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

TL;DR

This paper applies the Traveling Salesman Problem using Simulated Annealing and Metropolis Algorithm to find optimal sightseeing routes among Macao World Heritage Sites, considering real-time and distance data for different transportation modes.

Contribution

It introduces a novel application of TSP with real-time data and compares different algorithms and transportation modes for optimal sightseeing routes.

Findings

Optimal driving route takes about 78 minutes and covers 13.918 km.

Walking route takes about 115 minutes and covers 7.844 km.

Public transportation could be significantly improved based on route efficiency.

Abstract

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