A Parallel Ring Method for Solving a Large-scale Traveling Salesman Problem

A parallel approach for solving a large-scale Traveling Salesman Problem (TSP) is presented. The problem is solved in four stages by using the following sequence of procedures: decomposing the input set of points into two or more clusters, solving the TSP for each of these clusters to generate partial solutions, merging the partial solutions to create a complete initial solution M0, and finally optimizing this solution. Lin-KernighanHelsgaun (LKH) algorithm is used to generate the partial solutions. The main goal of this research is to achieve speedup and good quality solutions by using parallel calculations. A clustering algorithm produces a set of small TSP problems that can be executed in parallel to generate partial solutions. Such solutions are merged to form a solution, M0, by applying the ―Ring‖ method. A few optimization algorithms were proposed to improve the quality of M0 to generate a final solution Mf. The loss of quality of the solution by using the developed approach is negligible when compared to the existing best-known solutions but there is a significant improvement in the runtime with the developed approach. The minimum number of processors that are required to achieve the maximum speedup is equal to the number of clusters that are created.