Investigation of methods for solving a large dimensional routing problem

Abstract

In this paper, we researched methods for solving a large-scale vehicle routing problem. First, we provided the description of the problem that modern logistic companies encounter during the planning of transportations. As a solution for this problem, we used meta-heuristics and clustering algorithms. Existing studies and publications in the field of large-scale routing were analyzed, giving us the opportunity to assess the quality of the presented meta-heuristics and select those that lead to the best results. The definition of the routing problem is presented, as well as the description of requirements and limitations for the final solution. Then, in the main part of the work, we offer a brief overview of the Clark-Wright heuristic, which we use to build initial solutions. Also we give a brief description of Guided Local Search and Tabu Search algorithms. Both meta-heuristics help to improve the initial solution obtained using the local search algorithms, while avoiding falling into local minima. The K-Means and Mean-Shift clustering algorithms are described and used to speed up the calculation of the solution and eliminate unnecessary costs during routes optimization. Finally, to check the quality of the proposed solution, we developed software that implements the described meta-heuristics and clustering algorithms, and provides the routing results in the form of a route graph and its total length. The program was tested on the set of benchmarks of the Belgian roads, which were provided in the work of F. Arnold, M. Gendreau, K. Sorensen K. The results of comparison with the best solutions are provided along with the conclusion on the optimality of the results obtained. That allows us to assert that in less than ten minutes of solving a problem on each of the clusters, the developed software gives results that differ from the best known only by 5-7%. Further work will be aimed at improving the results by exchanging points between neighboring clusters.