private void AddEdgesToMST(Graph mst, List<Edge> edges)
{
foreach (var edge in edges)
{
if (edge.WhereBoth(x => mst.GetDegree(x) > 0)) //Both vertices of this edge are in the MST, introducing this edge creates cycle!
{
var v1 = edge.Either();
var v2 = edge.Other(v1);
var components = mst.CreateComponentTable();
if (components[v1] == components[v2])
{
// Both are in the same component, and a path exists.
// Travel the path to see if adding this edge makes it cheaper
var path = Algorithms.DijkstraPath(v1, v2, mst);
// However, we can remove a set of edges between two nodes
// When going from T1 to T3
// E.g.: T1 - v2 - v3 - v4 - T2 - v5 - v6 - T3
// The edges between T1, v2, v3, v4, T2 cost more than the path between T1 and T3.
// Removing those edges, and adding the new edge from T1 to T3, also connects
// T1 to T2, so still a tree!
var from = path.Start;
var last = path.Start;
int betweenTerminals = 0;
var subtractedPath = new Path(path.Start);
List<Edge> edgesInSubtraction = new List<Edge>();
Dictionary<Edge, List<Edge>> subtractions = new Dictionary<Edge, List<Edge>>();
for (int i = 0; i < path.Edges.Count; i++)
{
var pe = path.Edges[i];
betweenTerminals += pe.Cost;
last = pe.Other(last);
edgesInSubtraction.Add(pe);
if (mst.GetDegree(last) > 2 || mst.Terminals.Contains(last) || i == path.Edges.Count - 1)
{
var subtractedEdge = new Edge(from, last, betweenTerminals);
subtractions.Add(subtractedEdge, edgesInSubtraction);
edgesInSubtraction = new List<Edge>();
subtractedPath.Edges.Add(subtractedEdge);
from = last;
betweenTerminals = 0;
}
}
var mostCostly = subtractedPath.Edges[0];
for (int i = 1; i < subtractedPath.Edges.Count; i++)
{
if (subtractedPath.Edges[i].Cost > mostCostly.Cost)
mostCostly = subtractedPath.Edges[i];
}
if (mostCostly.Cost >= edge.Cost)
{
foreach (var e in subtractions[mostCostly])
mst.RemoveEdge(e, false);
mst.AddEdge(edge);
}
}
else // Connect the two disconnected components!
mst.AddEdge(edge);
}
else
mst.AddEdge(edge);
}
}
private void GetNeighbourSolutionWithSteinerNodeInsertionNeighbourhood(int breakout)
{
foreach (var degreeZero in CurrentSolution.Vertices.Where(x => CurrentSolution.GetDegree(x) == 0).ToList())
CurrentSolution.RemoveVertex(degreeZero);
var workingSolution = CurrentSolution.Clone();
// 1. Pick a random starting key vertex (deg > 2)
// 2. Follow path starting from one of its edges
// 3. After finding another key node in current solution, take this path as new path to insert
// 4. Optionally, explore in each starting direction from initial node and insert cheapest / most expensive path
var startingKeyNodes =
workingSolution.Vertices.Where(x => workingSolution.GetDegree(x) > 2)
.OrderByDescending(x => x.AverageScore)
.Take(breakout * (int)Math.Log(ProblemInstance.NumberOfVertices) * (int)Math.Log(ProblemInstance.NumberOfVertices))
.ToList();
var previousNodes = workingSolution.Vertices.Where(x => workingSolution.GetDegree(x) > 0).ToList();
foreach (var startingKeyNode in startingKeyNodes)
{
var path = new Path(startingKeyNode);
var edge =
ProblemInstance.GetEdgesForVertex(startingKeyNode)
.OrderByDescending(x => x.Other(startingKeyNode).AverageScore)
.Where(x => !workingSolution.ContainsEdge(x))
.Take(ProblemInstance.GetDegree(startingKeyNode)/2 + 1)
.RandomElement();
if (edge == null)
continue;
var fromVertex = startingKeyNode;
var toVertex = edge.Other(fromVertex);
path.Edges.Add(edge);
while (!workingSolution.ContainsVertex(toVertex) || workingSolution.GetDegree(toVertex) <= 2)
{
var prevFromVertex = fromVertex;
fromVertex = toVertex;
var edges = ProblemInstance.GetEdgesForVertex(fromVertex).ToList();
edge = edges.Where(x => x.WhereBoth(y => y != prevFromVertex) && x.WhereOne(y => !path.Vertices.Contains(y)))
.OrderByDescending(x => x.Other(fromVertex).Score)
.Take((ProblemInstance.GetDegree(fromVertex)/2) + 1)
.RandomElement();
if (edge == null)
break;
toVertex = edge.Other(fromVertex);
path.Edges.Add(edge);
}
foreach (var vertex in path.Vertices.Where(x => !workingSolution.ContainsVertex(x)))
workingSolution.AddVertex(vertex);
AddEdgesToMST(workingSolution, path.Edges);
//Prune current solution
IEnumerable<Vertex> degreeOne;
while ((degreeOne =
workingSolution.Vertices.Except(ProblemInstance.Terminals)
.Where(x => workingSolution.GetDegree(x) <= 1)).Any())
{
foreach (var degreeZeroSteiner in degreeOne.ToList())
workingSolution.RemoveVertex(degreeZeroSteiner);
}
//if (workingSolution.ComponentCheck() > 1)
// Debugger.Break();
//var mst = Algorithms.Kruskal(workingSolution);
//if (mst.TotalCost < workingSolution.TotalCost)
// Debugger.Break();
if (workingSolution.TotalCost < CurrentSolution.TotalCost)
{
//Console.Beep(2000, 150);
//Console.Beep(2100, 150);
foreach (var vertex in ProblemInstance.Vertices.Except(ProblemInstance.Terminals)
.Intersect(workingSolution.Vertices))
vertex.IncreaseScore(3);
CurrentSolution = workingSolution.Clone();
return;
}
}
foreach (var vertex in ProblemInstance.Vertices.Intersect(workingSolution.Vertices.Where(x => workingSolution.GetDegree(x) > 0).Except(previousNodes)))
vertex.DecreaseScore(1);
}
public static Dictionary<Vertex, Path> DijkstraPathToAll(Vertex from, Graph graph, bool onlyTerminals)
{
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes =
new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
Dictionary<Vertex, Path> paths = new Dictionary<Vertex, Path>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var n = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, n);
}
while (paths.Count < (onlyTerminals ? graph.Terminals.Count - 1 : graph.NumberOfVertices - 1))
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
if (current != from && (!onlyTerminals || graph.Terminals.Contains(current)))
{
// Travel back the path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = current;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
paths[current] = path;
}
}
return paths;
}
public static Path DijkstraPath(Vertex from, Vertex to, Graph graph)
{
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes =
new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var n = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, n);
comingFrom.Add(vertex, null);
}
while (!visited.Contains(to))
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
}
// Now travel back, to find the actual path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = to;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
return path;
}
public static List<Path> NearestTerminals(Vertex from, Graph graph, int n)
{
List<Path> foundPaths = new List<Path>();
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes = new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
if (graph.Terminals.Contains(from))
foundPaths.Add(new Path(from));
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var node = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, node);
comingFrom.Add(vertex, null);
}
while (!labels.IsEmpty() && foundPaths.Count < n)
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
if (graph.Terminals.Contains(current) && current != from)
{
// Now travel back, to find the actual path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = current;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
foundPaths.Add(path);
}
}
return foundPaths;
}
public static Graph RunSolver(Graph graph)
{
var solution = new Graph(graph.Vertices);
DijkstraState state = new DijkstraState();
// Create the states needed for every execution of the Dijkstra algorithm
foreach (var terminal in graph.Terminals)
state.AddVertexToInterleavingDijkstra(terminal, graph);
// Initialize
Vertex currentVertex = state.GetNextVertex();
FibonacciHeap<int, Vertex> labels = state.GetLabelsFibonacciHeap();
HashSet<Vertex> visited = state.GetVisitedHashSet();
Dictionary<Vertex, Path> paths = state.GetPathsFound();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes = state.GetNodeMapping();
Dictionary<Vertex, Edge> comingFrom = state.GetComingFromDictionary();
Dictionary<Vertex, int> components = solution.CreateComponentTable();
Dictionary<Vertex, double> terminalFValues = CreateInitialFValuesTable(graph);
int maxLoopsNeeded = graph.Terminals.Count * graph.NumberOfVertices;
int loopsDone = 0;
int updateInterval = 100;
int longestPath = graph.Terminals.Max(x => Algorithms.DijkstraToAll(x, graph).Max(y => y.Value));
while (state.GetLowestLabelVertex() != null)
{
if (loopsDone % updateInterval == 0)
Console.Write("\rRunning IDA... {0:0.0}% \r", 100.0 * loopsDone / maxLoopsNeeded);
loopsDone++;
if (state.GetLowestLabelVertex() != currentVertex)
{
// Interleave. Switch to the Dijkstra procedure of the vertex which currently has the lowest distance.
state.SetLabelsFibonacciHeap(labels);
state.SetVisitedHashSet(visited);
state.SetPathsFound(paths);
state.SetComingFromDictionary(comingFrom);
currentVertex = state.GetNextVertex();
labels = state.GetLabelsFibonacciHeap();
visited = state.GetVisitedHashSet();
paths = state.GetPathsFound();
nodes = state.GetNodeMapping();
comingFrom = state.GetComingFromDictionary();
}
// Do one loop in Dijkstra algorithm
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
if (currentNode.Key > longestPath / 2)
break; //Travelled across the half of longest distance. No use in going further.
// Consider all edges ending in unvisited neighbours
var edges = graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
if (current != currentVertex)
{
// Travel back the new path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = current;
while (pathVertex != currentVertex)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(currentVertex);
path.Edges.AddRange(pathEdges);
paths[current] = path;
}
// Find matching endpoints from two different terminals
var mutualEnd = state.FindPathsEndingInThisVertex(current);
if (mutualEnd.Count() > 1)
{
var terminals = mutualEnd.Select(x => x.Start).ToList();
// Step 1. Calculate new heuristic function value for this shared point.
// f(x) = (Cost^2)/(NumberOfTerminals^3)
var f1 = Math.Pow(mutualEnd.Sum(p => p.TotalCost), 2) / Math.Pow(terminals.Count, 3);
var f2 = Math.Pow(mutualEnd.Sum(p => p.TotalCost), 1) / Math.Pow(terminals.Count, 2);
var f3 = Math.Pow(mutualEnd.Sum(p => p.TotalCost), 3) / Math.Pow(terminals.Count, 2);
var terminalsAvgF = terminals.Select(x => terminalFValues[x]).Average();
var terminalsMinF = terminals.Select(x => terminalFValues[x]).Min();
var f = (new[] { f1, f2, f3 }).Max();
Debug.WriteLine("F value: {0}, Fmin: {3} - Connecting terminals: {1} via {2}", f, string.Join(", ", terminals.Select(x => x.VertexName)), current.VertexName, terminalsMinF);
// Do not proceed if f > avgF AND working in same component
if (terminals.Select(x => components[x]).Distinct().Count() == 1 && f > terminalsMinF)
continue;
Debug.WriteLine("Proceeding with connection...");
// Step 2. Disconnect terminals in mutual component.
foreach (var group in terminals.GroupBy(x => components[x]))
{
if (group.Count() <= 1)
continue;
HashSet<Edge> remove = new HashSet<Edge>();
var sameComponentTerminals = group.ToList();
for (int i = 0; i < sameComponentTerminals.Count-1; i++)
{
for (int j = i+1; j< sameComponentTerminals.Count; j++)
{
var removePath = Algorithms.DijkstraPath(sameComponentTerminals[i], sameComponentTerminals[j], solution);
foreach (var e in removePath.Edges)
remove.Add(e);
}
}
foreach (var e in remove)
solution.RemoveEdge(e, false);
}
components = solution.CreateComponentTable();
// Step 3. Reconnect all now disconnected terminals via shared endpoint
foreach (var t in terminals)
{
var path = Algorithms.DijkstraPath(t, current, graph);
foreach (var edge in path.Edges)
solution.AddEdge(edge);
// Update f value
terminalFValues[t] = f;
}
components = solution.CreateComponentTable();
}
}
// If this solution is connected, take MST
if (graph.Terminals.Select(x => components[x]).Distinct().Count() == 1)
{
// Clean up!
foreach (var vertex in solution.Vertices.Where(x => solution.GetDegree(x) == 0).ToList())
solution.RemoveVertex(vertex);
int componentNumber = graph.Terminals.Select(x => components[x]).Distinct().Single();
foreach (var vertex in components.Where(x => x.Value != componentNumber).Select(x => x.Key).ToList())
solution.RemoveVertex(vertex);
solution = Algorithms.Kruskal(solution);
return solution;
}
// If the solution is not connected, it is not a good solution.
return null;
}
