#region License Information
/* HeuristicLab
* Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
*
* This file is part of HeuristicLab.
*
* HeuristicLab is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* HeuristicLab is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with HeuristicLab. If not, see .
*/
#endregion
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using HeuristicLab.Optimization.Operators;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
[StorableClass]
[Item("SymbolicExpressionTreeBottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
public class SymbolicExpressionTreeBottomUpSimilarityCalculator : SolutionSimilarityCalculator {
private readonly HashSet commutativeSymbols = new HashSet { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
public SymbolicExpressionTreeBottomUpSimilarityCalculator() { }
protected override bool IsCommutative { get { return true; } }
public bool MatchVariableWeights { get; set; }
public bool MatchConstantValues { get; set; }
[StorableConstructor]
protected SymbolicExpressionTreeBottomUpSimilarityCalculator(bool deserializing)
: base(deserializing) {
}
protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)
: base(original, cloner) {
}
public override IDeepCloneable Clone(Cloner cloner) {
return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);
}
public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
if (t1 == t2)
return 1;
var map = ComputeBottomUpMapping(t1.Root, t2.Root);
return 2.0 * map.Count / (t1.Length + t2.Length);
}
public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
if (leftSolution == rightSolution)
return 1.0;
var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
if (t1 == null || t2 == null)
throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
var similarity = CalculateSimilarity(t1, t2);
if (similarity > 1.0)
throw new Exception("Similarity value cannot be greater than 1");
return similarity;
}
public Dictionary ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings
var compactedGraph = Compact(n1, n2);
var forwardMap = new Dictionary(); // nodes of t1 => nodes of t2
var reverseMap = new Dictionary(); // nodes of t2 => nodes of t1
// visit nodes in order of decreasing height to ensure correct mapping
var nodes1 = n1.IterateNodesPrefix().OrderByDescending(x => x.GetDepth()).ToList();
var nodes2 = n2.IterateNodesPrefix().ToList();
for (int i = 0; i < nodes1.Count; ++i) {
var v = nodes1[i];
if (forwardMap.ContainsKey(v))
continue;
var kv = compactedGraph[v];
ISymbolicExpressionTreeNode w = null;
for (int j = 0; j < nodes2.Count; ++j) {
var t = nodes2[j];
if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
continue;
w = t;
break;
}
if (w == null) continue;
// 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). the solution is
// to sort subtrees from under commutative labels (this will work because the subtrees are isomorphic!)
// while iterating over the two subtrees
var vv = IterateBreadthOrdered(v, comparer).ToList();
var ww = IterateBreadthOrdered(w, comparer).ToList();
int len = Math.Min(vv.Count, ww.Count);
for (int j = 0; j < len; ++j) {
var s = vv[j];
var t = ww[j];
Debug.Assert(!reverseMap.ContainsKey(t));
forwardMap[s] = t;
reverseMap[t] = s;
}
}
return forwardMap;
}
///
/// Creates a compact representation of the two trees as a directed acyclic graph
///
/// The root of the first tree
/// The root of the second tree
/// The compacted DAG representing the two trees
private Dictionary Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
var nodeMap = new Dictionary(); // K
var labelMap = new Dictionary(); // L
var childrenCount = new Dictionary(); // Children
var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
var list = new List();
var queue = new Queue();
foreach (var n in nodes) {
if (n.SubtreeCount == 0) {
var label = GetLabel(n);
if (!labelMap.ContainsKey(label)) {
var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
labelMap[z.Label] = z;
}
nodeMap[n] = labelMap[label];
queue.Enqueue(n);
} else {
childrenCount[n] = n.SubtreeCount;
}
}
while (queue.Any()) {
var n = queue.Dequeue();
if (n.SubtreeCount > 0) {
bool found = false;
var label = n.Symbol.Name;
var depth = n.GetDepth();
bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);
var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();
if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
for (int i = list.Count - 1; i >= 0; --i) {
var w = list[i];
if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))
continue;
// sort V and W when the symbol is commutative because we are dealing with unordered trees
var m = w.SymbolicExpressionTreeNode;
var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();
if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
found = nSubtrees.SequenceEqual(mSubtrees);
if (found) {
nodeMap[n] = w;
break;
}
}
if (!found) {
var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
list.Add(w);
nodeMap[n] = w;
}
}
if (n == n1 || n == n2)
continue;
var p = n.Parent;
if (p == null)
continue;
childrenCount[p]--;
if (childrenCount[p] == 0)
queue.Enqueue(p);
}
return nodeMap;
}
private IEnumerable IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
var list = new List { node };
int i = 0;
while (i < list.Count) {
var n = list[i];
if (n.SubtreeCount > 0) {
var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
list.AddRange(subtrees);
}
i++;
}
return list;
}
private string GetLabel(ISymbolicExpressionTreeNode node) {
if (node.SubtreeCount > 0)
return node.Symbol.Name;
var constant = node as ConstantTreeNode;
if (constant != null)
return MatchConstantValues ? constant.Value.ToString(CultureInfo.InvariantCulture) : node.Symbol.Name;
var variable = node as VariableTreeNode;
if (variable != null)
return MatchVariableWeights ? variable.Weight + variable.VariableName : variable.VariableName;
return node.ToString();
}
private class GraphNode {
public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
public string Label;
public int Depth;
public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
}
}
}