public bool extend()
{
if (citiesLeft.Count() != 0)
{
foreach (int i in citiesLeft)
{
double initialCost = matrix[path.Last()][i] + cost;
double[][] newMatrix = this.matrix.Select(a => a.ToArray()).ToArray();
for (int j = 0; j < matrix.Count(); j++)
{
newMatrix[path.Last()][j] = Double.PositiveInfinity;
newMatrix[j][i] = Double.PositiveInfinity;
}
List <int> newPath = path.Select(a => a).ToList();
newPath.Add(i);
List <int> newCitiesLeft = citiesLeft.Select(a => a).ToList();
newCitiesLeft.Remove(i);
BBState state = new BBState(newMatrix, newPath, newCitiesLeft, initialCost);
PriorityQueue.getInstance().insert(state);
}
return(false);
}
else
{
cost = matrix[path.Last()][0] + cost;
path.Add(0);
return(true);
}
}
//initializes the distances with the given list and sets the lastIndex which
//is used to track which elements have been checked
//public PriorityQueue(List<double> costs)
//{
// foreach (double distance in costs)
// {
// insert(distance);
// }
// lastIndex = costs.Count - 1;
//}
//adds element to the bottom of the tree and if its not the max value then bubble up
//Insert is O(log(|v|)) because Heapify is O(log(|v|)) and add is O(1)
public void insert(BBState state)
{
states.Add(state);
double cost = state.getCost();
this.cost.Insert(++lastIndex,cost);
pointers.Add(pointers.Count);
if (cost != Int32.MaxValue)
{
HeapifyUp(lastIndex);
}
}
//initializes the distances with the given list and sets the lastIndex which
//is used to track which elements have been checked
//public PriorityQueue(List<double> costs)
//{
// foreach (double distance in costs)
// {
// insert(distance);
// }
// lastIndex = costs.Count - 1;
//}
//adds element to the bottom of the tree and if its not the max value then bubble up
//Insert is O(log(|v|)) because Heapify is O(log(|v|)) and add is O(1)
public void insert(BBState state)
{
states.Add(state);
double cost = state.getCost();
this.cost.Insert(++lastIndex, cost);
pointers.Add(pointers.Count);
if (cost != Int32.MaxValue)
{
HeapifyUp(lastIndex);
}
}
//swaps the minimum with the lastIndexed item and bubbles down
//DeleteMin is O(log(|v|)), because of the reorder
public BBState deletemin()
{
int node = pointers[0];
pointers[0] = pointers[lastIndex];
pointers[lastIndex] = node;
cost[0] = cost[lastIndex];
cost[lastIndex] = -1;
//this make it O(log(|v|))
HeapifyDown(0);
lastIndex--;
BBState state = states.ElementAt(node);
return(state);
//return node;
}
/// <summary>
/// performs a Branch and Bound search of the state space of partial tours
/// stops when time limit expires and uses BSSF as solution
/// </summary>
/// <returns>results array for GUI that contains three ints: cost of solution, time spent to find solution, number of solutions found during search (not counting initial BSSF estimate)</returns>
public string[] bBSolveProblem()
{
string[] results = new string[3];
double bssf = Double.PositiveInfinity;
// TODO: Add your implementation for a branch and bound solver here.
//List<int> citiesLeft = new List<int>();
//double[][] matrix = new double[Cities.Length][];
//for (int i = 0; i < Cities.Length; i++)
//{
// citiesLeft.Add(i);
// matrix[i] = new double[Cities.Length];
// for (int j = 0; j < Cities.Length; j++)
// {
// if (i != j)
// matrix[i][j] = Cities[i].costToGetTo(Cities[j]);
// else
// matrix[i][j] = Double.PositiveInfinity;
// }
//}
//citiesLeft.RemoveAt(0);
double[][] matrix = new double[4][];
matrix[0] = new double[4] { Double.PositiveInfinity, 7, 3, 12 };
matrix[1] = new double[4] { 3, Double.PositiveInfinity, 6, 14 };
matrix[2] = new double[4] { 5, 8, Double.PositiveInfinity, 6 };
matrix[3] = new double[4] { 9, 3, 5, Double.PositiveInfinity };
BBState state = new BBState(matrix, new List<int>() { 0 }, new List<int>() { 1,2,3 },0);
//BBState state = new BBState(matrix, new List<int>() { 0 }, citiesLeft,0);
PriorityQueue.getInstance().insert(state);
BBState current;
while (!PriorityQueue.getInstance().isEmpty())
{
current = PriorityQueue.getInstance().deletemin();
if(state.extend())
{
if(current.getCost() < bssf)
{
bssf = current.getCost();
PriorityQueue.getInstance().trim(bssf);
}
}
}
results[COST] = "not implemented"; // load results into array here, replacing these dummy values
results[TIME] = "-1";
results[COUNT] = "-1";
return results;
}
/// <summary>
/// performs a Branch and Bound search of the state space of partial tours
/// stops when time limit expires and uses BSSF as solution
/// </summary>
/// <returns>results array for GUI that contains three ints: cost of solution, time spent to find solution, number of solutions found during search (not counting initial BSSF estimate)</returns>
public string[] bBSolveProblem()
{
string[] results = new string[3];
double bssf = Double.PositiveInfinity;
// TODO: Add your implementation for a branch and bound solver here.
//List<int> citiesLeft = new List<int>();
//double[][] matrix = new double[Cities.Length][];
//for (int i = 0; i < Cities.Length; i++)
//{
// citiesLeft.Add(i);
// matrix[i] = new double[Cities.Length];
// for (int j = 0; j < Cities.Length; j++)
// {
// if (i != j)
// matrix[i][j] = Cities[i].costToGetTo(Cities[j]);
// else
// matrix[i][j] = Double.PositiveInfinity;
// }
//}
//citiesLeft.RemoveAt(0);
double[][] matrix = new double[4][];
matrix[0] = new double[4] {
Double.PositiveInfinity, 7, 3, 12
};
matrix[1] = new double[4] {
3, Double.PositiveInfinity, 6, 14
};
matrix[2] = new double[4] {
5, 8, Double.PositiveInfinity, 6
};
matrix[3] = new double[4] {
9, 3, 5, Double.PositiveInfinity
};
BBState state = new BBState(matrix, new List <int>()
{
0
}, new List <int>()
{
1, 2, 3
}, 0);
//BBState state = new BBState(matrix, new List<int>() { 0 }, citiesLeft,0);
PriorityQueue.getInstance().insert(state);
BBState current;
while (!PriorityQueue.getInstance().isEmpty())
{
current = PriorityQueue.getInstance().deletemin();
if (state.extend())
{
if (current.getCost() < bssf)
{
bssf = current.getCost();
PriorityQueue.getInstance().trim(bssf);
}
}
}
results[COST] = "not implemented"; // load results into array here, replacing these dummy values
results[TIME] = "-1";
results[COUNT] = "-1";
return(results);
}
/**
* Solve the TSP using an include/exclude B&B strategy
*
* First, get an upper bound, bssf.
*
* Generate the initial Reduced Cost Matrix, (RCM) which
* will give us the initial lower bound.
*
*
*/
public void solveBranchAndBound()
{
// Stats
int totalStatesGenerated = 0, statesPruned = 0, maxStatesStored = 0;
bool initialBssfIsFinal = true;
// Get an upper bound
getGreedyRoute();
bssf = new TSPSolution(Route);
// Generate the RCM, and get it's lower bound from the reduction
double[,] rcm = generateRCM();
double lowerBound = reduceCM(ref rcm);
// Now we need to start throwing states on the queue and processing them..
PriorityQueue<BBState> stateQueue = new PriorityQueue<BBState>();
// Create initial state
BBState initialState = new BBState(rcm, lowerBound);
stateQueue.Enqueue(initialState, initialState.bound);
totalStatesGenerated = maxStatesStored = 1;
// Ok, now we kick off the process!
// Start the timer..
Stopwatch timer = new Stopwatch();
timer.Start();
BBState curState = null;
while (stateQueue.Count > 0)
{
/*if (timer.ElapsedMilliseconds > 30000) // 30 seconds
break; */
curState = stateQueue.Dequeue();
// If this state's lower bound is greater than BSSF, then we
// prune it out
if (curState.bound > costOfBssf())
{
statesPruned++;
continue;
}
// If it's not, then see if it's a complete solution. If it is,
// then update BSSF.
if (curState.isCompleteSolution(ref Cities))
{
bssf = new TSPSolution(curState.getRoute(ref Cities));
initialBssfIsFinal = false;
continue;
}
// If it's not a complete solution, but it's within range, then
// expand it into two child states, one with an included edge, one
// with the same edge excluded.
Tuple<int, int> edge = curState.getNextEdge();
if (edge == null)
continue;
// Ok, now we have the next edge to include and exclude in different states to maximize
// the difference in bounds. So we need to create states corresponding to each and put
// them in the queue.
BBState incState = new BBState(curState.cm, curState.bound, curState.includedEdges);
incState.includedEdges.Add(edge);
incState.cm[edge.Item1, edge.Item2] = double.PositiveInfinity;
incState.cm[edge.Item2, edge.Item1] = double.PositiveInfinity;
for (int t = 0; t < incState.cm.GetLength(0); t++)
incState.cm[t, edge.Item2] = double.PositiveInfinity;
for (int t = 0; t < incState.cm.GetLength(1); t++)
incState.cm[edge.Item1, t] = double.PositiveInfinity;
// Need to take out edges in incState that could be used to complete a premature cycle
if (incState.includedEdges.Count < incState.cm.GetLength(0) - 1)
{
int start = edge.Item1, end = edge.Item2, city;
city = getCityExited(start, incState.includedEdges);
while (city != -1)
{
start = city;
city = getCityExited(start, incState.includedEdges);
}
city = getCityEntered(end, incState.includedEdges);
while (city != -1)
{
end = city;
city = getCityEntered(end, incState.includedEdges);
}
while (start != edge.Item2)
{
incState.cm[end, start] = double.PositiveInfinity;
incState.cm[edge.Item2, start] = double.PositiveInfinity;
start = getCityEntered(start, incState.includedEdges);
}
}
// finish setting up the state and put it in the queue
incState.bound = curState.bound + reduceCM(ref incState.cm);
totalStatesGenerated++;
if (incState.bound > costOfBssf())
{
statesPruned++;
}
else
{
stateQueue.Enqueue(incState, incState.bound);
if (stateQueue.Count > maxStatesStored)
maxStatesStored = stateQueue.Count;
}
BBState exState = new BBState(curState.cm, curState.bound, curState.includedEdges);
exState.cm[edge.Item1, edge.Item2] = double.PositiveInfinity;
exState.bound = curState.bound + reduceCM(ref exState.cm);
totalStatesGenerated++;
if (exState.bound > costOfBssf())
{
statesPruned++;
}
else
{
stateQueue.Enqueue(exState, exState.bound);
if (stateQueue.Count > maxStatesStored)
maxStatesStored = stateQueue.Count;
}
}
timer.Stop();
Program.MainForm.tbElapsedTime.Text = " " + timer.Elapsed;
// update the cost of the tour.
Program.MainForm.tbCostOfTour.Text = " " + bssf.costOfRoute();
// do a refresh.
Program.MainForm.Invalidate();
String msg = "\tB&B RESULTS\n";
if (timer.ElapsedMilliseconds > 30000)
msg += "\nSearch timed out, 30 seconds expired.";
if (initialBssfIsFinal)
msg += "\nInitial BSSF (Greedy) is final solution.";
else
msg += "\nA better BSSF than the initial was found.";
msg += "\n\n\tSTATS:";
msg += "\nTotal States Created:\t" + totalStatesGenerated;
msg += "\nTotal States Pruned:\t" + statesPruned;
msg += "\nMax States Stored: \t" + maxStatesStored;
MessageBox.Show(msg);
return;
}
public bool extend()
{
if (citiesLeft.Count() != 0)
{
foreach (int i in citiesLeft)
{
double initialCost = matrix[path.Last()][i] + cost;
double[][] newMatrix = this.matrix.Select(a => a.ToArray()).ToArray();
for(int j = 0; j < matrix.Count(); j++)
{
newMatrix[path.Last()][j] = Double.PositiveInfinity;
newMatrix[j][i] = Double.PositiveInfinity;
}
List<int> newPath = path.Select(a => a).ToList();
newPath.Add(i);
List<int> newCitiesLeft = citiesLeft.Select(a => a).ToList();
newCitiesLeft.Remove(i);
BBState state = new BBState(newMatrix, newPath, newCitiesLeft, initialCost);
PriorityQueue.getInstance().insert(state);
}
return false;
}
else
{
cost = matrix[path.Last()][0] + cost;
path.Add(0);
return true;
}
}
