It is used as a benchmark for many optimization methods. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. In the theory of computational complexity, the decision version of the TSP (where given a length L, the task is to decide whether the graph has a tour of at most L) belongs to the class of NP-complete problems. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. ![]() ![]() Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot.
0 Comments
Leave a Reply. |