How To Solve Travelling Salesman Problem

How To Solve Travelling Salesman Problem-68
In each case, the solution appears in a fraction of a second.Now, these solutions are not guaranteed to be absolutely optimal; they may be a percent or two longer than the absolute best path (if you click “Solve” multiple times, you may see several different solutions, all of which are close in total path length).

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Instead of using the “Place” button to randomly place cities, you can place them manually by pressing “New” to clear the map and then click the mouse in the map to indicate the city locations.The temperature falls in a series of steps on an exponential decay schedule where, on each step, the temperature is 0.9 times that of the previous step.The process of annealing starts with a path which simply lists all of the cities in the order their positions were randomly selected (this is the path you'll see after pressing the “Place” button).Note that initially, when the temperature is high, there will be a greater probability of making such changes, but that as the temperature falls, only smaller increases in cost will be accepted.The total number of changes tested at each temperature level is arbitrarily set to 100 times the number of cities in the path, and after ten times the number of changes which decrease the path length as the number of cities are found, the temperature is decreased and the search continued.On each temperature step, a number of random transformations of the path are made.First of all, a segment of the path is selected, with its start and end cities chosen at random. As you can see, these numbers grow very rapidly, so as you increase the number of cities, the number of paths you have to compare blows up in a combinatorial explosion which makes finding the optimal path by brute force computation a hopeless undertaking.Try clicking “Place” and then “Solve” several times to create and solve new problems, then increase the number of cities to 50 and then 100 and try solving those problems.They will initially be connected by paths in the order you placed the cities.You can also add cities to maps created by the “Place” button by clicking in the map.

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