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Comparing Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) is an NP-complete problem. Different approximation algorithms have their advantages and disadvantages.

Mathematica's function FindShortestTour offers a choice of four methods ("OrZweig", "OrOpt", "TwoOpt", "CCA"), which may yield identical results.

This Demonstration provides another TSP algorithm called 3-Opt. Experiments show that the 3-Opt algorithm sometimes finds a better result than any of the four kinds of Mathematica FindShortestTour methods.

Contributed by: Frederick Wu
Additional contributions by: Daniel Lichtblau
Based on a program by: Sidong Zeng

Show Initialization Code

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Snapshot 1: with 30 points, FindShortestTour methods find a shorter result than the 3-Opt method

Snapshot 2: with 30 points, both 3-Opt and Mathematica's FindShortestTour methods find an optimal result

Snapshot 3: with 40 points, 3-Opt finds a shorter result than any of the FindShortestTour methods

FindShortestTour (Wolfram Mathematica Documentation Center)

Traveling Salesman Game (The Wolfram Demonstrations Project)

Traveling Salesman Problem (The Wolfram Demonstrations Project)

"Comparing Algorithms for the Traveling Salesman Problem" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ComparingAlgorithmsForTheTravelingSalesmanProblem/

Contributed by: Frederick Wu

Additional contributions by: Daniel Lichtblau

Based on a program by: Sidong Zeng

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