/////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////// BB Algorithm ////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////////////////////
#region MainBBAlgorithm
/// <summary>
/// performs a Branch and Bound search of the state space of partial tours
/// stops when time limit expires and uses BSSF as solution
/// Time Complexity: O((n^2)*(2^n) as that is the most dominant factor in the code, and it is a result
/// of the loop, for more details scroll to the comment above the loop in the function.
/// Space Complexity: O((n^2)*(2^n) as that is the most dominant factor in the code, and it is a result
/// of the loop, for more details scroll to the comment above the loop in the function.
/// </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];
// Helper variables
/* This part of the code takes O(1) space and time as we are just initializing some data */
int numOfCitiesLeft = Cities.Length;
int numOfSolutions = 0;
int numOfStatesCreated = 0;
int numOfStatesNotExpanded = 0;
// Initialize the time variable to stop after the time limit, which is defaulted to 60 seconds
/* This part of the code takes O(1) space and time as we are just initializing some data */
DateTime start = DateTime.Now;
DateTime end = start.AddSeconds(time_limit/1000);
// Create the initial root State and set its priority to its lower bound as we don't have any extra info at this point
/* This part of the code takes O(n^2) space and time as explained above */
State initialState = createInitialState();
numOfStatesCreated++;
initialState.setPriority(calculateKey(numOfCitiesLeft - 1, initialState.getLowerBound()));
// Create the initial BSSF Greedily
/* This part of the code takes O(n^2) time and O(n) space as explained above */
double BSSFBOUND = createGreedyInitialBSSF();
// Create the queue and add the initial state to it, then subtract the number of cities left
/* This part of the code takes O(1) time since we are just creating a data structure and
O(1,000,000) space which is just a constant so O(1) space as well*/
PriorityQueueHeap queue = new PriorityQueueHeap();
queue.makeQueue(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
State 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]);
State childState = new State(ref newPath, ref newLB, ref newCostMatrix, Cities.Length);
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;
}