377 lines
23 KiB
HTML
377 lines
23 KiB
HTML
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<div class="title">one_tree_lower_bound.h File Reference</div> </div>
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<div class="textblock"><code>#include <math.h></code><br />
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<code>#include <limits></code><br />
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<code>#include <set></code><br />
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<code>#include "ortools/base/integral_types.h"</code><br />
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<code>#include "<a class="el" href="christofides_8h_source.html">ortools/graph/christofides.h</a>"</code><br />
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<code>#include "<a class="el" href="minimum__spanning__tree_8h_source.html">ortools/graph/minimum_spanning_tree.h</a>"</code><br />
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<p><a href="one__tree__lower__bound_8h_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:adba1a0c02ca6636f5610de2337f3f697"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#adba1a0c02ca6636f5610de2337f3f697">step1_</a> (0)</td></tr>
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<tr class="separator:adba1a0c02ca6636f5610de2337f3f697"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6e4c1555a52b411d0e25bae82066dcc4"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a6e4c1555a52b411d0e25bae82066dcc4">iteration_</a> (0)</td></tr>
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<tr class="separator:a6e4c1555a52b411d0e25bae82066dcc4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad15ce7e24cde3d28bc88c4a32bf3a834"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#ad15ce7e24cde3d28bc88c4a32bf3a834">max_iterations_</a> (<a class="el" href="one__tree__lower__bound_8h.html#af85cb5d69bd041414717718f6a833325">max_iterations</a> > 0 ? <a class="el" href="one__tree__lower__bound_8h.html#af85cb5d69bd041414717718f6a833325">max_iterations</a> :MaxIterations(number_of_nodes))</td></tr>
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<tr class="separator:ad15ce7e24cde3d28bc88c4a32bf3a834"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a01198f1b6b698fc8c033ef878977c27d"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a01198f1b6b698fc8c033ef878977c27d">number_of_nodes_</a> (number_of_nodes)</td></tr>
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<tr class="separator:a01198f1b6b698fc8c033ef878977c27d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3947d19ac087ef2cd68c2409920339c4"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a3947d19ac087ef2cd68c2409920339c4">Next</a> ()</td></tr>
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<tr class="separator:a3947d19ac087ef2cd68c2409920339c4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a61aed6a943277e531b904cfdc3616890"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a61aed6a943277e531b904cfdc3616890">GetStep</a> () const</td></tr>
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<tr class="separator:a61aed6a943277e531b904cfdc3616890"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a33c2c5b8d838c77c2701a538f7f30ae4"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a33c2c5b8d838c77c2701a538f7f30ae4">OnOneTree</a> (CostType one_tree_cost, double <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a>, const std::vector< int > &<a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a>)</td></tr>
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<tr class="memitem:a2ad04ff9537d97fcabc58c86183890c3"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a2ad04ff9537d97fcabc58c86183890c3">OnNewWMax</a> (CostType one_tree_cost)</td></tr>
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<tr class="separator:a2ad04ff9537d97fcabc58c86183890c3"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:a717d5dae07519577a5ed09ac24a4708b"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a717d5dae07519577a5ed09ac24a4708b">to</a></td></tr>
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<tr class="memdesc:a717d5dae07519577a5ed09ac24a4708b"><td class="mdescLeft"> </td><td class="mdescRight">Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. <a href="#a717d5dae07519577a5ed09ac24a4708b">More...</a><br /></td></tr>
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<tr class="separator:a717d5dae07519577a5ed09ac24a4708b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6f353d8684dff1645f1601cd68b9a0be"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a6f353d8684dff1645f1601cd68b9a0be">therefore</a></td></tr>
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<tr class="separator:a6f353d8684dff1645f1601cd68b9a0be"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a095b3978da7ad09782c0be1a6572e352"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal w the current value of </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a></td></tr>
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<tr class="separator:a095b3978da7ad09782c0be1a6572e352"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af86d4c4e6a18908cda194651a9ab7beb"><td class="memItemLeft" align="right" valign="top">trees with all degrees equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a></td></tr>
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<tr class="separator:af86d4c4e6a18908cda194651a9ab7beb"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af85cb5d69bd041414717718f6a833325"><td class="memItemLeft" align="right" valign="top">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int </td><td class="memItemRight" valign="bottom"><a class="el" href="one__tree__lower__bound_8h.html#af85cb5d69bd041414717718f6a833325">max_iterations</a></td></tr>
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</table>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a61aed6a943277e531b904cfdc3616890"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a61aed6a943277e531b904cfdc3616890">◆ </a></span>GetStep()</h2>
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<td class="memname">double GetStep </td>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<td> const</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00165">165</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<a id="a6e4c1555a52b411d0e25bae82066dcc4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e4c1555a52b411d0e25bae82066dcc4">◆ </a></span>iteration_()</h2>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int iteration_ </td>
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<td>(</td>
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<td class="paramtype">0 </td>
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<h2 class="memtitle"><span class="permalink"><a href="#ad15ce7e24cde3d28bc88c4a32bf3a834">◆ </a></span>max_iterations_()</h2>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int max_iterations_ </td>
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<td>(</td>
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<td class="paramtype"><a class="el" href="one__tree__lower__bound_8h.html#af85cb5d69bd041414717718f6a833325">max_iterations</a> </td>
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<td class="paramname">, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">0 ? <a class="el" href="one__tree__lower__bound_8h.html#af85cb5d69bd041414717718f6a833325">max_iterations</a>  </td>
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<td class="paramname"><em>:MaxIterations</em>number_of_nodes </td>
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<td>)</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a3947d19ac087ef2cd68c2409920339c4">◆ </a></span>Next()</h2>
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<td class="memname">bool Next </td>
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<td>(</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00163">163</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a01198f1b6b698fc8c033ef878977c27d">◆ </a></span>number_of_nodes_()</h2>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int number_of_nodes_ </td>
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<td>(</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00161">161</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2ad04ff9537d97fcabc58c86183890c3">◆ </a></span>OnNewWMax()</h2>
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<td class="memname">void OnNewWMax </td>
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<td class="paramtype">CostType </td>
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<td class="paramname"><em>one_tree_cost</em></td><td>)</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00183">183</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a33c2c5b8d838c77c2701a538f7f30ae4">◆ </a></span>OnOneTree()</h2>
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<td class="memname">void OnOneTree </td>
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<td class="paramname"><em>one_tree_cost</em>, </td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00175">175</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#adba1a0c02ca6636f5610de2337f3f697">◆ </a></span>step1_()</h2>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int step1_ </td>
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<h2 class="memtitle"><span class="permalink"><a href="#af86d4c4e6a18908cda194651a9ab7beb">◆ </a></span>degrees</h2>
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<td class="memname">trees with all degrees equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of degrees</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00034">34</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal <a class="el" href="one__tree__lower__bound_8h.html#a095b3978da7ad09782c0be1a6572e352">w</a> the current value of int max_iterations</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00034">34</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal therefore</td>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00034">34</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a717d5dae07519577a5ed09ac24a4708b">◆ </a></span>to</h2>
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<td class="memname">trees with all <a class="el" href="one__tree__lower__bound_8h.html#af86d4c4e6a18908cda194651a9ab7beb">degrees</a> equal to</td>
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<p>Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. </p>
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<p>You may obtain a copy of the License at </p><div class="fragment"><div class="line">http:<span class="comment">//www.apache.org/licenses/LICENSE-2.0</span></div></div><!-- fragment --><p> Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. An implementation of the Held-Karp symmetric Traveling Salesman (TSP) lower bound algorithm, inspired by "Estimating the Held-Karp lower bound for the
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geometric TSP" by Christine L. Valenzuela and Antonia J. Jones, European Journal of Operational Research, Volume 102, Issue 1, 1 October 1997, Pages 157-175.</p>
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<p>The idea is to compute minimum 1-trees to evaluate a lower bound to the corresponding TSP. A minimum 1-tree is a minimum spanning tree on all nodes but one, to which are added the two shortest edges from the left-out node to the nodes of the spanning tree. The sum of the cost of the edges of the minimum 1-tree is a lower bound to the cost of the TSP. In order to improve (increase) this lower bound, the idea is to add weights to each nodes, weights which are added to the cost function used when computing the 1-tree. If weight[i] is the weight of node i, the cost function therefore becomes weighed_cost(i,j) = cost(i,j) + weight[i] + weight[j]. One can see that w = weighed_cost(minimum 1-tree) - Sum(2 * weight[i]) = cost(minimum 1-tree) + Sum(weight[i] * (degree[i] - 2)) is a valid lower bound to the TSP: 1) let T be the set of 1-trees on the nodes; 2) let U be the set of tours on the nodes; U is a subset of T (tours are </p>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00034">34</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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<p class="definition">Definition at line <a class="el" href="one__tree__lower__bound_8h_source.html#l00034">34</a> of file <a class="el" href="one__tree__lower__bound_8h_source.html">one_tree_lower_bound.h</a>.</p>
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