The document discusses the travelling salesperson problem (TSP), which aims to find the shortest route for a salesperson to visit every city only once and return home. Specifically, it seeks the minimum cost Hamiltonian circuit through a weighted graph. The TSP is easy to state but difficult to solve. An example is provided of finding the lowest cost route between 6 cities in India, which is solved using the nearest neighbor algorithm to sequentially visit the closest unvisited city from the current one.

1. Travelling Salesperson
Problem
Presented By:- Akshay Ingole(M.Sc II)
Date:- 11-2-2019
(TSP)

2. What is TSP?
 Design the shortest, or minimal cost,
route for a salesman who wants to
travel EVERY cities ONLY ONCE
and ,lastly, backs to home city.
 In graph, we need to find a tour that
starts at a node, visits every other
node exactly once, and returns to the
starting node.

3. What is TSP
 Definition: Find a path through a
weighted graph which starts and ends
at the same vertex, includes every
other vertex exactly once, and
minimizes the total cost of edges.
 Easy to State
 Difficult to Solve

4.  A route returning to the beginning is
known as a Hamiltonian Circuit
 A route not returning to the beginning is
known as a Hamiltonian Path

5. Travelling Salesman Problem
Example :-
The following list of cities and want to visit each
city once, return back to home:

 Pune (Home)(A)
 Bangalore(B)
 Chennai(C)
 Delhi(D)
 Kolkata(E)
 Shri Nagar(F)

6. Let say that , These are the distances from the cities and want
to go from Home-city(Pune) to Shri Nagar with minimum cost. In
which order/path he do these?

7. Travelling Salesman Problem Explanation :
We visit Cities As follows Using Above algorithm,
 A → E = 20
 E → C = 42
 C → B = 22
 B → D = 58
 D → F = 92
 F → A = 40
 Total Cost = 20 + 42 + 22 + 58 + 92 + 40 = 274

8. We Solve the problem using Nearest neighbor algorithm:
Algorithm:
1. Select a city as current city.
2. Find out the shortest edge connecting the current city and an
unvisited city.
3. Set the new city as current city.
4. Mark the previous current city as visited.
5. If all the cities are visited, then terminate.
6. Go to step 2

9. Thank
You….