1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) 20022018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)


4  *


5  * This file is part of HeuristicLab.


6  *


7  * HeuristicLab is free software: you can redistribute it and/or modify


8  * it under the terms of the GNU General Public License as published by


9  * the Free Software Foundation, either version 3 of the License, or


10  * (at your option) any later version.


11  *


12  * HeuristicLab is distributed in the hope that it will be useful,


13  * but WITHOUT ANY WARRANTY; without even the implied warranty of


14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the


15  * GNU General Public License for more details.


16  *


17  * You should have received a copy of the GNU General Public License


18  * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.


19  */


20  #endregion


21 


22  using System;


23  using System.Collections.Generic;


24  using System.Diagnostics;


25  using System.Globalization;


26  using System.Linq;


27  using HeuristicLab.Common;


28  using HeuristicLab.Core;


29  using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;


30  using HeuristicLab.Optimization.Operators;


31  using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;


32 


33  namespace HeuristicLab.Problems.DataAnalysis.Symbolic {


34  [StorableClass]


35  [Item("SymbolicExpressionTreeBottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottomup distance as a similarity metric.")]


36  public class SymbolicExpressionTreeBottomUpSimilarityCalculator : SolutionSimilarityCalculator {


37  private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };


38 


39  public SymbolicExpressionTreeBottomUpSimilarityCalculator() { }


40  protected override bool IsCommutative { get { return true; } }


41 


42  [StorableConstructor]


43  protected SymbolicExpressionTreeBottomUpSimilarityCalculator(bool deserializing)


44  : base(deserializing) {


45  }


46 


47  protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)


48  : base(original, cloner) {


49  }


50 


51  public override IDeepCloneable Clone(Cloner cloner) {


52  return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);


53  }


54 


55  public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {


56  if (t1 == t2)


57  return 1;


58 


59  var map = ComputeBottomUpMapping(t1.Root, t2.Root);


60  return 2.0 * map.Count / (t1.Length + t2.Length);


61  }


62 


63  public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {


64  if (leftSolution == rightSolution)


65  return 1.0;


66 


67  var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;


68  var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;


69 


70  if (t1 == null  t2 == null)


71  throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");


72 


73  var similarity = CalculateSimilarity(t1, t2);


74  if (similarity > 1.0)


75  throw new Exception("Similarity value cannot be greater than 1");


76 


77  return similarity;


78  }


79 


80  public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {


81  var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings


82  var compactedGraph = Compact(n1, n2);


83 


84  var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2


85  var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1


86 


87  // visit nodes in order of decreasing height to ensure correct mapping


88  var nodes1 = n1.IterateNodesPrefix().OrderByDescending(x => x.GetDepth()).ToList();


89  var nodes2 = n2.IterateNodesPrefix().ToList();


90  for (int i = 0; i < nodes1.Count; ++i) {


91  var v = nodes1[i];


92  if (forwardMap.ContainsKey(v))


93  continue;


94  var kv = compactedGraph[v];


95  ISymbolicExpressionTreeNode w = null;


96  for (int j = 0; j < nodes2.Count; ++j) {


97  var t = nodes2[j];


98  if (reverseMap.ContainsKey(t)  compactedGraph[t] != kv)


99  continue;


100  w = t;


101  break;


102  }


103  if (w == null) continue;


104 


105  // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly


106  // (as in the paper) because the trees are unordered (subtree order might differ). the solution is


107  // to sort subtrees from under commutative labels (this will work because the subtrees are isomorphic!)


108  // while iterating over the two subtrees


109  var vv = IterateBreadthOrdered(v, comparer).ToList();


110  var ww = IterateBreadthOrdered(w, comparer).ToList();


111  int len = Math.Min(vv.Count, ww.Count);


112  for (int j = 0; j < len; ++j) {


113  var s = vv[j];


114  var t = ww[j];


115  Debug.Assert(!reverseMap.ContainsKey(t));


116 


117  forwardMap[s] = t;


118  reverseMap[t] = s;


119  }


120  }


121 


122  return forwardMap;


123  }


124 


125  /// <summary>


126  /// Creates a compact representation of the two trees as a directed acyclic graph


127  /// </summary>


128  /// <param name="n1">The root of the first tree</param>


129  /// <param name="n2">The root of the second tree</param>


130  /// <returns>The compacted DAG representing the two trees</returns>


131  private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {


132  var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K


133  var labelMap = new Dictionary<string, GraphNode>(); // L


134  var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children


135 


136  var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F


137  var list = new List<GraphNode>();


138  var queue = new Queue<ISymbolicExpressionTreeNode>();


139 


140  foreach (var n in nodes) {


141  if (n.SubtreeCount == 0) {


142  var label = GetLabel(n);


143  if (!labelMap.ContainsKey(label)) {


144  var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };


145  labelMap[z.Label] = z;


146  }


147  nodeMap[n] = labelMap[label];


148  queue.Enqueue(n);


149  } else {


150  childrenCount[n] = n.SubtreeCount;


151  }


152  }


153  while (queue.Any()) {


154  var n = queue.Dequeue();


155  if (n.SubtreeCount > 0) {


156  bool found = false;


157  var label = n.Symbol.Name;


158  var depth = n.GetDepth();


159 


160  bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);


161  var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();


162  if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));


163 


164  for (int i = list.Count  1; i >= 0; i) {


165  var w = list[i];


166  if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))


167  continue;


168 


169  // sort V and W when the symbol is commutative because we are dealing with unordered trees


170  var m = w.SymbolicExpressionTreeNode;


171  var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();


172  if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));


173 


174  found = nSubtrees.SequenceEqual(mSubtrees);


175  if (found) {


176  nodeMap[n] = w;


177  break;


178  }


179  }


180 


181  if (!found) {


182  var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };


183  list.Add(w);


184  nodeMap[n] = w;


185  }


186  }


187 


188  if (n == n1  n == n2)


189  continue;


190 


191  var p = n.Parent;


192  if (p == null)


193  continue;


194 


195  childrenCount[p];


196 


197  if (childrenCount[p] == 0)


198  queue.Enqueue(p);


199  }


200 


201  return nodeMap;


202  }


203 


204  private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {


205  var list = new List<ISymbolicExpressionTreeNode> { node };


206  int i = 0;


207  while (i < list.Count) {


208  var n = list[i];


209  if (n.SubtreeCount > 0) {


210  var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;


211  list.AddRange(subtrees);


212  }


213  i++;


214  }


215  return list;


216  }


217 


218  private static string GetLabel(ISymbolicExpressionTreeNode node) {


219  if (node.SubtreeCount > 0)


220  return node.Symbol.Name;


221 


222  var constant = node as ConstantTreeNode;


223  if (constant != null)


224  return constant.Value.ToString(CultureInfo.InvariantCulture);


225 


226  var variable = node as VariableTreeNode;


227  if (variable != null)


228  return variable.Weight + variable.VariableName;


229 


230  return node.ToString();


231  }


232 


233  private class GraphNode {


234  public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;


235  public string Label;


236  public int Depth;


237  public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }


238  }


239  }


240  }

