Identification of the most efficient algorithm to find Hamiltonian Path in practical conditions

Travelling Salesman Problem (TSP) is a real-world Non-deterministic polynomial-time hard - combinatorial optimization problem. Given several points (cities) to be visited, the objective of the problem is to find the shortest possible route (called Hamiltonian Path) that visits each point exactly once and returns back to the starting point. Several exact, approximate and heuristic algorithms have been proposed to solve the TSP. The objective of this paper is to compare 10 such different algorithms on the basis of cost of the path found and time taken to find that solution in order to identify an algorithm which works most efficiently and thus, can be used in practical scenarios. Therefore, the comparative analysis has been made without time constraints as a preliminary test and then with a constraint of 1 second to determine the most efficient algorithm. This algorithm was then used at the core of the web-based tool (a practical use case) developed for release in public domain which helps users find an optimal round-trip route (i.e. Hamiltonian Path) among the points marked on the map. Google Maps API was used for providing map interface and obtaining real-time distance/duration data (matrix) in the web-application front end.