As some of you may already be aware, I've been working on and off for the past couple months to develop a heuristic for solving the travelling salesman problem. The point of the TSP is to find the optimal Hamiltonian circuit in a Graph. A couple days ago, I finished my implementation (after finally getting some time to actually code the thing) and it finds a Hamiltonian cycle! For the graph pictured here, it actually finds the solution to the TSP! Do I have more testing to do with different Graphs? Absolutely.

Currently, I'm working on implementing the Held-Karp algorithm, which is the current best solution, having a time complexity of O(n^2 * 2^n) and finding a Hamiltonian circuit that is 99.5% optimal. Once I get that going, I will have a point of comparison. For small graphs, I can solve the TSP by hand. As they grow in size though, having a Held-Karp implementation will be a nice control.

Be warned- a tutorial introducing Hamiltonian circuits to follow!

Currently, I'm working on implementing the Held-Karp algorithm, which is the current best solution, having a time complexity of O(n^2 * 2^n) and finding a Hamiltonian circuit that is 99.5% optimal. Once I get that going, I will have a point of comparison. For small graphs, I can solve the TSP by hand. As they grow in size though, having a Held-Karp implementation will be a nice control.

Be warned- a tutorial introducing Hamiltonian circuits to follow!

### 7 Comments On This Entry

Page 1 of 1

#### AdamSpeight2008

21 May 2011 - 01:31 PM
Would you consider writing an Extension Method for the GrapheNet Library? Even though though a large chunk of the codebase is written using Nemerle, and extension could in any .net language.

Page 1 of 1

### ← March 2020 →

S | M | T | W | T | F | S |
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 |

8 | 9 | 10 | 11 | 12 | 13 | 14 |

15 | 16 | 17 | 18 | 19 | 20 | 21 |

22 | 23 | 24 | 25 | 26 | 27 | 28 |

29 |
30
| 31 |

### My Blog Links

### Recent Entries

### Recent Comments

### Search My Blog

### 1 user(s) viewing

**1**Guests

**0**member(s)

**0**anonymous member(s)