Handlungsreisendenproblem

The Handlungsreisendenproblem, also known as the Traveling Salesman Problem (TSP), is an optimization problem in graph theory and computer science. It is a problem of determining the shortest possible route that visits a finite number of cities and returns to the original city.

In the TSP, a set of cities is given, and an integer distance is associated with each edge between each pair of cities. The objective is to find the shortest possible tour that visits each city exactly once and returns to the original city. The problem is NP-hard, meaning that the running time of algorithms for solving the problem increases exponentially with the size of the input.

In 1930, the mathematician Karl Menger formulated the TSP as a problem of trying to find the shortest possible path between a set of points in a graph. The problem gained popularity in the 1950s and 1960s when it was applied to real-world problems such as sales routing and transportation logistics.

The TSP has a wide range of applications in areas such as logistics, transportation, and telecommunications. Solving the TSP is a valuable tool for companies and organizations that operate fleets of vehicles to provide delivery services, package transportation, or utility maintenance.

There are different approaches to solving the TSP, such as exact methods and approximation algorithms. Exact methods can find optimal solutions for small instances of the TSP but are impractical for larger instances. Approximation algorithms, on the other hand, can solve large instances of the TSP but may not always find the optimal solution.