Question

An autonomous military drone is required to fly over 14 locations as part of surveillance operation. It must plan a route to minimise the distance travelled. Treating this as a TSP in which the drone starts from one of the locations, how many possible routes might the drone take?

iv.

The drone's onboard processor can process five hundred million (that is, 500 000 000) routes per second. How long would it take it to evaluate every possible solution?

Changes to the intended operation require that an additional three locations be added to the drone's route. How long would it now take the drone to evaluate every possible solution?

Show the working used to calculate your answers. Give your answers in everyday units, for example using hours, minutes and seconds as appropriate

Answer 1

An autonomous military drone is required to fly over 14 locations as part of surveillance operation

total possible route=

since drone can choose any of loaction out of 14 means total 14 choice after selecting one choice there are 13 location and drone choose any location out of 13 then 12 location remaining and drone choose any of location from 12 loaction and so on.......

total possible way of choosing loaction = 14* 13 * 12 *...............2*1 =14! = 87178291200 possibel route

b]

since drone can procees 500,000,000 route in 1 second

then 1 route can process = 1/500,000,000 second

then 87178291200 route can process = (1*87178291200) / 500,000,000 = 174.356582 second

= 2 minute 54.356582 second

c]

if we add 3 more location then we have 14+3 =17 loaction then possible route

17*16*15..........*3*2*1 = 17! = 355687428096000 route

since drone can procees 500,000,000 route in 1 second

then 1 route can process = 1/500,000,000 second

then 355687428096000 route can process = (1*355687428096000) / 500,000,000 = 711,374.856 second

= 11856 minute 14.856 second = 197 hours 36 minute 14.856 second = 8 days 5 hours 36 minutes 14.856 second