void branchAndBound(knapsack &k, int maxTime)
// Implement a Branch and Bound search for an optimal solution.
// Searches for the best decision for objects n and greater, as long
// as more than maxTime seconds have not elapsed. Tries
// to keep or not keep object n, and then iterates to n+1. Stores
// the best solution found so far in bestSolution.
{
clock_t endTime, startTime = clock();
deque<knapsack> problem;
deque<knapsack>::iterator itr;
int number,bestValue=0;
knapsack bestSolution;
double time=0;
cout<<"Branching and Bounding"<<endl;
// Initially, decisions have not been made about any objects,
// so set num = 0.
k.setNum(0);
// Add the empty knapsack subproblem to the list
problem.push_front(k);
// Branch and Bound search goes here
while (!(problem.empty()) && (time<=maxTime)) //for each object in the deque
{
k = problem.back(); // current instance is now the last object in the deque
while((k.getNum()!=k.getNumObjects()) && (k.bound()> bestValue) && (time<=maxTime))
/*if we haven't considered all the objects left and the bound of the current instance
is not worse than our best-so-far solution and we are not out of time*/
{
//delete the last object from the deque because we are currently solving it
problem.pop_back();
number=k.getNum();
k.setNum(number+1); //we are now considering the next object
if(k.getCostBound()-k.getCurrentCost()>k.getCost(number))
{
problem.push_back(k); //push the 'don't select' instacne before the take instance
k.select(number);
}
problem.push_back(k); //push the remaining instance
endTime=clock();//update current time
time=((double)(endTime-startTime))/CLOCKS_PER_SEC;
}
if (k.getCurrentValue() > bestValue){// replace best values if current ones are better
bestValue = k.getCurrentValue();
bestSolution = k;
}
problem.pop_back(); //delete the last object from the deque since it is fathomed
}
cout << "Best value found: " << bestValue << endl;
cout << bestSolution;
k.outFile(bestSolution);
}
