This applet shows a few heuristics based solutions to the popular Travelling Salesperson Problem.
The Travelling Salesperson Problem is to find a path through, a given number of cities, N, beginning and ending at the same city. The run time for finding a solution for this problem would be exponential depending on the number of cities, if a brute force technique is employed. So the idea is to use heuristic-based algorithms, which would run in polynomial time, while producing a result (tour) that would be near the optimal solution (which can only be found using a brute-force approach).