
f4c3@1031:             int min = 0;
f4c3@1031:             Cost min_val =
f4c3@1031:               costDiff(_path.front(), _path.back(), n);
kpeter@1033: 
f4c3@1031:             for (unsigned int i=1; i<_path.size(); ++i) {
f4c3@1031:               Cost tmp = costDiff(_path[i-1], _path[i], n);
f4c3@1031:               if (tmp < min_val) {
f4c3@1031:                 min = i;
f4c3@1031:                 min_val = tmp;
f4c3@1031:               }
f4c3@1031:             }
kpeter@1033: 
f4c3@1031:             _path.insert(_path.begin()+min, n);
kpeter@1033:             _total += min_val;
f4c3@1031:           }
kpeter@1033: 
f4c3@1031:         private:
f4c3@1031:           const FullGraph &_gr;
f4c3@1031:           const CostMap &_cost;
f4c3@1031:           std::vector<Node> &_path;
kpeter@1033:           Cost &_total;
f4c3@1031:       };
kpeter@1033: 
kpeter@1033:       // Implementation of a special insertion method for the cheapest
kpeter@1033:       // selection rule
kpeter@1033:       class CheapestInsertion {
f4c3@1031:         TEMPLATE_GRAPH_TYPEDEFS(FullGraph);
f4c3@1031:         public:
kpeter@1033:           CheapestInsertion(const FullGraph &, const CostMap &,
kpeter@1033:                             std::vector<Node> &, Cost &total_cost) :
kpeter@1033:             _total(total_cost) {}
kpeter@1033: 
f4c3@1031:           void insert(Cost diff) const {
kpeter@1033:             _total += diff;
f4c3@1031:           }
f4c3@1031: 
f4c3@1031:         private:
kpeter@1033:           Cost &_total;
kpeter@1033:       };
kpeter@1033: 
f4c3@1031:   };
kpeter@1033: 
f4c3@1031: }; // namespace lemon
f4c3@1031: 
f4c3@1031: #endif