//**********************************************BBAlgorithm*********************************************************************************
/// <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];
// TODO: Add your implementation for a branch and bound solver here.
//Initalize variables. Takes O(1) space and time
int numOfCitiesLeft = Cities.Length;
int numOfSolutions = 0;
int numOfStatesCreated = 0;
int numOfStatesNotExpanded = 0;
//Initalize time variable for stopping the algorithm after the default of 60 seconds. Takes O(1) space and time
DateTime start = DateTime.Now;
DateTime end = start.AddSeconds(time_limit / 1000);
//Create initial root state and set its priority to its lower bound. Takes O(n^2) space and time as discussed above
TSPState initialState = createInitialState();
numOfStatesCreated++;
initialState.setPriority(calculateKey(numOfCitiesLeft - 1, initialState.getLowerBound()));
//Create initial BSSF greedily
double bssfBound = createGreedyBssf();
PriorityQueue queue = new PriorityQueue(Cities.Length);
queue.insert(initialState);
// Branch and Bound until the queue is empty, we have exceeded the time limit, or we found the optimal solution
/* This loop will have a iterate 2^n times approximately with expanding and pruning for each state, then for each state it
* does O(n^2) work by reducing the matrix, so over all O((n^2)*(2^n)) time and space as well as it creates a nxn
* matrix for each state*/
while (!queue.isEmpty() && DateTime.Now < end && queue.getMinLB() != bssfBound)
{
// Grab the next state in the queue
TSPState currState = queue.deleteMin();
// check if lower bound is less than the BSSF, else prune it
if (currState.getLowerBound() < bssfBound)
{
// Branch and create the child states
for (int i = 0; i < Cities.Length; i++)
{
// First check that we haven't exceeded the time limit
if (DateTime.Now >= end)
{
break;
}
// Make sure we are only checking cities that we haven't checked already
if (currState.getPath().Contains(Cities[i]))
{
continue;
}
// Create the State
double[,] oldCostMatrix = currState.getCostMatrix();
double[,] newCostMatrix = new double[Cities.Length, Cities.Length];
// Copy the old array in the new one to modify the new without affecting the old
for (int k = 0; k < Cities.Length; k++)
{
for (int l = 0; l < Cities.Length; l++)
{
newCostMatrix[k, l] = oldCostMatrix[k, l];
}
}
City lastCityinCurrState = (City)currState.getPath()[currState.getPath().Count - 1];
double oldLB = currState.getLowerBound();
setUpMatrix(ref newCostMatrix, Array.IndexOf(Cities, lastCityinCurrState), i, ref oldLB);
double newLB = oldLB + reduceMatrix(ref newCostMatrix);
ArrayList oldPath = currState.getPath();
ArrayList newPath = new ArrayList();
foreach (City c in oldPath)
{
newPath.Add(c);
}
newPath.Add(Cities[i]);
TSPState childState = new TSPState(ref newPath, ref newLB, ref newCostMatrix);
numOfStatesCreated++;
// Prune States larger than the BSSF
if (childState.getLowerBound() < bssfBound)
{
City firstCity = (City)childState.getPath()[0];
City lastCity = (City)childState.getPath()[childState.getPath().Count - 1];
double costToLoopBack = lastCity.costToGetTo(firstCity);
// If we found a solution and it goes back from last city to first city
if (childState.getPath().Count == Cities.Length && costToLoopBack != double.MaxValue)
{
childState.setLowerBound(childState.getLowerBound() + costToLoopBack);
bssf = new TSPSolution(childState.getPath());
bssfBound = bssf.costOfRoute();
numOfSolutions++;
numOfStatesNotExpanded++; // this state is not expanded because it is not put on the queue
}
else
{
// Set the priority for the state and add the new state to the queue
numOfCitiesLeft = Cities.Length - childState.getPath().Count;
childState.setPriority(calculateKey(numOfCitiesLeft, childState.getLowerBound()));
queue.insert(childState);
}
}
else
{
numOfStatesNotExpanded++; // States that are pruned are not expanded
}
}
}
currState = null;
}
numOfStatesNotExpanded += queue.getSize(); // if the code terminated before queue is empty, then those states never got expanded
Console.WriteLine("Number of states generated: " + numOfStatesCreated);
Console.WriteLine("Number of states not Expanded: " + numOfStatesNotExpanded);
Console.WriteLine("Max Number of states put in queue: " + queue.getMaxNumOfItems());
end = DateTime.Now;
TimeSpan diff = end - start;
double seconds = diff.TotalSeconds;
results[COST] = System.Convert.ToString(bssf.costOfRoute()); // load results into array here, replacing these dummy values
results[TIME] = System.Convert.ToString(seconds);
results[COUNT] = System.Convert.ToString(numOfSolutions);
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()
{
Stopwatch timer = new Stopwatch();
timer.Start();
initialBSSF = true;
greedySolveProblem();
string[] results = new string[3];
int n = Cities.Length;
double[,] baseMatrix = new double[n, n];
int count;
ReducedMatrix currentCity;
queue = new PriorityQueue();
ReducedMatrix reduced;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i == j)
{
baseMatrix[i, j] = Double.PositiveInfinity;
}
else
{
baseMatrix[i, j] = Cities[i].costToGetTo(Cities[j]);
}
}
}
reduced = new ReducedMatrix(baseMatrix, Cities.Length, Cities[0]);
reduced.reduce();
queue.add(reduced);
count = 0;
totalStates = 1;
while (true)
{
if (queue.getSize() > maxStroedStates)
{
maxStroedStates = queue.getSize();
}
if (timer.ElapsedMilliseconds > time_limit)
{
break;
}
currentCity = queue.remove();
if (currentCity == null)
{
break;
}
if (currentBssf < currentCity.bound)
{
break;
}
for (int i = 1; i < n; i++)
{
if (currentCity.matrix[currentCity.cityNumber, i] != INFINITY)
{
ReducedMatrix newMatrix = new ReducedMatrix(currentCity, Cities[i], i);
newMatrix.cancel(currentCity.cityNumber, i);
newMatrix.reduce();
if (newMatrix.Route.Count == Cities.Length)
{
if (newMatrix.bound < currentBssf)
{
numBSSFUpdates++;
bssf = new TSPSolution(newMatrix.Route);
currentBssf = newMatrix.bound;
}
count++;
break;
}
if (newMatrix.bound < currentBssf)
{
queue.add(newMatrix);
totalStates++;
}
else
{
numStatesPruned++;
}
}
}
}
timer.Stop();
numStatesPruned += queue.getSize();
String track;
track = "MAX #of stored states " + maxStroedStates + "\n";
track += "#of BSSF updates " + numBSSFUpdates + "\n";
track += "Total states created " + totalStates + "\n";
track += "Total states pruned " + numStatesPruned + "\n";
MessageBox.Show(track);
results[COST] = bssf.costOfRoute().ToString(); // load results into array here, replacing these dummy values
results[TIME] = timer.Elapsed.ToString();
results[COUNT] = count.ToString();
return(results);
}
/// <summary>
/// solve the problem. This is the entry point for the solver when the run button is clicked
/// right now it just picks a simple solution.
/// </summary>
public void solveProblemBandB()
{
//initialize BSSF with a greedy algorithm
Algorithms algorithms = new Algorithms();
bssf = new TSPSolution(algorithms.greedy(Cities));
Node.bssf = bssf.costOfRoute();
int maxQsize = 0;
int totalStates = 0;
int timeSeconds = Convert.ToInt32(Program.MainForm.textBoxTime.Text);
//set up priority queue and stopwatch
PriorityQueue PQ = new PriorityQueue();
PQ.insert(new Node(Cities));
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
while(PQ.getSize() > 0 && stopwatch.Elapsed.TotalSeconds < timeSeconds)
{
//pop node off of queue and check lower bound against bssf
Node node = PQ.deleteMin();
if(node.lowerBound > Node.bssf)
{
Node.prunes++;
break;
}
Node include = null;
Node exclude = null;
double maxDif = Double.NegativeInfinity;
//search for include/exclude edge that gives max difference in lower bound
double[,] matrix = node.rCmatrix;
for (int i = 0; i < node.matrixLength; i++)
{
if (node.exited[i] == -1)
{
for (int j = 0; j < node.matrixLength; j++)
{
if (matrix[i, j] == 0)
{
Node tempInclude = new Node(node, true, i, j);
Node tempExclude = new Node(node, false, i, j);
double potentialMaxDif = tempExclude.lowerBound - tempInclude.lowerBound;
if (potentialMaxDif > maxDif)
{
maxDif = potentialMaxDif;
include = tempInclude;
exclude = tempExclude;
}
}
}
}
}
//check if found a bssf
if(include.totalEdges == include.matrixLength && include.lowerBound < Node.bssf)
{
Node.bssfUpdates++;
Node.bssf = include.lowerBound;
Node.bssfNode = include;
}
else if(include.lowerBound < Node.bssf)//add include node to queue
{
PQ.insert(include);
int currentQSize = PQ.getSize();
if(currentQSize > maxQsize)
{
maxQsize = currentQSize;
}
}
else//prune include node
{
Node.prunes++;
}
if(exclude.lowerBound < Node.bssf)//add exclude node to queue
{
PQ.insert(exclude);
int currentQSize = PQ.getSize();
if (currentQSize > maxQsize)
{
maxQsize = currentQSize;
}
}
else//prune exclude node
{
Node.prunes++;
}
totalStates += 2;//2 states are created per while-loop iteration
}
stopwatch.Stop();
//if stopwatch is < 30, then we have found an optimal solution
bool isOptimal = false;
if(stopwatch.Elapsed.TotalSeconds < timeSeconds)
{
isOptimal = true;
}
//prune number of items left in the queue
Node.prunes += PQ.getSize();
//if a bssf has been found better than the greedy solution
if(Node.bssfNode != null)
{
Node solution = Node.bssfNode;
ArrayList route = solution.getRoute(Cities);
// call this the best solution so far. bssf is the route that will be drawn by the Draw method.
bssf = new TSPSolution(route);
}
//display stats
if (isOptimal)
{
Program.MainForm.tbCostOfTour.Text = " " + bssf.costOfRoute() + "*";
}
else
{
Program.MainForm.tbCostOfTour.Text = " " + bssf.costOfRoute();
}
Program.MainForm.tbElapsedTime.Text = " " + stopwatch.Elapsed.TotalSeconds;
// do a refresh.
Program.MainForm.Invalidate();
//print more stats
Console.WriteLine();
Console.WriteLine("Max # of stored states: " + maxQsize);
Console.WriteLine("# of BSSF updates: " + Node.bssfUpdates);
Console.WriteLine("Total # of states created: " + totalStates);
Console.WriteLine("Total # of states pruned: " + Node.prunes);
Node.resetStaticVariables();
}