public object Clone()
{
var clone = new SolutionCandidate
{
LowerBound = this.LowerBound,
Assignments = new List <int>(this.Assignments)
};
return(clone);
}
int CalculateLowerBound(SolutionCandidate branch)
{
var lowerBound = 0;
// Add the costs for the already fixed agents:
for (var agent = 0; agent < branch.Assignments.Count; agent++)
{
var task = branch.Assignments[agent];
lowerBound += costMatrix[agent, task];
}
// Add "minimum cost" for remaining agents:
for (var agent = branch.Assignments.Count; agent < numAgents; agent++)
{
lowerBound += minimumCosts[agent];
}
return(lowerBound);
}
public List <int> FindAssignment(out int solutionCost)
{
// Initialize first solution candidate:
var currentSolution = new SolutionCandidate()
{
Assignments = new List <int>()
};
for (var i = 0; i < numAgents; i++)
{
currentSolution.Assignments.Add(i);
currentSolution.LowerBound += costMatrix[i, i];
}
// Prepare queue and initialize it with an empty candidate:
var queue = new IntervalHeap <SolutionCandidate>(); // A queue or a stack could be used instead.
queue.Add(new SolutionCandidate()
{
Assignments = new List <int>()
});
// Here is the main algorithm...
while (!queue.IsEmpty)
{
// Get next candidate. If a priority queue is used, the "next" candidate is the
// most promising (with lowest lower bound):
var candidate = queue.DeleteMin();
// Branch out:
for (var task = 0; task < numTasks; task++)
{
// Only create the branch if the current task is not already taken by an agent:
if (!candidate.Assignments.Contains(task)) // A HashSet on the side could speed up the .Contains() call...
{
var branch = (SolutionCandidate)candidate.Clone();
branch.Assignments.Add(task);
branch.LowerBound = CalculateLowerBound(branch);
// Only use the generated branch if its lower bound is strictly better than
// the currently found solution cost.
// This is the "bound" part in "Branch and Bound":
if (branch.LowerBound >= currentSolution.LowerBound)
{
continue;
}
// Do we have a solution?
if (branch.Assignments.Count == numAgents)
{
currentSolution = branch;
}
else // If not, use it for further extension:
{
queue.Add(branch);
}
}
}
}
solutionCost = currentSolution.LowerBound;
return(currentSolution.Assignments);
}
