For this Critical Thinking assignment, you will solve a real-world optimization problem using graph theory.
Part I: Complete the following steps:
- Select a real-world optimization problem that is an example of the Traveling Salesman Problem (TSP).
- Create a graph modeling the real-world scenario corresponding to the problem. Use weights to represent the variable that you are optimizing.
- Find an optimal solution for the problem using the concepts studied in this module.
Part II: Based on your work in Part I, discuss the following:
- Discuss your rationale for your choice of the real-world optimization problem. How were you able to identify that it was an example of the TSP? Why is this example relevant?
- Describe how you created the graph modeling the real-world scenario corresponding to the problem.
- Determine if the graph is complete. If so, use your graph to describe the formula for computing the number of Hamilton circuits.
- Explain in detail how you solved the problem.
- Describe a method for finding a non-optimal solution to the problem.
- Consider another variable that could be optimized in the problem. How would your answers to Part I be affected by this change?
- Discuss the advantages of using graph theory to solve this problem.
You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.
The second file should be a 2-3-page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:
- Your paper should be 2-3 pages in length (not counting the title page and references page) and should cite and integrate at least two credible outside sources. The CSU Global Library is a great place to find resources. Your textbook is a credible resource.
- Include a title page, introduction, body, conclusion, and a reference page.
- The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
- The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
- The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
- Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)
- Document formatting, citations, and style should conform to the CSU Global Writing Center (Links to an external site.). A short summary containing much that you need to know about paper formatting, citations, and references is contained in the Template Paper (Links to an external site.). If you need assistance with your writing style or you need writing tips or tutorials, visit the CSU Global Writing Center (Links to an external site.).