Why are heuristics used for solving the Travelling Salesman Problem?

Heuristics are used for solving the Travelling Salesman Problem (TSP) primarily because they can find near-optimal routes quickly. The TSP is a computational problem that requires determining the shortest possible route that visits a set of cities and returns to the original city. As the number of cities increases, the number of possible routes grows exponentially, making brute-force methods impractical for larger datasets due to the extensive computation time involved.

Heuristics simplify this problem by providing efficient strategies to approximate a solution without guaranteeing the absolute shortest path. Techniques such as nearest neighbor, genetic algorithms, or simulated annealing can produce satisfactory solutions faster, making them practical for real-world applications where an exact solution may be computationally infeasible. This advantage makes heuristics a valuable tool in tackling complex optimization problems like the TSP.