How Can the Traveling Salesman Problem Be Solved?

[steve22]

Hi Guys

I like to know how can a problem like the travling salesman be tackled. I have made some notes below about tackling TSP problems but can someone confirm to me have I said the right things and is there any other way u can tackle the TSP


The traveling salesman can be tackled using Greedy Algorithm, Constraint Satisfaction Algorithms. A Greedy Algorithm works in stages. At each stage. You take the best at that particular state without regard to the future. The hope is that by choosing the best local decision it will lead to the best global solution.

Another way to tackle the traveling salesman is using the Constraint Satisfaction problem(CSP) Sometimes there may be many solutions that satisfy all the constraints but each solution has a different cost associated with it. In that case a solution is required that not only satisfies all the constraints but also minimizes the cost of the solution this is how CSP is used . A Constraint Satisfaction Problem is characterized by a set of variables {x1, x2, .., xn}. for each variable xi a domain Di with the possible values for that variable. Here are some simple examples of constraint satisfaction problems. CSP can be solved by a variety of search algorithms.


Standard Backtracking is used to generate solutions by checking that the constraints are satisfied as we assign the values. If a situation is reached when no valid assignment can be made to a variable then the algorithm “backtracks” to the previous node in the search tree and tries a different assignment.

Backtracking with Forward Checking works by checking each variable not already assigned to see if it has at least one value that satisfies the constraints. This is called a choice point. Once a value is assigned it reduces the domain of values that can be validly assigned to other variables.

Generalised Forward Checking involves assigning variables out of turn in the situation where the domain of the variable has been reduced to only one possible value. In this situation the variable is assigned and the domains of other unassigned variables are further reduced.

 

[mgb_phys]

You can always try all possible routes and then sort the distances !
There is a non NP algorithm to determine if a chosen route is within a certain factor of the perfect solution so you can at least determine a 'good enough' solution - sorry can't remember the name.

 

[piercas]

Hello,

I can confirm that the methods you mentioned, such as Greedy Algorithm and Constraint Satisfaction Problem, are commonly used to tackle the Traveling Salesman Problem (TSP). These approaches have been studied and applied extensively in the field of computer science.

In addition to the methods you mentioned, other approaches such as Dynamic Programming, Branch and Bound, and Genetic Algorithms have also been used to solve TSP. Each method has its own strengths and limitations, and the choice of which method to use depends on the specific problem and its constraints.

It is important to note that the TSP is a well-known NP-hard problem, which means that there is no known algorithm that can solve it efficiently for all inputs. Therefore, in practice, most algorithms for TSP are heuristic approaches that aim to find a good solution, rather than the optimal one.

I hope this helps answer your question. Keep exploring and experimenting with different methods to find the most suitable one for your problem. Good luck!