1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) 20022014 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.Linq;


25  using HeuristicLab.Common;


26  using HeuristicLab.Core;


27  using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;


28  using HeuristicLab.Optimization.Operators;


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


30 


31  namespace HeuristicLab.Problems.DataAnalysis.Symbolic {


32  [StorableClass]


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


34  public class BottomUpSimilarityCalculator : SingleObjectiveSolutionSimilarityCalculator {


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


36 


37  public BottomUpSimilarityCalculator() { }


38 


39  public override IDeepCloneable Clone(Cloner cloner) {


40  return new BottomUpSimilarityCalculator(this, cloner);


41  }


42 


43  protected BottomUpSimilarityCalculator(BottomUpSimilarityCalculator original, Cloner cloner)


44  : base(original, cloner) {


45  }


46 


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


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


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


50 


51  if (t1 == null  t2 == null)


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


53 


54  var similarity = CalculateSolutionSimilarity(t1, t2);


55  if (similarity > 1.0)


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


57 


58  return similarity;


59  }


60 


61  public double CalculateSolutionSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {


62  if (t1 == t2)


63  return 1;


64 


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


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


67  }


68 


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


70  var compactedGraph = Compact(n1, n2);


71 


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


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


74 


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


76  foreach (var v in n1.IterateNodesPrefix().OrderByDescending(x => compactedGraph[x].Depth)) {


77  if (forwardMap.ContainsKey(v))


78  continue;


79  var kv = compactedGraph[v];


80  ISymbolicExpressionTreeNode w = null;


81  foreach (var t in n2.IterateNodesPrefix()) {


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


83  continue;


84  w = t;


85  break;


86  }


87  if (w == null) continue;


88 


89  // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly (as in the paper) because the trees are unordered (subtree order might differ)


90  // the solution is to sort subtrees by label using IterateBreadthOrdered (this will work because the subtrees are isomorphic!) and simultaneously iterate over the two subtrees


91  var eV = IterateBreadthOrdered(v).GetEnumerator();


92  var eW = IterateBreadthOrdered(w).GetEnumerator();


93 


94  while (eV.MoveNext() && eW.MoveNext()) {


95  var s = eV.Current;


96  var t = eW.Current;


97 


98  if (reverseMap.ContainsKey(t)) {


99  throw new Exception("A mapping to this node already exists.");


100  }


101 


102  forwardMap[s] = t;


103  reverseMap[t] = s;


104  }


105  }


106 


107  return forwardMap;


108  }


109 


110  /// <summary>


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


112  /// </summary>


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


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


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


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


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


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


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


120 


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


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


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


124 


125  foreach (var n in nodes) {


126  if (n.SubtreeCount == 0) {


127  var label = n.ToString();


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


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


130  labelMap[z.Label] = z;


131  list.Add(z);


132  }


133  nodeMap[n] = labelMap[label];


134  queue.Enqueue(n);


135  } else {


136  childrenCount[n] = n.SubtreeCount;


137  }


138  }


139  while (queue.Any()) {


140  var n = queue.Dequeue();


141 


142  if (n.SubtreeCount > 0) {


143  var label = n.Symbol.Name;


144  bool found = false;


145  var depth = n.GetDepth();


146 


147  bool sort = commutativeSymbols.Contains(label);


148  var nNodes = n.Subtrees.Select(x => nodeMap[x]).ToList();


149  if (sort) nNodes.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));


150 


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


152  var w = list[i];


153 


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


155  continue;


156 


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


158  var m = w.SymbolicExpressionTreeNode;


159  var mNodes = m.Subtrees.Select(x => nodeMap[x]).ToList();


160  if (sort) mNodes.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));


161 


162  if (nNodes.SequenceEqual(mNodes)) {


163  nodeMap[n] = w;


164  found = true;


165  break;


166  }


167  }


168 


169  if (!found) {


170  var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth, ChildrenCount = n.SubtreeCount };


171  list.Add(w);


172  nodeMap[n] = w;


173  }


174  }


175 


176  var p = n.Parent;


177  if (p == null)


178  continue;


179 


180  childrenCount[p];


181 


182  if (childrenCount[p] == 0)


183  queue.Enqueue(p);


184  }


185 


186  return nodeMap;


187  }


188 


189  private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node) {


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


191  int i = 0;


192  while (i < list.Count) {


193  var n = list[i];


194  if (n.SubtreeCount > 0) {


195  var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x.ToString(), StringComparer.Ordinal) : n.Subtrees;


196  list.AddRange(subtrees);


197  }


198  i++;


199  }


200  return list;


201  }


202 


203  private class GraphNode {


204  public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;


205  public string Label;


206  public int Depth;


207  public int ChildrenCount;


208  }


209  }


210  }

