The Traveling Salesman Problem (TSP) is one of the challenging problems in operations research. Basically, TSP is about optimizing the route for the salesperson to efficiently visit the list of cities and return to the starting point. Although the problem's premise is simple, its computational complexity makes it a significant focus for both theoretical studies and practical implementations.

Understanding Traveling Salesman Problem's Complexity 

The primary challenge of the TSP stems from its combinatorial nature. If a salesman visits n cities, they must evaluate (n−1)!/2 possible routes due to the flexibility in choosing the starting point and reversing the route. This factorial increase means that even a small number of cities results in a massive number of possible routes. For instance, with 20 cities, the salesman must consider about 60 billion routes. This phenomenon, termed a "combinatorial explosion," makes brute force methods impractical for large datasets.