PST-Prim Heuristic for the Open Vehicle Routing Problem

Abstract

The objective of this paper is to present and demonstrate the validation of the functioning of a recursive heuristic based on the algorithm of Prim and that gives solution to the open vehicle routing problem (OVRP). Today this problem has a considerable approach, so a literature review that sets the theoretical basis for the work, is made. The OVRP is formally shown and the covering tree with paths (PST) is defined. Next, the subroutine that follows the PST-Prim algorithm is indicated to construct the PST of any graph, as well as the modification that must be made to arrive at the PST-Prim Heuristic that gives solution to the OVRP. An illustrative example of the construction of PST to an example graph is presented. To illustrate and validate its effectiveness of the heuristic, it is used to solve 17 widely used problems to verify and compare the behavior of this type of algorithms. In addition, the PST-Prim heuristic performance is compared with other seven algorithms; the value of the objective function and the computation time for each algorithm on the 17 instances is presented. The PST-Prim propose the best solutions on 12 of the 17 instances. At the end, the performance, use and importance of the heuristic is discussed.