# Category: Travelling salesman problem

Supnick matrix
A Supnick matrix or Supnick array – named after Fred Supnick of the City College of New York, who introduced the notion in 1957 – is a Monge array which is also a symmetric matrix.
2-opt
In optimization, 2-opt is a simple local search algorithm for solving the traveling salesman problem.The 2-opt algorithm was first proposed by Croes in 1958, although the basic move had already been s
Multi-fragment algorithm
The multi-fragment (MF) algorithm is a heuristic or approximation algorithm for the travelling salesman problem (TSP) (and related problems). This algorithm is also sometimes called the "greedy algori
Set TSP problem
In combinatorial optimization, the set TSP, also known as the generalized TSP, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the traveling sales
Lin–Kernighan heuristic
In combinatorial optimization, Lin–Kernighan is one of the best heuristics for solving the symmetric travelling salesman problem. It belongs to the class of local search algorithms, which take a tour
Nearest neighbour algorithm
The nearest neighbour algorithm was one of the first algorithms used to solve the travelling salesman problem approximately. In that problem, the salesman starts at a random city and repeatedly visits
Travelling salesman problem
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
Variable neighborhood search
Variable neighborhood search (VNS), proposed by Mladenović & Hansen in 1997, is a metaheuristic method for solving a set of combinatorial optimization and global optimization problems.It explores dist
Arc routing
Arc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a gra
Held–Karp algorithm
The Held–Karp algorithm, also called Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman prob
In Pursuit of the Traveling Salesman
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. Cook, published in 2011 by the Princeton University Press, wi
Christofides algorithm
The Christofides algorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric spac
3-opt
In optimization, 3-opt is a simple local search algorithm for solving the travelling salesperson problem and related problems. Compared to the simpler 2-opt algorithm, it is slower but can generate hi