# What is the traveling salesman problem explain using suitable examples?

## What is the traveling salesman problem explain using suitable examples?

In the traveling salesman Problem, a salesman must visits n cities. We can say that salesman wishes to make a tour or Hamiltonian cycle, visiting each city exactly once and finishing at the city he starts from. There is a non-negative cost c (i, j) to travel from the city i to city j.

How do you solve Travelling salesman problems?

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.

### Has the traveling salesman problem been solved?

Scientists in Japan have solved a more complex traveling salesman problem than ever before. The previous standard for instant solving was 16 “cities,” and these scientists have used a new kind of processor to solve 22 cities. They say it would have taken a traditional von Neumann CPU 1,200 years to do the same task.

Which algorithm is used for Travelling Salesman Problem?

The water flow-like algorithm (WFA) is a relatively new metaheuristic that performs well on the object grouping problem encountered in combinatorial optimization. This paper presents a WFA for solving the travelling salesman problem (TSP) as a graph-based problem.

## What is backtracking in DAA?

Backtracking is a technique based on algorithm to solve problem. It uses recursive calling to find the solution by building a solution step by step increasing values with time. It removes the solutions that doesn’t give rise to the solution of the problem based on the constraints given to solve the problem.

How can we solve travel salesman problem using branch and bound?

In order to solve the problem using branch n bound, we use a level order. First, we will observe in which order, the nodes are generated. While creating the node, we will calculate the cost of the node simultaneously. If we find the cost of any node greater than the upper bound, we will remove that node.

### Which statement is true about traveling salesman problem?

The only known way to verify that a provided solution is the shortest possible solution is to actually solve the entire TSP. Since it takes exponential time to solve NP, the solution cannot be checked in the real polynomial time. Hence, this problem is NP-hard, but not in NP.

Which of the problems Cannot be solved by backtracking method?

Which of the problems cannot be solved by backtracking method? Explanation: N-queen problem, subset sum problem, Hamiltonian circuit problems can be solved by backtracking method whereas travelling salesman problem is solved by Branch and bound method. 2.

## What is travelling salesman problem in mathematics?

traveling salesman problem, an optimization problem in graph theory in which the nodes (cities) of a graph are connected by directed edges (routes), where the weight of an edge indicates the distance between two cities.

What is travelling salesman problem and how is it modeled as a graph problem?

The traveling nalesman problem (TSP) is to find a tour of minimal cost. The TSP can be modeled as a graph problem by considering a complete graph G = /V, E), and assigning each edge uu E E the cost o., A tour is then a circuit in G that meets every node. In this context, tours are sometimes called Eamiltonian c~rcuits.

### Is the traveling salesman problem solved?

This supplied a mathematical explanation for the apparent computational diculty of \fnding optimal tours. The current record for the largest Traveling Salesman Problem including 85,900 cities, was solved in 2006 as explained in [3].

Is the traveling salesman problem NP-hard or NP-soft?

Therefore, the Traveling Salesman Problem is classi\fed as NP-Hard. 14 5.0 SOME KNOWN ALGORITHMS Since a globally optimal solution has not been found, there are many algorithms that give locally optimal solutions.

## What is the backtracking problem?

This problem requires finding the shortest path between n given cities, so that we can only visit each city once before returning to the triggered city. Backtracking is a brute force algorithm.

What is the initial value of backtracking?

Backtracking is a brute force algorithm. Try all the possibilities once and find the best solution. The subset tree is used here. Because you can’t go to a city many times, add the mark of a city. The initial value is 0.