Modification of the Bellman–Ford Algorithm for Finding the Optimal Route in Multilayer Network Structures

Abstract

One of the actual tasks of the contemporary logistics business using the “just in time” supply planning concept, is to distribute manufactured goods among the objects of the distribution network in the most efficient manner at the lowest possible cost. The article is devoted to the problem of finding the optimal path in network structures. The problem statement for multilayer data transmission networks (MDTN), which is one of the possible representations of multimodal transport networks, is considered. Thus, each MDTN layer can be represented as a separate type of transport. The problem is solved by modifying the Bellman–Ford mathematical programming algorithm. Load testing of the modified method was performed, and a comparative analysis was given, including an assessment of speed and performance, proving the effectiveness of the results of the study. Based on the results of comparative analysis, recommendations for using a modified version of the Bellman–Ford algorithm for application in practical problems in optimizing logistics networks are proposed. The results obtained can be used in practice not only in logistics networks but also in the construction of smart energy networks, as well as in other subject areas that require optimization of multilayer graph structures.