PLZ HELP! Mathematics(TSP)!

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tsp maths formulation

Hi there! I'm working on some robotics and i use the Traveling Salesman Problem to make some paths. At the moment i'm trying to model this game:
the salesman starts from a city (say 1) and has n cities to travel but he has only T time units. Assuming that every travel between 2 cities is one time unit then which is the best path to take?

This means i have to reformulate the problem in some way. I have thought of a solution but how can i gurrante if it is the optimal or not? What maths to use???
 

Try reading again my post - you will understand what i want. If you want to test a heuristic (P time) for an NP problem you must first find an exact solution for the optimal problem. Since what i want starts from the TSP BUT IT ISN'T TSP i must first know if my formulation is the OPTIMAL or not (so to find another).
 

Hi.

This topic belongs to a special kind of mathematics, called Graph Theory.
 

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