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The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved.
The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing. In these applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the concept distance represents travelling times or cost, or a similarity measure between DNA fragments. In many applications, additional constraints such as limited resources or time windows make the problem considerably harder.
In the theory of computational complexity, the decision version of TSP belongs to the class of NP-complete problems. Thus, it is assumed that there is no efficient algorithm for solving TSPs. In other words, it is likely that the worst case running time for any algorithm for TSP increases exponentially with the number of cities, so even some instances with only hundreds of cities will take many CPU years to solve exactly.

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The act of going from one place to another; "he enjoyed selling but he hated the travel"

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When traveling abroad, the odds favor a safe and incident-free trip, however, travelers can be subject to difficulties, crime and violence. Some safety considerations include being aware of one's surroundings, avoiding being the target of a crime, leaving copies of one's passport and itinerary information with trusted people, obtaining medical insurance valid in the country being visited and registering with one's national embassy when arriving in a foreign country.

I love travelling. Travel gives me time to think, ideate, observe and learn new things - culture, food, history. I love to travel different different places in this world. Goa is my one of the best choice. There are very nice sightseeing, attractions to see.

Resorts In Goa