# How branch and bound can be used to solve Travelling salesman problem using?

## How branch and bound can be used to solve Travelling salesman problem using?

Given a set of cities and distance between every pair of cities, the problem is to find the shortest possible tour that visits every city exactly once and returns to the starting point. For example, consider the graph shown in figure on right side.

## Which method is used to find the solution of a Travelling salesman problem?

To solve the TSP using the Brute-Force approach, you must calculate the total number of routes and then draw and list all the possible routes. Calculate the distance of each route and then choose the shortest one—this is the optimal solution. This method breaks a problem to be solved into several sub-problems.

How can you reduce a particular column in Travelling salesman problem using branch and bound?

Row Reduction-

1. Reduce that particular row.
2. Select the least value element from that row.
3. Subtract that element from each element of that row.
4. This will create an entry ‘0’ in that row, thus reducing that row.

### How do you calculate lower bound in travel salesman problem?

A lower bound can be found by removing a vertex, then finding a minimum spanning tree: Use Prim’s or Kruskal’s algorithm to find the length of the minimum spanning tree. Add to this the lengths of the two shortest edges connected to the missing vertex.

### What is branch and bound algorithm technique?

Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. The algorithm explores branches of this tree, which represent subsets of the solution set.

Is the travelling salesman problem a branch or bound problem?

In this article we will briefly discuss about the travelling salesman problem and the branch and bound method to solve the same. What is the problem statement ?

#### Which is an example of branch and bound?

For example, in Job Assignment Problem, we get a lower bound by assigning least cost job to a worker. In branch and bound, the challenging part is figuring out a way to compute a bound on best possible solution. Below is an idea used to compute bounds for Traveling salesman problem.

#### Which is the root node in the traveling salesman problem?

1. The Root Node: Without loss of generality, we assume we start at vertex “0” for which the lower bound has been calculated above. Dealing with Level 2: The next level enumerates all possible vertices we can go to (keeping in mind that in any path a vertex has to occur only once) which are, 1, 2, 3… n (Note that the graph is complete).

Which is the best way to solve the travelling salesman problem?

Reduce that particular row. Select the least value element from that row. Subtract that element from each element of that row. This will create an entry ‘0’ in that row, thus reducing that row. Reduce the elements of row-1 by 4. Reduce the elements of row-2 by 5. Reduce the elements of row-3 by 6. Reduce the elements of row-4 by 2.