Guide for the 380CT Assignment on TSP

The actual part you need to submit is the Metaheuristics section. The rest is meant to introduce you to the basics.

Ensure you have Jupyter.
- Either install Jupyter alone or Anaconda.
Familiarise yourself with Jupyter functionaility. Consider taking LinkedIn Learning courses (free through the university) or any suitable alternatives. Here is a recommended set (e.g. each member of the group takes one):
Load and study Investigating TSP.ipynb.
- Can you improve any of the functions to make them more efficient?
- See how large you can make n while testing exhaustive_search().
- Check that greedy_nearest_neighbours() is correct. If not then fix it!
Read the Wikipedia article on TSP. Pay attention to th Computing a solution section, and especially to the 2-opt and 3-opt techniques for defining neighbourhoods.
Experiment with generating your own graph families. For example:
- Euclidean graphs: generate points using (x,y) coordinates, then generate the adjacency matrix by calculating all the required distances. Recall that the distance between two points (x₁,y₁) and (x₂,y₂) is sqrt[(x₁-x₂)²+(y₁-y₂)²].
- Graphs with obvious shortest cycle: think of a graph where all the distances are 2 except for the edges on a predefined cycle, where the distance is 1. Such a graph would be useful for testing/debugging the nearest neighbours greedy search.

You can use Template.ipynb to start writing the part you need to submit (about meta-heuristics).
I propose you work as follows (You don't have to follow this though!):
- Ensure you are familiar with the TSP problem, 2-opt and 3-opt local search techniques. (See this Wikipedia article)
- Decide which meta-heuristics you want to try. Watch the guest lecture videos and check the literature related to TSP and the meta-heuristics you are thinking of.
You may try Google Colab and/or Microsoft Azure if that helps you work better, but please be aware that I am not sure about their GDPR compliance.

I should emphasise here that "exhaustive search" and "greedy" are *not meta-heuristics, nor are 2-opt and 3-opt. Ensure this is clear to you.

Bibliography

Applegate, DL, Bixby, RE, Chvátal, V, Cook, WJ, 2007, The Traveling Salesman Problem: A Computational Study, Princeton University Press, Princeton.
Cook, WJ 2012, In Pursuit of the Traveling Salesman: Mathematics at the Limit of Computation, Princeton University Press, Princeton.
Glover, F, & Kochenberger, GA (eds) 2002, Handbook of Metaheuristics, Kluwer Academic Publishers, Secaucus.
Gutin, G, & Punnen, AP (eds) 2002, The Traveling Salesman Problem and Its Variations, Springer, New York, NY.
Pintea, C.-M., 2014. Advances in Bio-inspired Computing for Combinatorial Optimization Problems. 1st ed. 2014.
Steven, SS 2008, The Algorithm Design Manual, Springer, England.
- You may also find its companion website useful.
Talbi, E.-G., 2009. Metaheuristics from design to implementation, Hoboken, NJ: John Wiley & Sons.