This presentation discusses about the Traveling Salesmen Problem and its implications in Soft Computing

1. Department of Information Technology 1Soft Computing (ITC4256 )
Dr. C.V. Suresh Babu
Professor
Department of IT
Hindustan Institute of Science & Technology
Travelling Salesmen Problem (TSP)

2. Department of Information Technology 2Soft Computing (ITC4256 )
Introduction
• The Traveling Salesman Problem (often called TSP) is a classic
algorithmic problem in the field of computer science and
operations research. It is focused on optimization. In this
context, better solution often means a solution that is cheaper,
shorter, or faster. TSP is a mathematical problem.

3. Department of Information Technology 3Soft Computing (ITC4256 )
What is TSP?
• Given a collection of cities and the cost of travel between each
pair of them, the traveling salesman problem, or TSP for short,
is to find the cheapest way of visiting all of the cities and
returning to your starting point.
• In the standard version we study, the travel costs are
symmetric in the sense that traveling from city X to city Y costs
just as much as traveling from Y to X.

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Illustration

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What is TSP?
• The simplicity of the statement of the problem is deceptive --
the TSP is one of the most intensely studied problems in
computational mathematics and yet no effective solution
method is known for the general case.
• Indeed, the resolution of the TSP would settle the P versus NP
problem and fetch a $1,000,000 prize from the Clay
Mathematics Institute.

6. Department of Information Technology 6Soft Computing (ITC4256 )

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8. Department of Information Technology 8Soft Computing (ITC4256 )
What is TSP?
Although the complexity of the TSP is still unknown, for over 50
years its study has led the way to improved solution methods in
many areas of mathematical optimization.
• Number of TSP Tours
• Santa TSP
• TSP Cake

9. Department of Information Technology 9Soft Computing (ITC4256 )
Question: Which of the following is a Hamilton
circuit of the graph?
i. ABCDEFGA
ii. ACBEGFDA
iii.CBGEDFAC
iv.CEGBADFC
Note: A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start
and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have
to start and end at the same vertex.

10. Department of Information Technology 10Soft Computing (ITC4256 )

11. Department of Information Technology 11Soft Computing (ITC4256 )