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# Travelling salesman problem- 1 city can be visited more than once

Question-

How to solve the travelling salesman problem without the restriction of not visiting a city more then once-

Given a weighted graph, the starting node(sn), and a set of nodes(S) to visit. Find a route starting from and ending at (sn) and covering all nodes in S. One node can be visited more than once.

Plz let me know the algorithm(clearly) at the earliest......(it is easy but urgent)...
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ManiBhushan Kumar
Asked:
1 Solution

Project managerCommented:
Some Links for ur reference for the Alogorithm

http://www.codeproject.com/cpp/tspapp.asp
http://www.pcug.org.au/~dakin/tspbb.htm
http://ai-depot.com/Articles/51/TSP.html
http://hermetic.nofadz.com/misc/ts3/ts3demo.htm

For Quick Reference:

The Metropolis algorithm ..., developed to simulate the behaviour of atoms in thermal equilibrium at a particular temperature, begins with an initial configuration with energy E0. Each subsequent iteration involves performing a small random perturbation to the current configuration i (with associated energy Ei), then the energy, Ej, of the resulting configuration j is calculated. If the change in energy E'' = Ej - Ei <= 0, the configuration j is accepted with probability 1 and becomes the current configuration of the next iteration. If E'' > 0, then configuration j is accepted with probability exp(- E''/kT), with the aim of obtaining a Boltzman distribution. If configuration j is rejected the current configuration i remains unchanged. After a large number of iterations the accepted configurations approximate a Boltzman distribution at a particular temperature, T.

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