Assignment 1 (worth 25% for COMP815; worth 50% for COMP701)
Your first Assignment is as follows: You are to find the best GA paramaters for
solving the TSP for a specific map of 200 cities. First, you need to run the GA with
Matlab’s fixed default parameters 10 times on the same 200-city network topology
and record the fval values after each run. You will then experiment with different
parameter settings for 40 cities and 100 cities (again using the same city network
topology so that you can compare the effectiveness of your parameter changes.) You
will run the GA again for ten times for different parameter settings for 40 and 100
cities. The task is for you to identify, on the basis of the results for 40 and 100 cities,
what the best set of parameters will be for 200 cities. You will then use those
parameters for 10 runs and compare the results with the original 10 runs for 200 cities
against the default parameters. You will need to submit your results in a report. Here
are the tasks in more detail. You should pay particular attention to the questions in
boldfont. And don’t forget that the spreadsheets have been introduced for a reason.
(a) Your first task is to learn how to fix the 200 cities and their locations so that the
map does not change each time you run the algorithm. Load the travelling
salesman demo following the instructions from your first workshop. At line 28,
you can change the number of cities to 200 or any number you like. When you
save the file, you will need to save it in a separate folder. Add the path to your
new file without changing the folder. If you change the folder, not all the
functions in Matlab will be available to you. After you run the algorithm the first
time, you will find the random distributions of the cities in the variable ‘locations’
(a 200x2 matrix) and the distances between them in ‘distances’. You can fix the
map on a University computer if you have a memory stick or use the desktop as a
temporary filespace.
(i) After your first run with 200 cities, edit the Matlab code by removing (or
commenting out with a ‘%’ sign at the start of each line) lines 29 to 39, and lines
46-56.
(ii) Then save the new code version back to your memory stick or to your
desktop or other temporary filespace. Call your code
‘my_travelling_salesman_demo’. Your file will have an ‘.m’ suffix automatically
to denote a Matlab code file. You will not be allowed to save the code back to the
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Matlab demos directory for obvious reasons. Do not change folder. Instead, add
the path to your file when asked by Matlab.
(iii) For the remainder of your session, your map and distances are fixed. If
you suspend your work and want to start again at a future time, load your
‘my_travelling_salesman_demo’ file to get your fixed city network back.
(b) This is just one way of making sure your map does not change with each run. See
http://au.mathworks.com/help/matlab/ref/save.html and
http://au.mathworks.com/help/matlab/ref/load.html for more information on how
to save and load variable values for future use. If you use the GUI, you can use the
same random city network as for the first run, but you will need to finish all your
experiments in one session.
Also, if you don’t like the way that distance is calculated based on graph
coordinates in the range 0-1, you can multiply the distance calculation in line 53
of the code by, say, 1000, to give more realistic distances.
(c) First, before you do anything else, run the GA with the default parameters 10
times on the same map of 200 cities, and store the results of the default population
size, the output fval and generation values in three columns in a spread sheet. Call
these columns ‘ga_200_default’.
(d) Now, for your first set of 10 experimental runs, change the number of cities to 40
(and fix the topology using save and load). Change the population size to 40 and
store the 10 fval results in separate columns of a spreadsheet, with a clear header.
Then change the population size to 100 and run again for 10 times, storing the
results of fval next to the previous results.
(e) Now set the number of cities to 100 (with fixed topology) and repeat (c) with
population sizes 40 and 100.
Does the change in population size between 40 and 100 make a difference
between 40 and 100 cities? Explain and justify your answer. Depending on
your answer, decide on the ideal population size for the remainder of your
experiments.
(f) Go back to your 40 city network and your chosen population size. Change the
fitness scaling to ‘proportional’ from the default ‘rank’. Run the algorithm 10
times and store the results of fval. Keeping the same parameter values, run the
algorithm 10 times for 100 cities and store the results.
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(g) Change the number of cities back to 40. Change the fitness scaling to ‘Top’ and
run the algorithm 10 times, storing each result of fval. Do the same for 100 cities.
(Your population size is fixed at this stage, so there is no need to change that.)
What is the best scaling method? Justify and explain your answer. Depending
on your answer, decide on the ideal scaling method for the remainder of your
experiments.
(h) Go back to your 40 city network. Change the Selection method from ‘stochastic
uniform’ to ‘Roulette’. Run the algorithm 10 times, storing each result of fval.
Change the selection method to ‘Tournament’ and run the algorithm 10 times,
storing each result of fval. Now repeat for your 100 city network.
Do the changes in selection method make a difference? Explain and justify
your answer. Depending on your answer, decide on the ideal selection method
for the remainder of your experiments.
(i) Finally, return to your 40 city network. Change the number of generations from
500 to 1000 and run the algorithm 10 times, storing the results of fval. Repeat for
your 100 city network.
Does the change in the number of generations make a difference? Explain
and justify your answer. Depending on your answer, decide on the ideal
number of generations for the remainder of your experiments.
(j) Now that you have decided on your best parameters based on your experiments
with 40 and 100 cities, run the algorithm on 200 cities 10 times, using your own
chosen parameters. Compare the fval results with your original results using default
parameters in (c) above.
Your assignment report should describe your choice of best parameters for
solving the TSP for 200 cities. Your analysis should explain why your parameter
changes made a difference in comparison to the original default parameters.
Your report for this part of the coursework should be no more than 6 double
column pages, or 8 single column pages, including any screen shots, maps and
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tables of results. You can download double-column format templates from AUT
Online (in the Assessment folder).
Your report should be written in a professional manner and in line with publication
expectations. Please look at the paper, ‘A genetic algorithm for solving the travelling
salesman problem’ by Philip, Taofiki and Kehinde, IJACSA, 2(1), 26-29, and
available in the Assessment folder of AUT Online, for an example of how to construct
a report containing GA experiments. You will be provided with a report template also
so that your report looks like a submission to an IEEE conference.
Notice how the paper first introduces the area and demonstrates to the reader that the
authors understand the problem and what they are going to do about it. Then the paper
introduces the methods they have adopted, followed by implementation. There is a
separate section on results and discussion, followed by a separate conclusion.
If you follow this template, you will stand the best chance of maximizing your
coursework marks for this assignment. Also, you will have gained valuable
experience in how to present the results of research concisely and with evaluation,
which is a skill much valued by employers everywhere.
For COMP815 students: Hints for your Research Project.
You have much scope for enhancing the experiments into an expanded Research
Project, if you wish, as follows, after more reading of GA material:

Change or add your own chromosome mutation/recombination operators

Change or add another selection strategy

Change the graph to a different type of search problem

Change the problem to an asymmetrical problem

Change the nature of the problem altogether (e.g. numerical optimization)

See if your chosen parameters continue to be the best parameters for even
bigger city networks.
If you are interested in focusing on genetic algorithms for your Research Report, look at
some of the other demos in the globaloptim toolbox and see how the interface changes with
the different demos. In particular, look in more detail at
http://www.mathworks.com/help/toolbox/gads/index.html (the web page you opened at the
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very beginning of the workshop) to see if any other global optimization technique interests
you.
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