comparing_tsp_solvers

Universal platform to quantify different traveling salesman problem (TSP) solvers. Two different approaches are demonstrated her. Namely a brute force algorim and the quantum Grover algorithm. A demo of both of which can be found in demo.ipynb.

Traveling Salesman Problem

The traveling salesman is the seemingly simple task to find a minimum route to connect a number of N cities on a map, such that the total distance to pass to visit all cities is minimal. One can find (N-1)! possible paths for a round tour through all available stops. This is feasible for a hand full of cities e.g for 5 we find 4!=24 paths. However only doubling the cities to 8 already yields 7! = 5040 possible trips. Therefore economists have been showing interest in solving this problem with the lowest possible computational cost since many centuries.

Installation

This package is installed by navigating to the top folder of this repo (where this README file is stored) and running pip as follows. NOTE: do not forget the dot after -e

pip install -e .

The required python packages are installed automatically as they are specified in the pyproject.toml file.

Tests

Tests are written with the pytest package and can be executed by running the following command in the repositories top folder.

python -m pytest ./tests

Program specification

Program name: Comparing TSP solvers Function: Universal platform to quantify different traveling salesman problem (TSP) solvers Inputs: number of cities, grid-size of city map, type of solver Output: optimal routes connecting all cities on a round trip Description: The python modules provides a uniform test bed for different TSP solvers. An abstract base class handling city generation on a map is implemented calculating total and inter-city distances while validating output sequences. Here two different approaches are implemented. Namely a brute force algorim and the quantum Grover algorithm Error checking:

Cities dictionaries are checked for their uniformity and coordinates
Possible sequences are checked for their validity

Grover

After taking the input cities and distances, the program encodes all cities as quantum states and precalculates the overall distances of all routes. It then uses Grover algorithm to amplify the optimal states whose distances are below the user-defined threshold. The optimal states will appear with high probabilities in the measurement. Reference: https://github.com/Naphann/Solving-TSP-Grover.

Brute force solver

The brute force solver finds all (n-1)! possible tours for the traveling salesman and calculates their distances. The most optimal route is returned by searching for the entry with the shortest distsance.

Contribution

This project has been written by Jonathan Huang and Andreas Nickl within the course 'Quantum Software and Programming' at University of Technology Sydney.

Jonathan Huang

Research on Grover algorithm and its application on the traveling salesman problem
Implementation of the Grover algorithm in qiskit

Andreas Nickl

Setup and structuring of the given python module
Class implementation of the Grover algorithm
Unit tests in pytest

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