1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2013 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_NEAREST_NEIGHBOUR_TSP_H |
---|
20 | #define LEMON_NEAREST_NEIGHBOUR_TSP_H |
---|
21 | |
---|
22 | /// \ingroup tsp |
---|
23 | /// \file |
---|
24 | /// \brief Nearest neighbor algorithm for symmetric TSP |
---|
25 | |
---|
26 | #include <deque> |
---|
27 | #include <vector> |
---|
28 | #include <limits> |
---|
29 | #include <lemon/full_graph.h> |
---|
30 | #include <lemon/maps.h> |
---|
31 | |
---|
32 | namespace lemon { |
---|
33 | |
---|
34 | /// \ingroup tsp |
---|
35 | /// |
---|
36 | /// \brief Nearest neighbor algorithm for symmetric TSP. |
---|
37 | /// |
---|
38 | /// NearestNeighborTsp implements the nearest neighbor heuristic for solving |
---|
39 | /// symmetric \ref tsp "TSP". |
---|
40 | /// |
---|
41 | /// This is probably the simplest TSP heuristic. |
---|
42 | /// It starts with a minimum cost edge and at each step, it connects the |
---|
43 | /// nearest unvisited node to the current path. |
---|
44 | /// Finally, it connects the two end points of the path to form a tour. |
---|
45 | /// |
---|
46 | /// This method runs in O(n<sup>2</sup>) time. |
---|
47 | /// It quickly finds a relatively short tour for most TSP instances, |
---|
48 | /// but it could also yield a really bad (or even the worst) solution |
---|
49 | /// in special cases. |
---|
50 | /// |
---|
51 | /// \tparam CM Type of the cost map. |
---|
52 | template <typename CM> |
---|
53 | class NearestNeighborTsp |
---|
54 | { |
---|
55 | public: |
---|
56 | |
---|
57 | /// Type of the cost map |
---|
58 | typedef CM CostMap; |
---|
59 | /// Type of the edge costs |
---|
60 | typedef typename CM::Value Cost; |
---|
61 | |
---|
62 | private: |
---|
63 | |
---|
64 | GRAPH_TYPEDEFS(FullGraph); |
---|
65 | |
---|
66 | const FullGraph &_gr; |
---|
67 | const CostMap &_cost; |
---|
68 | Cost _sum; |
---|
69 | std::vector<Node> _path; |
---|
70 | |
---|
71 | public: |
---|
72 | |
---|
73 | /// \brief Constructor |
---|
74 | /// |
---|
75 | /// Constructor. |
---|
76 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
---|
77 | /// \param cost The cost map. |
---|
78 | NearestNeighborTsp(const FullGraph &gr, const CostMap &cost) |
---|
79 | : _gr(gr), _cost(cost) {} |
---|
80 | |
---|
81 | /// \name Execution Control |
---|
82 | /// @{ |
---|
83 | |
---|
84 | /// \brief Runs the algorithm. |
---|
85 | /// |
---|
86 | /// This function runs the algorithm. |
---|
87 | /// |
---|
88 | /// \return The total cost of the found tour. |
---|
89 | Cost run() { |
---|
90 | _path.clear(); |
---|
91 | if (_gr.nodeNum() == 0) { |
---|
92 | return _sum = 0; |
---|
93 | } |
---|
94 | else if (_gr.nodeNum() == 1) { |
---|
95 | _path.push_back(_gr(0)); |
---|
96 | return _sum = 0; |
---|
97 | } |
---|
98 | |
---|
99 | std::deque<Node> path_dq; |
---|
100 | Edge min_edge1 = INVALID, |
---|
101 | min_edge2 = INVALID; |
---|
102 | |
---|
103 | min_edge1 = mapMin(_gr, _cost); |
---|
104 | Node n1 = _gr.u(min_edge1), |
---|
105 | n2 = _gr.v(min_edge1); |
---|
106 | path_dq.push_back(n1); |
---|
107 | path_dq.push_back(n2); |
---|
108 | |
---|
109 | FullGraph::NodeMap<bool> used(_gr, false); |
---|
110 | used[n1] = true; |
---|
111 | used[n2] = true; |
---|
112 | |
---|
113 | min_edge1 = INVALID; |
---|
114 | while (int(path_dq.size()) != _gr.nodeNum()) { |
---|
115 | if (min_edge1 == INVALID) { |
---|
116 | for (IncEdgeIt e(_gr, n1); e != INVALID; ++e) { |
---|
117 | if (!used[_gr.runningNode(e)] && |
---|
118 | (min_edge1 == INVALID || _cost[e] < _cost[min_edge1])) { |
---|
119 | min_edge1 = e; |
---|
120 | } |
---|
121 | } |
---|
122 | } |
---|
123 | |
---|
124 | if (min_edge2 == INVALID) { |
---|
125 | for (IncEdgeIt e(_gr, n2); e != INVALID; ++e) { |
---|
126 | if (!used[_gr.runningNode(e)] && |
---|
127 | (min_edge2 == INVALID||_cost[e] < _cost[min_edge2])) { |
---|
128 | min_edge2 = e; |
---|
129 | } |
---|
130 | } |
---|
131 | } |
---|
132 | |
---|
133 | if (_cost[min_edge1] < _cost[min_edge2]) { |
---|
134 | n1 = _gr.oppositeNode(n1, min_edge1); |
---|
135 | path_dq.push_front(n1); |
---|
136 | |
---|
137 | used[n1] = true; |
---|
138 | min_edge1 = INVALID; |
---|
139 | |
---|
140 | if (_gr.u(min_edge2) == n1 || _gr.v(min_edge2) == n1) |
---|
141 | min_edge2 = INVALID; |
---|
142 | } else { |
---|
143 | n2 = _gr.oppositeNode(n2, min_edge2); |
---|
144 | path_dq.push_back(n2); |
---|
145 | |
---|
146 | used[n2] = true; |
---|
147 | min_edge2 = INVALID; |
---|
148 | |
---|
149 | if (_gr.u(min_edge1) == n2 || _gr.v(min_edge1) == n2) |
---|
150 | min_edge1 = INVALID; |
---|
151 | } |
---|
152 | } |
---|
153 | |
---|
154 | n1 = path_dq.back(); |
---|
155 | n2 = path_dq.front(); |
---|
156 | _path.push_back(n2); |
---|
157 | _sum = _cost[_gr.edge(n1, n2)]; |
---|
158 | for (int i = 1; i < int(path_dq.size()); ++i) { |
---|
159 | n1 = n2; |
---|
160 | n2 = path_dq[i]; |
---|
161 | _path.push_back(n2); |
---|
162 | _sum += _cost[_gr.edge(n1, n2)]; |
---|
163 | } |
---|
164 | |
---|
165 | return _sum; |
---|
166 | } |
---|
167 | |
---|
168 | /// @} |
---|
169 | |
---|
170 | /// \name Query Functions |
---|
171 | /// @{ |
---|
172 | |
---|
173 | /// \brief The total cost of the found tour. |
---|
174 | /// |
---|
175 | /// This function returns the total cost of the found tour. |
---|
176 | /// |
---|
177 | /// \pre run() must be called before using this function. |
---|
178 | Cost tourCost() const { |
---|
179 | return _sum; |
---|
180 | } |
---|
181 | |
---|
182 | /// \brief Returns a const reference to the node sequence of the |
---|
183 | /// found tour. |
---|
184 | /// |
---|
185 | /// This function returns a const reference to a vector |
---|
186 | /// that stores the node sequence of the found tour. |
---|
187 | /// |
---|
188 | /// \pre run() must be called before using this function. |
---|
189 | const std::vector<Node>& tourNodes() const { |
---|
190 | return _path; |
---|
191 | } |
---|
192 | |
---|
193 | /// \brief Gives back the node sequence of the found tour. |
---|
194 | /// |
---|
195 | /// This function copies the node sequence of the found tour into |
---|
196 | /// an STL container through the given output iterator. The |
---|
197 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
---|
198 | /// For example, |
---|
199 | /// \code |
---|
200 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
---|
201 | /// tsp.tourNodes(nodes.begin()); |
---|
202 | /// \endcode |
---|
203 | /// or |
---|
204 | /// \code |
---|
205 | /// std::list<FullGraph::Node> nodes; |
---|
206 | /// tsp.tourNodes(std::back_inserter(nodes)); |
---|
207 | /// \endcode |
---|
208 | /// |
---|
209 | /// \pre run() must be called before using this function. |
---|
210 | template <typename Iterator> |
---|
211 | void tourNodes(Iterator out) const { |
---|
212 | std::copy(_path.begin(), _path.end(), out); |
---|
213 | } |
---|
214 | |
---|
215 | /// \brief Gives back the found tour as a path. |
---|
216 | /// |
---|
217 | /// This function copies the found tour as a list of arcs/edges into |
---|
218 | /// the given \ref lemon::concepts::Path "path structure". |
---|
219 | /// |
---|
220 | /// \pre run() must be called before using this function. |
---|
221 | template <typename Path> |
---|
222 | void tour(Path &path) const { |
---|
223 | path.clear(); |
---|
224 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
---|
225 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
---|
226 | } |
---|
227 | if (int(_path.size()) >= 2) { |
---|
228 | path.addBack(_gr.arc(_path.back(), _path.front())); |
---|
229 | } |
---|
230 | } |
---|
231 | |
---|
232 | /// @} |
---|
233 | |
---|
234 | }; |
---|
235 | |
---|
236 | }; // namespace lemon |
---|
237 | |
---|
238 | #endif |
---|