[11219] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[12017] | 3 | * Copyright (C) 2002-2015 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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[12155] | 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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[12155] | 38 |
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[11910] | 39 | public SymbolicExpressionTreeBottomUpSimilarityCalculator() { }
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[12155] | 40 | protected override bool IsCommutative { get { return true; } }
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[11219] | 41 |
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[12287] | 42 | public bool MatchVariableWeights { get; set; }
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| 43 | public bool MatchConstantValues { get; set; }
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| 44 |
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[11918] | 45 | [StorableConstructor]
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[11921] | 46 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(bool deserializing)
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[11918] | 47 | : base(deserializing) {
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| 48 | }
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| 49 |
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[11910] | 50 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)
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[11486] | 51 | : base(original, cloner) {
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[11239] | 52 | }
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| 53 |
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[11219] | 54 | public override IDeepCloneable Clone(Cloner cloner) {
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[11910] | 55 | return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);
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[11219] | 56 | }
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| 57 |
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[11486] | 58 | public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
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| 59 | if (t1 == t2)
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| 60 | return 1;
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| 61 |
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| 62 | var map = ComputeBottomUpMapping(t1.Root, t2.Root);
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| 63 | return 2.0 * map.Count / (t1.Length + t2.Length);
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[11219] | 64 | }
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| 65 |
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| 66 | public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
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[12155] | 67 | if (leftSolution == rightSolution)
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| 68 | return 1.0;
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| 69 |
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[11219] | 70 | var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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| 71 | var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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| 72 |
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| 73 | if (t1 == null || t2 == null)
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| 74 | throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
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| 75 |
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[11486] | 76 | var similarity = CalculateSimilarity(t1, t2);
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[11224] | 77 | if (similarity > 1.0)
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| 78 | throw new Exception("Similarity value cannot be greater than 1");
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| 79 |
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| 80 | return similarity;
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[11219] | 81 | }
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| 82 |
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[11221] | 83 | public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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[11486] | 84 | 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] | 85 | var compactedGraph = Compact(n1, n2);
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[11219] | 86 |
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| 87 | var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
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| 88 | var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
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| 89 |
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[11225] | 90 | // visit nodes in order of decreasing height to ensure correct mapping
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[12017] | 91 | var nodes1 = n1.IterateNodesPrefix().OrderByDescending(x => x.GetDepth()).ToList();
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[11487] | 92 | var nodes2 = n2.IterateNodesPrefix().ToList();
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[11894] | 93 | for (int i = 0; i < nodes1.Count; ++i) {
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| 94 | var v = nodes1[i];
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[11225] | 95 | if (forwardMap.ContainsKey(v))
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| 96 | continue;
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[11219] | 97 | var kv = compactedGraph[v];
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| 98 | ISymbolicExpressionTreeNode w = null;
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[11894] | 99 | for (int j = 0; j < nodes2.Count; ++j) {
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| 100 | var t = nodes2[j];
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[11225] | 101 | if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
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| 102 | continue;
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[11219] | 103 | w = t;
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| 104 | break;
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| 105 | }
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| 106 | if (w == null) continue;
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| 107 |
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[12017] | 108 | // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly
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| 109 | // (as in the paper) because the trees are unordered (subtree order might differ). the solution is
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| 110 | // to sort subtrees from under commutative labels (this will work because the subtrees are isomorphic!)
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| 111 | // while iterating over the two subtrees
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[11894] | 112 | var vv = IterateBreadthOrdered(v, comparer).ToList();
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| 113 | var ww = IterateBreadthOrdered(w, comparer).ToList();
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| 114 | int len = Math.Min(vv.Count, ww.Count);
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| 115 | for (int j = 0; j < len; ++j) {
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| 116 | var s = vv[j];
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| 117 | var t = ww[j];
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[11486] | 118 | Debug.Assert(!reverseMap.ContainsKey(t));
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[11225] | 119 |
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[11219] | 120 | forwardMap[s] = t;
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| 121 | reverseMap[t] = s;
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| 122 | }
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| 123 | }
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| 124 |
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| 125 | return forwardMap;
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| 126 | }
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| 127 |
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| 128 | /// <summary>
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| 129 | /// Creates a compact representation of the two trees as a directed acyclic graph
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| 130 | /// </summary>
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[11229] | 131 | /// <param name="n1">The root of the first tree</param>
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| 132 | /// <param name="n2">The root of the second tree</param>
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[11219] | 133 | /// <returns>The compacted DAG representing the two trees</returns>
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[11229] | 134 | private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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| 135 | var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
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| 136 | var labelMap = new Dictionary<string, GraphNode>(); // L
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[11219] | 137 | var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
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| 138 |
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[11221] | 139 | var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
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[11487] | 140 | var list = new List<GraphNode>();
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[11219] | 141 | var queue = new Queue<ISymbolicExpressionTreeNode>();
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| 142 |
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| 143 | foreach (var n in nodes) {
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| 144 | if (n.SubtreeCount == 0) {
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[12017] | 145 | var label = GetLabel(n);
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[11229] | 146 | if (!labelMap.ContainsKey(label)) {
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| 147 | var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
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| 148 | labelMap[z.Label] = z;
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[11225] | 149 | }
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[11229] | 150 | nodeMap[n] = labelMap[label];
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[11219] | 151 | queue.Enqueue(n);
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| 152 | } else {
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| 153 | childrenCount[n] = n.SubtreeCount;
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| 154 | }
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| 155 | }
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| 156 | while (queue.Any()) {
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[11229] | 157 | var n = queue.Dequeue();
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| 158 | if (n.SubtreeCount > 0) {
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[11894] | 159 | bool found = false;
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[11229] | 160 | var label = n.Symbol.Name;
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| 161 | var depth = n.GetDepth();
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[11219] | 162 |
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[11894] | 163 | bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);
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| 164 | var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();
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| 165 | if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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[11219] | 166 |
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[11229] | 167 | for (int i = list.Count - 1; i >= 0; --i) {
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| 168 | var w = list[i];
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[11894] | 169 | if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))
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[11219] | 170 | continue;
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| 171 |
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| 172 | // sort V and W when the symbol is commutative because we are dealing with unordered trees
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[11229] | 173 | var m = w.SymbolicExpressionTreeNode;
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[11894] | 174 | var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();
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| 175 | if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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[11219] | 176 |
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[11894] | 177 | found = nSubtrees.SequenceEqual(mSubtrees);
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| 178 | if (found) {
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[11229] | 179 | nodeMap[n] = w;
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[11219] | 180 | break;
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| 181 | }
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[11229] | 182 | }
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[11219] | 183 |
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| 184 | if (!found) {
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[11486] | 185 | var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
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[11229] | 186 | list.Add(w);
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| 187 | nodeMap[n] = w;
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| 188 | }
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| 189 | }
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[11219] | 190 |
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[11486] | 191 | if (n == n1 || n == n2)
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| 192 | continue;
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| 193 |
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[11229] | 194 | var p = n.Parent;
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[11219] | 195 | if (p == null)
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| 196 | continue;
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| 197 |
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| 198 | childrenCount[p]--;
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| 199 |
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| 200 | if (childrenCount[p] == 0)
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| 201 | queue.Enqueue(p);
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[11220] | 202 | }
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[11219] | 203 |
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[11229] | 204 | return nodeMap;
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[11219] | 205 | }
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| 206 |
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[11486] | 207 | private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
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[11219] | 208 | var list = new List<ISymbolicExpressionTreeNode> { node };
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| 209 | int i = 0;
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| 210 | while (i < list.Count) {
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| 211 | var n = list[i];
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| 212 | if (n.SubtreeCount > 0) {
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[11486] | 213 | var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
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[11219] | 214 | list.AddRange(subtrees);
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| 215 | }
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| 216 | i++;
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| 217 | }
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| 218 | return list;
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| 219 | }
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| 220 |
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[12287] | 221 | private string GetLabel(ISymbolicExpressionTreeNode node) {
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[11486] | 222 | if (node.SubtreeCount > 0)
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| 223 | return node.Symbol.Name;
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| 224 |
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| 225 | var constant = node as ConstantTreeNode;
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| 226 | if (constant != null)
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[12287] | 227 | return MatchConstantValues ? constant.Value.ToString(CultureInfo.InvariantCulture) : node.Symbol.Name;
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[11965] | 228 |
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[11486] | 229 | var variable = node as VariableTreeNode;
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[11965] | 230 | if (variable != null)
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[12287] | 231 | return MatchVariableWeights ? variable.Weight + variable.VariableName : variable.VariableName;
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[11486] | 232 |
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| 233 | return node.ToString();
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| 234 | }
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| 235 |
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[11229] | 236 | private class GraphNode {
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| 237 | public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
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| 238 | public string Label;
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| 239 | public int Depth;
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[11894] | 240 | public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
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[11219] | 241 | }
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| 242 | }
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| 243 | }
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