/// <summary>
/// Searches for best solution using branch and bound strategy.
/// </summary>
private static void BranchAndBound()
{
SolutionCandidate candidate = GetMostPromisingCandidate();
while (candidate != null)
{
SolutionCandidate branch = candidate.GetBranch();
while (branch != null)
{
CalculateBound(branch);
if (branch.UpperBound < _currentSolution.UpperBound)
{
branch.IsPromising = false;
}
else if (branch.IsComplete && branch.UpperBound > _currentSolution.UpperBound)
{
_currentSolution = branch;
MarkNotPromisingCandidates();
}
_candidates.Add(branch);
branch = candidate.GetBranch();
}
_candidates.Remove(candidate);
candidate = GetMostPromisingCandidate();
}
}
/// <summary>
/// Calculates solution candidate branch upper bound.
/// </summary>
/// <param name="branch">Branch.</param>
private static void CalculateBound(SolutionCandidate branch)
{
for (int i = 0; i < branch.Assignements.Length; i++)
{
branch.UpperBound += _costTable[i, branch.Assignements[i]];
}
for (int i = branch.Assignements.Length; i < N; i++)
{
branch.UpperBound += _maxValues[i];
}
}
/// <summary>
/// Creates initial solution.
/// </summary>
/// <returns>Initial solution.</returns>
private static SolutionCandidate CreateInitialSolution()
{
SolutionCandidate initialSolution = new SolutionCandidate(N, new int[N]);
for (int i = 0; i < N; i++)
{
initialSolution.Assignements[i] = i;
initialSolution.UpperBound += _costTable[i, i];
}
return(initialSolution);
}
/// <summary>
/// Prepares variables for solving.
/// </summary>
private static void Prepare()
{
_currentSolution = CreateInitialSolution();
_candidates = new List <SolutionCandidate>();
_candidates.Add(new SolutionCandidate(N));
_maxValues = new int[N];
for (int i = 0; i < N; i++)
{
_maxValues[i] = GetMaxValue(i);
}
}
/// <summary>
/// Gets most promising solution candidate from currently found solution candidates.
/// </summary>
/// <returns>Most promising solution candidate; null, if no such candidate exists.</returns>
private static SolutionCandidate GetMostPromisingCandidate()
{
SolutionCandidate bestCandidate = null;
foreach (SolutionCandidate candidate in _candidates)
{
if (!candidate.IsComplete && candidate.IsPromising && (bestCandidate == null || candidate.UpperBound > bestCandidate.UpperBound))
{
bestCandidate = candidate;
}
}
return(bestCandidate);
}
