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README.md

TSP algorithms survey

An animation of four algorithms trying to solve a traveling salesman problem.

algorithms

Given a set of 200 cities four algorithms are used to find the shortest tour of all 200 cities. The algorithms are:

  1. Random path, start a city and randomly select the next city from the remaining not visited cities until all cities are visited.
  2. Greedy, start a city select as next city the unvisited city that is closest to the current city
  3. 2-Opt, First create a random tour, and then optimize this with the 2-opt algorithm
  4. Simulated Annealing. First create a random tour, and then optimize this with 2-opt in combination with simualted annealing.

results

lenth greedy 2opt sa optimal random
p15 284.38 284.38 284.38 284.38 818
att48 40526 35579 33607 33523 157530
rand200 36226 31887 30944 x 327452
time greedy 2opt sa
p15 1ms 5ms 11.12
att48 6ms .24s 11s
rand200 10ms 18s 14.5s

citation

If you find the code useful in your research, please consider citing:

  @article{he2017empirical,
    title={An Empirical Analysis of Approximation Algorithms for the Euclidean Traveling Salesman Problem},
    author={He, Yihui and Xiang, Ming},
    journal={arXiv preprint arXiv:1705.09058},
    year={2017}
  }

Paper and 实验报告 latex code are also available.

setups

To create the animation you will need python (Version 2) and ffmpeg.

For python you need one additional library (matplotlib) and its dependcies. You can install it with:

pip install matplotlib

To create the animation use:

make .anim
make

This should create a file called sa.mp4. This should be playable with vlc.

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evaluation of various algorithms for traveling salesman problem

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