The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.In the theory of computational complexity, the decision version of the TSP (where, given a length L, the task is to decide whether the graph has any tour shorter than L) belongs to the class of NP-complete problems.Ant colony optimization (ACO), inspired by the foraging behaviour of real ants, is one of the most attractive approximation algorithms.Accordingly, this study develops a modified ant algorithm, named ACS-TSPTW, based on the ACO technique to solve the TSPTW.A Java Program that solves the Travelling Salesman Problem using the Ant System algorithm.
Even though the problem is computationally difficult, a large number of heuristics and exact algorithms are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated within a small fraction of 1%.
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?
" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
Under the current configuration, the solutions produced by the algorithm are around 7795 after an execution time of 1.5 seconds.
The code uploaded to this Git Hub Repository corresponds to a Maven Java Project.