Parameterising Simulated Annealing for the Travelling Salesman Problem

Abstract

The Travelling Salesman Problem is a well known NP-Hard problem. Given a list of cities, find the shortest path that visits all cities once.

Simulated annealing is a well known stochastic method for solving optimisation problems and is a well known non-exact algorithm for solving the TSP. However, it's effectiveness is dependent on initial parameters such as the starting temperature and cooling rate which is often chosen empirically.

The goal of this project is to:

• Determine if the optimal starting temperature and cooling rate can be parameterised off the input
• Visualise the solving process of the TSP

Usage

Running the code

Examples of common commands to run the files are shown below. However, both src/main.py and src/benchmark.py have a --help that explains the optional flags.

# To visualise annealing on a problem set from the input file
python3 -m src.main -f <input_file>

# To visualise TSP on a random graph with <city_count> number of cities
python3 -m src.main -c <city_count>

# Benchmark the parameters using all problems in the data folder
python3 -m src.benchmark

Keyboard Controls

There are also ways to control the visualisation through key presses while it plays.

Key	Action
Space Bar	Pauses or unpauses the solver
Left / Right arrow	Control how frequently the frame is redrawn
c	Toggles showing the cities as nodes (this is off by default as it causes lag)

Creating your own model

If you would like to create your own instance of the TSP problem and visualise it:

1. Create a new file
2. Within this file ensure you have the line NODE_COORD_SECTION, and below that EOF.
3. Between those two lines, you can place the coordinates of the cities, i.e. for the nth city, have a line like <n> <x> <y>, where x and y are the x and y coordinates of the city.
4. Run python3 -m src.main -f <file>, where <file> is the path to the file you have just made.

Files

File / Folder	Purpose
data	This contains TSP problems in .tsp files and their optimal solution in .opt.tour files, taken from TSPLIB
report	The report detailing the Simulated Annealing and the experimentation
results	The output directory containing results of the tests
src/benchmark.py	Code for benchmarking different temperatures and cooling rates using the problems in the data folder
src/main.py	Driver code to start the visualisation
src/setup.py	Code for loading in city coordinates from a file, or generating random ones
src/solvers.py	Module containing the python implementations of TSP solving algorithms

FAQ

What do you use to generate the graphics?

This project uses the p5py library for visualisation. Unfortunately, (to of my knowledge) this may not work with WSL.

What are the results of your experimentation?

Overall the benefit from implementing SA was quite negligible. The calculation for max iterations was not ideal in the testing - which I believe resulted in skewed results (mostly for calculating the ideal cooling rate). If you are interested in viewing the results, they can be seen in the conclusion of the report here.

What can I do to contribute?

Pog.

This is more of a "what I would I do if I have more time" but whatever, let's say you actually are interested. Disclaimer - the code isn't particularly polished (from me pivoting project ideas multiple times).

• If you're up for a challenge, it would be interesting to implement LKH (Lin-Kernighan heuristic) efficiently
• Implement other algorithms - they just need to extend the Solver abstract class to work with the frontend
• Add a whatever city you want and it's coordinates to data/world.tsp!