Purdue Global University Traveling Salesman Problem and Algorithms

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Snvfny1993

Engineering

Purdue Global University

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Written Assignment Summary (in journal-style format):

Topic assigned to student is "Traveling Salesman Problem"

Your assignment is to write a research paper using Microsoft Word with a minimum of 1500 words and a maximum of 2500 words (not including the References section) on one of 18 Operations Research topics assigned to individual student (i.e., no team assignments) in the given table below. Each student must submit their own individual paper via Bb. It must be word-processed, single-spaced and fully justified. Also, you must have a margin size of 1 inch on all sides (i.e., where the top, bottom, left and right sides are even) of your submitted assignment. Font size for text must be 12 pt and the font type should be Times New Roman throughout this assignment unless otherwise specified below.

Your paper will address different topics/algorithms relevant to the field of Operations Research. The title should be in 14 pt bold-type font and centered, and your name should appear beneath the title (not in bold, but in 12 pt size font). Next, the Abstract section should summarize what your research paper is about, followed by a line called Keywords where you list in horizontal format (i.e., across the page as in many journal articles show) 3-4 words/phrases that are significant to your topic. In addition, each research paper should have a minimum of the following headings:

Introduction – Introduce the topic.

Literature Review – Research and review the literature (When was it created? Who made it?, What are other researchers doing with it?, etc.)

Explanation of the Algorithm/Heuristic Methodology – How does it work?
Examples of Algorithm/Heuristic Usage – Discuss concrete examples of how it is used today in the world. Any

equations used must be properly formatted or you will lose points. Do not use pictures for formulas/equations.Summary/Conclusions – Sum it all up!
References – APA formatted sources...only correct APA will be accepted; otherwise, you will lose points.

These headings should be in bold-type font with 12 pt size. NOTE: This assignment is worth 15% of your grade. Thus, grammar, spelling, punctuation, capitalization, and formatting are critical as much as the technical content of your paper. You must also use a minimum of 3 refereed journal articles (<=10 years old). Additional sources may be used as well and all must be included in the References section.

Next, proper in-text citations MUST appear as (Author, year) and/or Author (year) within the research paper. The style of references that will be used for this assignment is the APA-style. Additional APA formatting information can be found at the Purdue OWL website at

page1image2509136592page1image2509137136

http://owl.english.purdue.edu/owl/resource/560/06/ and click the appropriate “Reference List” item on theleft column for the type of source you are using. Be sure that this is done EXACTLY as shown, or you will lose points for a missing comma or period... or even if you forget to italicize the periodical or book title, etc. Formatting is a very important element when putting together your research. Heavy deductions will be incurred if this is violated.

Unformatted Attachment Preview

IEGR 461 - OPERATIONS RESEARCH: DETERMINISTIC MODELS Research Assignment (Due on Sunday, 3/10/19 by 11:59 pm via Bb only) Submit the paper as both .docx & .pdf files. Submit your research articles as .pdf files only. Written Assignment Summary (in journal-style format): Your assignment is to write a research paper using Microsoft Word with a minimum of 1500 words and a maximum of 2500 words (not including the References section) on one of 18 Operations Research topics assigned to individual student (i.e., no team assignments) in the given table below. Each student must submit their own individual paper via Bb. It must be word-processed, single-spaced and fully justified. Also, you must have a margin size of 1 inch on all sides (i.e., where the top, bottom, left and right sides are even) of your submitted assignment. Font size for text must be 12 pt and the font type should be Times New Roman throughout this assignment unless otherwise specified below. Your paper will address different topics/algorithms relevant to the field of Operations Research. The title should be in 14 pt bold-type font and centered, and your name should appear beneath the title (not in bold, but in 12 pt size font). Next, the Abstract section should summarize what your research paper is about, followed by a line called Keywords where you list in horizontal format (i.e., across the page as in many journal articles show) 3-4 words/phrases that are significant to your topic. In addition, each research paper should have a minimum of the following headings: Introduction - Introduce the topic. Literature Review - Research and review the literature (When was it created? Who made it?, What are other researchers doing with it?, etc.) Explanation of the Algorithm/Heuristic Methodology - How does it work? Examples of Algorithm/Heuristic Usage - Discuss concrete examples of how it is used today in the world. Any equations used must be properly formatted or you will lose points. Do not use pictures for formulas/equations. Summary/Conclusions - Sum it all up! References - APA formatted sources...only correct APA will be accepted; otherwise, you will lose points. These headings should be in bold-type font with 12 pt size. NOTE: This assignment is worth 15% of your grade. Thus, grammar, spelling, punctuation, capitalization, and formatting are critical as much as the technical content of your paper. You must also use a minimum of 3 refereed journal articles (
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Explanation & Answer

Attached.

Running head: TRAVELLING SALESMAN PROBLEM

Travelling Salesman Problem
Student’s Name
Institutional Affiliation
Instructor
Date

1

TRAVELLING SALESMAN PROBLEM

2
Abstract

TSP is illustrated as an algorithmic problem in the department of operation research and
computer science, the concentrate of optimization of the problems. The travelling salesman problem
was found in the year 1800 by the Thomas Kirkman and W.R. Hamilton the great mathematician of
those times. In 1930, Merril M. Flood considered travelling as a mathematics concept after he was
attempting to solve the route problem by the use of school bus. For the cost-efficient and fast means
of delivering good and services ordered through logistically online challenges, the travelling
salesman problem is an applicable method in this kind of department. Algorithms in this concept
refer to as the set of rules used in solving and calculating problem operation particularly by the use of
computers. In conclusion, the concept of travelling salesman problem has been approved applicable
in real life situations whereby in the department of touring it has assisted in utilising the minimal cost
of the fare.

Keywords: Optimizations, Traveling Salesman Problem and Algorithms

TRAVELLING SALESMAN PROBLEM

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Introduction
Travelling Salesman Problem (TSP) is known as a hard combinatorial problem; its site
platform delivers historical perspective case. TSP is illustrated as an algorithmic problem in the
department of operation research and computer science, the concentrate of optimization of the
problems. Mostly the challenges involve the expression of mathematics using the graph to explain the
locations inform of nodes. In 1964, a journal contest attempt to challenge its followers to look for
minimum routes to tour 33 cities in the U.S. The challenge was purposely met for the journal
followers, but it ends challenging the system of the computer. Earlier, the challenge of 49 cities has
been solved by S. Johnson, G. Danzig and R. Fulkerson in the year 1954. However, in the year 2004,
the problem to find the minimum Travelling Salesman Problem visiting 24,978 Sweden cities was
calculated. The challenge solved using clusters of 96 dual processors, and at that period the
cumulative CPU amounted to 84.8. Within the period of 500 to 50 years, the factor that has
contributed to the increase in the size of the problem is advances in the computers (Eisenbrand &
Koenemann, 2017). Despite all the improvement of this problem size, the Travelling Salesman
Problem remains a difficult challenge. The main problem in this field of advancement is that no
matter how the speed of these computers increases, there will always be a problem which is hard to
solve. Therefore the main aim of this operation research is to
Literature Review
The travelling salesman problem was found in the year 1800 by the Thomas Kirkman and
W.R. Hamilton the great mathematician of those times. Hamilton’s engaged in the recreational
puzzle; thus he was capable of discovering the Hamiltonian cycle by the use of Icosian Game. Later,
the general form of travelling salesman problem was studied in the 1930s by a unique mathematician

TRAVELLING SALESMAN PROBLEM

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at Harvard University known as Karl Menger. He described the issues by considering brute force
algorithms and observing the non-minimal of the nearest neighbour heuristic (Ozden, Smith & Gue,
2017). The challenge was to search the location of infinite points whose pairs paths was recognized
as the shortest distances for point’s connection. However, this task could be solved by attempting the
solutions many finitely times. The law of this method could push numerous trials the numbers of
permutations if the points were unknown. This rule was established the beginning point to the last
point, to give the shortest route.
In 1930, Merril M. Flood considered travelling as a mathematics concept after he was
attempting to solve the route problem by the use of school bus. Afterwards, the idea of travelling
salesman problem was introduced at Princeton University by Hassler Whitney. Then, between 1950
to 1960 the challenges of scientific circles increased in the USA and Europe when RAND corporation
in Santa Monica provided prices for the procedure to solve the challenge. Some of the people who
contributed in awarding the process to solve the problem were Selmer M. Johnson, George Dantzig
and Delbert Ray Fulkerson the me...


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