1. Randomised algorithms for travelling salesman problem
Aim:You are required to implement the Monte Carlo algorithm to solve the Odyssey of
Ulysses 22 cities Travelling Salesman Problem (TSP). The problem (ulysses22.tsp) is
available at TSPLIB (Links to an external site.)Links to an external site.. For your interest,
here is an article about this problem: The Optimized Odyssey (Links to an external
site.)Links to an external site..Requirements:You can use any programming languages to
complete this assignment. However, if you want to use languages other than Matlab/Octave,
you should make your program executable/runnable. For example, if you use Java, you need
to compile it. If you use Python, make sure it can be run in a python online IDE such as
TutorialPoint (Links to an external site.)Links to an external site.. Your program should be
able to read in the ulysses22.tsp file. Calculate distance based on Geographical distance.
Please read this document (Links to an external site.)Links to an external site. (Section 2.4)
to learn how to calculate Geographical distance. In order to check whether your
implementation of the Geographical distance calculation is correct or not, you can download
this file (Links to an external site.)Links to an external site., which gives you the optimal
tour with the optimal distance of 7013. Implement the Monte Carlo algorithm. Execute 30
independent runs of your Monte Carlo algorithm with 1000 iterations and record the
average distance and standard deviation from results of the 30 runs. Write a report to
report your results. In the report, you should briefly introduce the Monte Carlo algorithm by
using a flowchart and pseudo-code, discuss the pros and cons. You should also show
intermediate solutions and their lengths at 1st, 500th and 1000th iterations during a typical
run of your algorithm. You should plot a figure to show how the cost changes over the 1000
interactions of a typical run. You should also list all the average result and standard
deviations obtained from the 30 runs of the algorithm.Marking Scheme (total 10
points):Correct calculation of the geographical distance. (1 marks).Correct implementation
of the Monte Carlo algorithm (4 marks)Report: Satisfied requirement 6 (5
marks).http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsp/ulysses22.tsp
https://www.zib.de/groetschel/pubnew/paper/groetschelpadberg2001a.pdf
https://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/tsp95.pdf
http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsp/ulysses22.opt.tour #Randomised
#algorithms #travelling #salesman #problem