An optimal real-time solution for limited-TSP: Using smart algorithms to find an optimal TSP real-time solution over limited destinations

Abstract

TSP, the Traveling Salesman Problem is a famous hard problem in computer science. Finding an optimal solution for TSP in a map consisting of huge number of locations will take huge amount of time (possibly years). A traveller (salesman) needs to visit a limited number of locations out of these thousands locations (each building is an address or location). It is desirable to solve TSP efficiently with real-time factors (traffic, distance, real-time delays). Online applications like Google maps, Yahoo maps, and many others do not give efficient solutions for a multiple-destinations queries. Minimizing the number of locations to exactly the number of destinations asked in the query (by the traveller) will make the optimal hard solution time-acceptable. This paper uses smart heuristics, intelligent algorithm A*, traditional graph Hamilton circuit algorithm, as well as efficient data structures to finding an efficient cycle path between multiple addresses, and hence finding and optimal solution for TSP in real-time. The main idea is to build a virtual graph VG built from a minimized list of vertices (equals exactly to desired list of destinations) and a list of virtual edges that are computed using the smart algorithms A*.