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Traveling Salesman Problem
Algorithms

## Detailed Description

This group contains basic heuristic algorithms for the the symmetric traveling salesman problem (TSP). Given an undirected full graph with a cost map on its edges, the problem is to find a shortest possible tour that visits each node exactly once (i.e. the minimum cost Hamiltonian cycle).

These TSP algorithms are intended to be used with a metric cost function, i.e. the edge costs should satisfy the triangle inequality. Otherwise the algorithms could yield worse results.

LEMON provides five well-known heuristics for solving symmetric TSP:

- NearestNeighborTsp Neareast neighbor algorithm
- GreedyTsp Greedy algorithm
- InsertionTsp Insertion heuristic (with four selection methods)
- ChristofidesTsp Christofides algorithm
- Opt2Tsp 2-opt algorithm

NearestNeighborTsp, GreedyTsp, and InsertionTsp are the fastest solution methods. Furthermore, InsertionTsp is usually quite effective.

ChristofidesTsp is somewhat slower, but it has the best guaranteed approximation factor: 3/2.

Opt2Tsp usually provides the best results in practice, but it is the slowest method. It can also be used to improve given tours, for example, the results of other algorithms.

## Classes

class | ChristofidesTsp< CM >
| Christofides algorithm for symmetric TSP. More...
class | GreedyTsp< CM >
| Greedy algorithm for symmetric TSP. More...
class | InsertionTsp< CM >
| Insertion algorithm for symmetric TSP. More...
class | NearestNeighborTsp< CM >
| Nearest neighbor algorithm for symmetric TSP. More...
class | Opt2Tsp< CM >
| 2-opt algorithm for symmetric TSP. More...

## Files

file | christofides_tsp.h
| Christofides algorithm for symmetric TSP.
file | greedy_tsp.h
| Greedy algorithm for symmetric TSP.
file | insertion_tsp.h
| Insertion algorithm for symmetric TSP.
file | nearest_neighbor_tsp.h
| Nearest neighbor algorithm for symmetric TSP.
file | opt2_tsp.h
| 2-opt algorithm for symmetric TSP.