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The optimal route of sightseeing orders for visiting every Macao WorldHeritage Site at exactly once was calculated with Simulated Annealing andMetropolis Algorithm(SAMA) after considering real required time or travelingdistance between pairs of sites by either driving a car, taking a bus, or onfoot. We found out that, with the optimal tour path, it took roughly 78 minutesfor driving a car, 115 minutes on foot, while 117 minutes for taking a bus. Onthe other hand, the optimal total distance for driving a car would be 13.918 kmwhile for pedestrians to walk, 7.844 km. These results probably mean that thereis large space for the improvement on public transportation in this city.Comparison of computation time demanded between the brute-force enumeration ofall possible paths and SAMA was also presented, together with animation of theprocesses for the algorithm to find out the optimal route. It is expected thatcomputation time is astronomically increasing for the brute-force enumerationwith more number of sites, while it only takes SAMA much less order ofmagnitude in time to calculate the optimal solution for larger number of sites.Several optimal options of routes were also provided in each transportationmethod. However, it is possible that in some types of transportation therecould be only one optimal route having no circular or mirrored duplicates.

Applications of Traveling Salesman Problem on the Optimal Sightseeing  Orders of Macao World Heritage Sites with Real Time or Distance Values  Between Every Pair of Sites