private TspState GreedyCalc(TspState state)
{
var n = state.CostMatrix.GetLength(0);
while (!state.IsComplete)
{
TspState cheapestBranch = null;
var cheapestBranchValue = double.PositiveInfinity;
for (var toCity = 0; toCity < n; ++toCity)
{
if (!state.CanVisit(toCity))
{
continue;
}
var testBranch = state.Visit(toCity);
if (testBranch.LowerBound >= cheapestBranchValue)
{
continue;
}
cheapestBranch = testBranch;
cheapestBranchValue = testBranch.LowerBound;
}
if (cheapestBranch == null)
{
return(null);
}
state = cheapestBranch;
}
return(state);
}
private TspState(TspState fromState, int toCity)
{
_size = fromState._size;
CostMatrix = (double[, ])fromState.CostMatrix.Clone();
LowerBound = fromState.LowerBound;
var fromCity = fromState.CurrentCity;
Debug.Assert(toCity < _size && toCity >= 0);
Debug.Assert(fromCity == -1 || !double.IsPositiveInfinity(CostMatrix[fromCity, toCity]), "Navigating to illegal city");
Debug.Assert(fromState.NearComplete ? fromState.Path[0] == toCity : !fromState.Path.Contains(toCity), "Path contains illegal duplicate");
Path = fromState.Path.AppendToCopy(toCity);
CurrentCity = toCity;
// The cost matrix does not change when starting from nothing
if (fromCity == -1)
{
return;
}
// Cannot go from toCity to CurrentCity (backwards)
CostMatrix[toCity, fromCity] = double.PositiveInfinity;
// The lower bound is increased by the cost of the path
LowerBound += CostMatrix[fromCity, toCity];
// Nothing else can go to toCity (inf toCity column)
for (var row = 0; row < _size; ++row)
{
CostMatrix[row, toCity] = double.PositiveInfinity;
}
// The current node now can't go to anything as it's no longer the head of the path (inf fromCity row)
for (var col = 0; col < _size; ++col)
{
CostMatrix[fromCity, col] = double.PositiveInfinity;
}
// Reduce the new state
Reduce();
}
//if (_mode == HardMode.Modes.Hard)
//{
// var upperBound = double.PositiveInfinity;
// for (var startCity = 0; startCity < _cities.Length; ++startCity)
// {
// var testState = BranchBoundCalc(baseState, startCity);
// if (testState == null || testState.LowerBound >= upperBound) continue;
// upperBound = testState.LowerBound;
// bestState = testState;
// }
//}
//else
/////////////////////////////////////////////////////////////////////////////////////////////
// These additional solver methods will be implemented as part of the group project.
////////////////////////////////////////////////////////////////////////////////////////////
/// <summary>
/// finds the greedy tour starting from each city and keeps the best (valid) one
/// </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[] GreedySolveProblem()
{
var results = new string[3];
var timer = new Stopwatch();
Debug.Assert(_cities.Length > 0);
timer.Start();
var costMatrix = new TspState(_cities).CostMatrix;
if (_mode == HardMode.Modes.Hard)
{
// CostOfBssf() is still used because new TspState reduces the matrix once
var cost = double.PositiveInfinity;
for (var startCity = 0; startCity < _cities.Length; ++startCity)
{
var thisResult = FastGreedyCalc(startCity, costMatrix);
if (thisResult.Item1 >= cost)
{
continue;
}
cost = thisResult.Item1;
_bssf = new TspSolution(thisResult.Item2.Select(i => _cities[i]));
}
}
else
{
var cityIndexes = FastGreedyCalc(0, costMatrix);
_bssf = new TspSolution(cityIndexes.Item2.Select(i => _cities[i]));
}
timer.Stop();
results[Cost] = CostOfBssf().ToString(CultureInfo.InvariantCulture);
results[Time] = timer.Elapsed.ToString();
results[Count] = (_cities.Length + 1).ToString();
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[] BranchBoundSolveProblem()
{
var results = new string[3];
var timer = new Stopwatch();
Debug.Assert(_cities.Length > 0);
var baseState = new TspState(_cities);
timer.Start();
var n = _cities.Length;
var queue = new FastPriorityQueue <TspState>(n * n * n);
baseState = baseState.Visit(0);
queue.Enqueue(baseState, baseState.Heuristic());
// The current best complete route
var bestState = GreedyCalc(baseState);
var upperBound = bestState?.LowerBound ?? double.PositiveInfinity;
var stored = 0;
var pruned = 0;
var maxStates = 0;
var updates = 0;
while (queue.Count > 0)
{
if (queue.Count > maxStates)
{
maxStates = queue.Count;
}
// Get best state to check based on heuristic.
// Runs in O(log n) time.
var state = queue.Dequeue();
// Branch
for (var toCity = 0; toCity < n; ++toCity)
{
// If we can't visit the city, no need to consider it
if (!state.CanVisit(toCity))
{
continue;
}
var branchState = state.Visit(toCity);
// Bound
if (branchState.LowerBound < upperBound)
{
if (branchState.IsComplete)
{
++updates;
// On a complete instance, no need to add it to the queue.
Debug.Assert(branchState.CostMatrix.Cast <double>().All(double.IsPositiveInfinity),
"Cost Matrix is not all infinity");
upperBound = branchState.LowerBound;
bestState = branchState;
continue;
}
++stored;
if (queue.Count + 5 >= queue.MaxSize)
{
queue.Resize(queue.MaxSize * 2);
}
// Runs in O(log n) time
queue.Enqueue(branchState, branchState.Heuristic());
}
else
{
++pruned;
}
}
// Abandon ship and give the best result otherwise
if (timer.ElapsedMilliseconds > _timeLimit)
{
break;
}
}
timer.Stop();
Debug.Assert(bestState != null && bestState.IsComplete);
_bssf = StateToSolution(bestState);
results[Cost] = CostOfBssf().ToString(CultureInfo.InvariantCulture); // load results array
results[Time] = timer.Elapsed.ToString();
results[Count] = $"{maxStates}/{updates}/{stored}/{pruned}";
return(results);
}
private TspSolution StateToSolution(TspState state)
{
return(new TspSolution(state.Path.Select(cityIndex => _cities[cityIndex])));
}
