What is the Traveling Salesperson Problem (TSP)?

The Traveling Salesperson Problem (TSP) is fundamentally an optimization problem that requires a salesperson to determine the most efficient route that visits a set of cities and returns to the original city, with the aim of minimizing the total distance or cost associated with the trip. This encapsulates the essence of TSP: it is not merely about visiting all cities, but also about optimizing the path taken while ensuring that each city is visited exactly once before returning to the starting point.

This problem is widely studied in various fields, including operations research, computer science, and logistics, because of its practical implications in route planning and resource allocation. The difficulty of TSP arises from its combinatorial nature; as the number of cities increases, the number of possible routes grows factorially, making it challenging to solve efficiently.

Thus, the correct answer focuses on the comprehensive visit to all cities while also considering the optimization aspect, which is central to the definition and goal of the TSP.