Travelling Salesperson Problem

1. Travelling Salesman Problem
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S7 – ANALYSIS AND DESIGN OF ALGORITHMS

2. What is Travelling Salesman Problem?
The travelling salesman problem (also called the traveling salesperson problem or TSP) asks the following question:
"Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city
exactly once and returns to the origin city?"
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Dynamic Programming

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Weighted Directed Graph Cost Adjacency Matrix
Example

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9. General Formula

10. In this Example

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Answer = 35

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Travelling Salesman using
Branch and Bound Algorithm

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Weighted Directed Graph Cost Adjacency Matrix
Example

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1 2 3
4

17. ∞
∞
1 2

24. • No. of Permutations are less than Bruteforce method.
• The problem was first formulated in 1930 and is one of
the most intensively studied problems in optimization.
• Even though the problem is computationally difficult,
many heuristics and exact algorithms are known
• The TSP has several applications even in its purest
formulation, such as planning, logistics, and the
manufacture of microchips.
CONCLUSION
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25. ThankFOR YOUR ATTENTION
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