# In the Quasi Traveling Salesman Problem (QTSP) we are given an undirected comple

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In the Quasi Traveling Salesman Problem (QTSP) we are given an undirected complete graph G(V,E) with node set V and edge set E. We assume that node 1∈V represents the depot and nodes {2,…,n}∈V are the customers. The aim is to find a route starting and finishing at node 1∈V in such a way the total distance travelled is minimized and at least n-2 customers are visited (only one customer may be not visited). A feasible solution to the problem is one single route starting and finishing at the depot, which visits a subset of at least n-2 customers.
The nature of this coursework is to demonstrate your ability to research and report on the literature on the above problem and on your ability to program two heuristic approaches from the literature.
Section 1: State-of-the-art? Literature Review ˂1000 words˃
In this part you present a literature review on the more general and well-known Travelling Salesman Problem (TSP). It must include a short desсrіption of the origin of this problem and its complexity, but the focus should be on discussing what you think is the state-of-the-art today of:
optimal algorithms for the TSP; and
heuristics for the TSP.
You do not need to go into detail about how the methods work. It is expected that you will discuss at least one optimal algorithm as well as at least one heuristic method, since it is quite hard to identify an approach that outperforms all others. You must refer to the literature.
Section 2: Instances for the TSP˂100 words˃
Use the internet to find the data of three instances for the Traveling Salesman Problem (TSP) of which other researchers have identified either an optimal solution or a best-known feasible solution. The number of nodes in each instance should be at least 20 nodes. At least one of the instances should have at least 100 nodes. Report the best known solutions (or the optimal solution if known).
You do not need to include all the data of an instance in your report! Please do not list. For example, the costs on each of the edges, or the sequence of the optimal route in the known optimal solution.
Section 3: Construction heuristic ˂400 words˃
Select from the literature of the TSP a construction heuristic and adapt it to solve the QSTP (Quasi-TSP). You will also need to program in Python. You will then test the algorithm on each of the three instances selected in Section 2 and compare the results with the TSP solutions from the literature.
Explain in this section of the report:
The details of how the algorithm works. It should not be a print-out of your Python code, but a higher-level desсrіption of how it works using pseudo-code. Refer to the literature you have used.
The results you get on each of the instances: running time of you Python algorithm and the total cost obtained.
Appendices
You have to add your Python code in the appendix. Also, you may include extra material in appropriate sections here as you feel is necessary or desirable. There is no limit on what you provide but avoid excessively long appendices! Think wisely about what to include here. The appendices do not contribute much to the mark you can obtain; a thoughtful use of appendices may help me understand some points in the main text, but if it is too long and contains irrelevant material may then negatively affect your mark.
The web is a useful resource, and you are allowed to search for open-access codes of algorithms for the TSP and use these codes to learn from. You will not be penalized if you reuse parts of such code; it may sometimes be better to adopt this approach than to try to write your own codes from scratch. You must clearly refer in this case to the website and authors of these codes carefully in your report and acknowledge precisely which parts you have reused.
You are free to choose which heuristics you want to implement, as long as these are methods from the literature. You get marks for writing a good report on these methods, referring properly to the literature, and for implementing them correctly in Python.
It is not of such importance that you would use “smart tricks” to speed up the running times of your code. The latter aspect would require a more in-depth knowledge of Python and computer programming than what we can see in this module. The only criteria are: (1) the code implements the method from the literature, (2) it works. Hence the actual running times, while you need to report them, are not that important. (You will not lose marks if, for example, your code is slower than the “state-of-the-art” implementations, which is very likely the case!)
Report running times in seconds. Use the method we have seen in the lectures. If you get the result “0 sec” from Python, report in your table “˂1s”.
FORMAT OF REPORT
Preferably, follow the format suggested in this assignment. Number sections. You can introduce subsections as deemed appropriate.
Tables and figures can be included and do not count towards the word count. Make sure they are clearly readable and also make sense when printed in black and white. Tables receive their desсrіption at the top of the table, figures at the bottom. Number all tables and figures.
Nature of Assessment: This is a SUMMATIVE ASSESSMENT. See ‘Weighting’ section above for the percentage that this assignment counts towards your final module mark.
Word Limit: +/-10% either side of the word count (see above) is deemed to be acceptable. Any text that exceeds an additional 10% will not attract any marks. The relevant word count includes items such as cover page, executive summary, title page, table of contents, tables, figures, in-text citations and section headings, if used. The relevant word count excludes your list of references and any appendices at the end of your coursework submission.
You should always include the word count (from Microsoft Word, not Turnitin), at the end of your coursework submission, before your list of references.
Title/Cover Page: You must include a title/ cover page that includes: your Student ID, Module Code, Assignment Title, Word Count. This assignment will be marked anonymously, please ensure that your name does not appear on any part of your assignment.
References: You should use the Harvard style to reference your assignment.

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