[11219] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[14186] | 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[11219] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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[11486] | 24 | using System.Diagnostics;
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| 25 | using System.Globalization;
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[11219] | 26 | using System.Linq;
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| 27 | using HeuristicLab.Common;
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| 28 | using HeuristicLab.Core;
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| 29 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 30 | using HeuristicLab.Optimization.Operators;
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| 31 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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| 32 |
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[11221] | 33 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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[11219] | 34 | [StorableClass]
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[11910] | 35 | [Item("SymbolicExpressionTreeBottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
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[12281] | 36 | public class SymbolicExpressionTreeBottomUpSimilarityCalculator : SolutionSimilarityCalculator {
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[11486] | 37 | private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
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[12280] | 38 |
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[12281] | 39 | public SymbolicExpressionTreeBottomUpSimilarityCalculator() { }
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[12280] | 40 | protected override bool IsCommutative { get { return true; } }
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| 41 |
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[11918] | 42 | [StorableConstructor]
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[11947] | 43 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(bool deserializing)
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[11918] | 44 | : base(deserializing) {
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| 45 | }
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| 46 |
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[11910] | 47 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)
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[11486] | 48 | : base(original, cloner) {
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[11239] | 49 | }
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| 50 |
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[11219] | 51 | public override IDeepCloneable Clone(Cloner cloner) {
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[11910] | 52 | return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);
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[11219] | 53 | }
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| 54 |
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[11486] | 55 | public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
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| 56 | if (t1 == t2)
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| 57 | return 1;
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| 58 |
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| 59 | var map = ComputeBottomUpMapping(t1.Root, t2.Root);
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| 60 | return 2.0 * map.Count / (t1.Length + t2.Length);
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[11219] | 61 | }
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| 62 |
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| 63 | public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
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[12281] | 64 | if (leftSolution == rightSolution)
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| 65 | return 1.0;
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| 66 |
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[11219] | 67 | var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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| 68 | var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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| 69 |
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| 70 | if (t1 == null || t2 == null)
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| 71 | throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
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| 72 |
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[11486] | 73 | var similarity = CalculateSimilarity(t1, t2);
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[11224] | 74 | if (similarity > 1.0)
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| 75 | throw new Exception("Similarity value cannot be greater than 1");
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| 76 |
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| 77 | return similarity;
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[11219] | 78 | }
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| 79 |
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[11221] | 80 | public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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[11486] | 81 | var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings
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[11221] | 82 | var compactedGraph = Compact(n1, n2);
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[11219] | 83 |
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| 84 | var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
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| 85 | var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
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| 86 |
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[11225] | 87 | // visit nodes in order of decreasing height to ensure correct mapping
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[11986] | 88 | var nodes1 = n1.IterateNodesPrefix().OrderByDescending(x => x.GetDepth()).ToList();
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[11487] | 89 | var nodes2 = n2.IterateNodesPrefix().ToList();
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[11894] | 90 | for (int i = 0; i < nodes1.Count; ++i) {
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| 91 | var v = nodes1[i];
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[11225] | 92 | if (forwardMap.ContainsKey(v))
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| 93 | continue;
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[11219] | 94 | var kv = compactedGraph[v];
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| 95 | ISymbolicExpressionTreeNode w = null;
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[11894] | 96 | for (int j = 0; j < nodes2.Count; ++j) {
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| 97 | var t = nodes2[j];
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[11225] | 98 | if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
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| 99 | continue;
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[11219] | 100 | w = t;
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| 101 | break;
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| 102 | }
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| 103 | if (w == null) continue;
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| 104 |
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[11986] | 105 | // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly
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| 106 | // (as in the paper) because the trees are unordered (subtree order might differ). the solution is
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| 107 | // to sort subtrees from under commutative labels (this will work because the subtrees are isomorphic!)
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| 108 | // while iterating over the two subtrees
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[11894] | 109 | var vv = IterateBreadthOrdered(v, comparer).ToList();
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| 110 | var ww = IterateBreadthOrdered(w, comparer).ToList();
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| 111 | int len = Math.Min(vv.Count, ww.Count);
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| 112 | for (int j = 0; j < len; ++j) {
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| 113 | var s = vv[j];
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| 114 | var t = ww[j];
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[11486] | 115 | Debug.Assert(!reverseMap.ContainsKey(t));
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[11225] | 116 |
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[11219] | 117 | forwardMap[s] = t;
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| 118 | reverseMap[t] = s;
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| 119 | }
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| 120 | }
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| 121 |
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| 122 | return forwardMap;
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| 123 | }
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| 124 |
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| 125 | /// <summary>
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| 126 | /// Creates a compact representation of the two trees as a directed acyclic graph
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| 127 | /// </summary>
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[11229] | 128 | /// <param name="n1">The root of the first tree</param>
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| 129 | /// <param name="n2">The root of the second tree</param>
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[11219] | 130 | /// <returns>The compacted DAG representing the two trees</returns>
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[11229] | 131 | private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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| 132 | var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
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| 133 | var labelMap = new Dictionary<string, GraphNode>(); // L
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[11219] | 134 | var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
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| 135 |
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[11221] | 136 | var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
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[11487] | 137 | var list = new List<GraphNode>();
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[11219] | 138 | var queue = new Queue<ISymbolicExpressionTreeNode>();
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| 139 |
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| 140 | foreach (var n in nodes) {
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| 141 | if (n.SubtreeCount == 0) {
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[11986] | 142 | var label = GetLabel(n);
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[11229] | 143 | if (!labelMap.ContainsKey(label)) {
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| 144 | var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
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| 145 | labelMap[z.Label] = z;
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[11225] | 146 | }
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[11229] | 147 | nodeMap[n] = labelMap[label];
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[11219] | 148 | queue.Enqueue(n);
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| 149 | } else {
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| 150 | childrenCount[n] = n.SubtreeCount;
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| 151 | }
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| 152 | }
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| 153 | while (queue.Any()) {
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[11229] | 154 | var n = queue.Dequeue();
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| 155 | if (n.SubtreeCount > 0) {
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[11894] | 156 | bool found = false;
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[11229] | 157 | var label = n.Symbol.Name;
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| 158 | var depth = n.GetDepth();
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[11219] | 159 |
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[11894] | 160 | bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);
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| 161 | var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();
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| 162 | if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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[11219] | 163 |
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[11229] | 164 | for (int i = list.Count - 1; i >= 0; --i) {
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| 165 | var w = list[i];
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[11894] | 166 | if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))
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[11219] | 167 | continue;
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| 168 |
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| 169 | // sort V and W when the symbol is commutative because we are dealing with unordered trees
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[11229] | 170 | var m = w.SymbolicExpressionTreeNode;
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[11894] | 171 | var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();
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| 172 | if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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[11219] | 173 |
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[11894] | 174 | found = nSubtrees.SequenceEqual(mSubtrees);
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| 175 | if (found) {
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[11229] | 176 | nodeMap[n] = w;
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[11219] | 177 | break;
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| 178 | }
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[11229] | 179 | }
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[11219] | 180 |
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| 181 | if (!found) {
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[11486] | 182 | var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
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[11229] | 183 | list.Add(w);
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| 184 | nodeMap[n] = w;
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| 185 | }
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| 186 | }
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[11219] | 187 |
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[11486] | 188 | if (n == n1 || n == n2)
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| 189 | continue;
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| 190 |
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[11229] | 191 | var p = n.Parent;
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[11219] | 192 | if (p == null)
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| 193 | continue;
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| 194 |
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| 195 | childrenCount[p]--;
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| 196 |
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| 197 | if (childrenCount[p] == 0)
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| 198 | queue.Enqueue(p);
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[11220] | 199 | }
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[11219] | 200 |
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[11229] | 201 | return nodeMap;
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[11219] | 202 | }
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| 203 |
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[11486] | 204 | private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
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[11219] | 205 | var list = new List<ISymbolicExpressionTreeNode> { node };
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| 206 | int i = 0;
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| 207 | while (i < list.Count) {
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| 208 | var n = list[i];
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| 209 | if (n.SubtreeCount > 0) {
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[11486] | 210 | var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
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[11219] | 211 | list.AddRange(subtrees);
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| 212 | }
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| 213 | i++;
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| 214 | }
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| 215 | return list;
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| 216 | }
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| 217 |
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[11986] | 218 | private static string GetLabel(ISymbolicExpressionTreeNode node) {
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[11486] | 219 | if (node.SubtreeCount > 0)
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| 220 | return node.Symbol.Name;
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| 221 |
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| 222 | var constant = node as ConstantTreeNode;
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| 223 | if (constant != null)
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[11964] | 224 | return constant.Value.ToString(CultureInfo.InvariantCulture);
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| 225 |
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[11486] | 226 | var variable = node as VariableTreeNode;
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[11964] | 227 | if (variable != null)
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| 228 | return variable.Weight + variable.VariableName;
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[11486] | 229 |
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| 230 | return node.ToString();
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| 231 | }
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| 232 |
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[11229] | 233 | private class GraphNode {
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| 234 | public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
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| 235 | public string Label;
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| 236 | public int Depth;
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[11894] | 237 | public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
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[11219] | 238 | }
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| 239 | }
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| 240 | }
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