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<a href="arc__flow__builder_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// This code builds an arc-flow generator for vector-bin-packing problems.</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// see https://people.math.gatech.edu/~tetali/PUBLIS/CKPT.pdf</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// It implements a non-recursive version of algorithm 1 described in:</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// http://www.dcc.fc.up.pt/~fdabrandao/papers/arcflow_manuscript.pdf</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// And in (poster version):</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// http://www.dcc.fc.up.pt/~fdabrandao/papers/arcflow_poster.pdf</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// Available at:</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// https://drive.google.com/open?id=1y-Vs1orv-QHO4lb2sjVWrZr9GQd5d2st</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// https://drive.google.com/open?id=1fsWRqgNJ_3ClrhoKIeVc1EOd5s8Mj33i (poster)</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// Some improvements are not yet implemented:</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// - Lifted stated: when storing a state of the dynamic programming forward</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// pass, one can lift a state. A lifted state of a state S is a maximal</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// increase of S that does not lose any state in the forward pass.</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// A simple example is the following:</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// bin, 1 dimension, capacity 5</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// 2 item of size 2.</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// After adding item 1 in the DP pass, the state is (2).</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// The lifted state is (3) that is (5) - (2) which is the maximal increase</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// of (2) that does not loose any state.</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// To limit time spent computing this, one can lift a state only if the</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// remaining number of item is below a threshold.</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// - Disable the backward pass (compress state towards the bin capacity).</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Although this reduces the graph a lot, this simplication is not valid</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// when the cost is not the number of bins, but a function of the capacity</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// used (useful for fair allocation).</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#ifndef OR_TOOLS_PACKING_ARC_FLOW_BUILDER_H_</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="preprocessor">#define OR_TOOLS_PACKING_ARC_FLOW_BUILDER_H_</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include <cstdint></span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include <set></span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include <vector></span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">namespace </span>packing {</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// Arc flow gragh built from a vector bin packing problem.</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// The first node will always be the source. The last will always be the sink</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// of the arc-flow graph.</span></div><div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html"> 56</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html">ArcFlowGraph</a> {</div><div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html"> 57</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html">Arc</a> {</div><div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a07a87b2e6ed927503e2f95f119c9fc23"> 58</a></span>  <span class="keywordtype">int</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a07a87b2e6ed927503e2f95f119c9fc23">source</a>;</div><div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a17744967a9eda456c21490b51b74917a"> 59</a></span>  <span class="keywordtype">int</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a17744967a9eda456c21490b51b74917a">destination</a>;</div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a0540161270ce77bf9080009fb3263264"> 60</a></span>  <span class="keywordtype">int</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a0540161270ce77bf9080009fb3263264">item_index</a>;</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// Needed for std::set.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#aa35720e78eab1f8a077d383799ebed93">operator<</a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html">Arc</a>& other) <span class="keyword">const</span>;</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  };</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> </div><div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#ab3158b0035dffc988c5c8051c97fb37a"> 66</a></span>  std::vector<Arc> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#ab3158b0035dffc988c5c8051c97fb37a">arcs</a>;</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// All the nodes explored during the DP phase.</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// In the forward pass, these are the consumed capacity of the bin at this</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// state. In the backward pass, this is pushed up towards the max capacity</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// of the bin. In the final compression phase, this is pushed down towards</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// the initial zero state.</span></div><div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#a405100e4926c5c9e6f758d909ce466d6"> 72</a></span>  std::vector<std::vector<int>> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#a405100e4926c5c9e6f758d909ce466d6">nodes</a>;</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// Debug info.</span></div><div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#adb8bf668c7c57251a2afc53d91f8c079"> 74</a></span>  int64_t <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#adb8bf668c7c57251a2afc53d91f8c079">num_dp_states</a>;</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> };</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Main method.</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Arc flow builder. The input must enforce the following constraints:</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// - item_dimensions_by_type.size() == demand_by_type.size() == num types</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// - for each type t:</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// item_dimensions_by_type[t].size() == bin_dimensions.size() ==</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// num_dimensions</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <a class="code" href="structoperations__research_1_1packing_1_1_arc_flow_graph.html">ArcFlowGraph</a> <a class="code" href="namespaceoperations__research_1_1packing.html#abf4185c48db1dd3fb87f9d05081de446">BuildArcFlowGraph</a>(</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">const</span> std::vector<int>& bin_dimensions,</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> std::vector<std::vector<int>>& item_dimensions_by_type,</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">const</span> std::vector<int>& demand_by_type);</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> } <span class="comment">// namespace packing</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> } <span class="comment">// namespace operations_research</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="preprocessor">#endif // OR_TOOLS_PACKING_ARC_FLOW_BUILDER_H_</span></div><div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc_html_aa35720e78eab1f8a077d383799ebed93"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#aa35720e78eab1f8a077d383799ebed93">operations_research::packing::ArcFlowGraph::Arc::operator<</a></div><div class="ttdeci">bool operator<(const Arc &other) const</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8cc_source.html#l00393">arc_flow_builder.cc:393</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_html_a405100e4926c5c9e6f758d909ce466d6"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#a405100e4926c5c9e6f758d909ce466d6">operations_research::packing::ArcFlowGraph::nodes</a></div><div class="ttdeci">std::vector< std::vector< int > > nodes</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00072">arc_flow_builder.h:72</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_html_ab3158b0035dffc988c5c8051c97fb37a"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#ab3158b0035dffc988c5c8051c97fb37a">operations_research::packing::ArcFlowGraph::arcs</a></div><div class="ttdeci">std::vector< Arc > arcs</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00066">arc_flow_builder.h:66</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc_html_a07a87b2e6ed927503e2f95f119c9fc23"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a07a87b2e6ed927503e2f95f119c9fc23">operations_research::packing::ArcFlowGraph::Arc::source</a></div><div class="ttdeci">int source</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00058">arc_flow_builder.h:58</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc_html_a17744967a9eda456c21490b51b74917a"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a17744967a9eda456c21490b51b74917a">operations_research::packing::ArcFlowGraph::Arc::destination</a></div><div class="ttdeci">int destination</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00059">arc_flow_builder.h:59</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc_html_a0540161270ce77bf9080009fb3263264"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html#a0540161270ce77bf9080009fb3263264">operations_research::packing::ArcFlowGraph::Arc::item_index</a></div><div class="ttdeci">int item_index</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00060">arc_flow_builder.h:60</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_html_adb8bf668c7c57251a2afc53d91f8c079"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph.html#adb8bf668c7c57251a2afc53d91f8c079">operations_research::packing::ArcFlowGraph::num_dp_states</a></div><div class="ttdeci">int64_t num_dp_states</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00074">arc_flow_builder.h:74</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_html"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph.html">operations_research::packing::ArcFlowGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00056">arc_flow_builder.h:56</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1packing_html_abf4185c48db1dd3fb87f9d05081de446"><div class="ttname"><a href="namespaceoperations__research_1_1packing.html#abf4185c48db1dd3fb87f9d05081de446">operations_research::packing::BuildArcFlowGraph</a></div><div class="ttdeci">ArcFlowGraph BuildArcFlowGraph(const std::vector< int > &bin_dimensions, const std::vector< std::vector< int >> &item_dimensions_by_type, const std::vector< int > &demand_by_type)</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8cc_source.html#l00399">arc_flow_builder.cc:399</a></div></div>
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<div class="ttc" id="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc_html"><div class="ttname"><a href="structoperations__research_1_1packing_1_1_arc_flow_graph_1_1_arc.html">operations_research::packing::ArcFlowGraph::Arc</a></div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8h_source.html#l00057">arc_flow_builder.h:57</a></div></div>
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