A biased random-key genetic algorithm for the two-level hub location routing problem with directed tours

In this article, a solution is proposed through a population-based metaheuristic for the Two-level Hub Location Routing Problem with Directed Tours (THLRP-DT). Hubs are facilities used to handle and dispatch resources on a given network. The goal of the THLRP-DT is to locate a set of hubs on a network and to route resources from sources to destinations, where the hubs are connected by means of an oriented cycle, and the spokes form clusters. Each cluster is composed of a unique hub, including none or some spoke nodes, connected in an oriented cycle structure. This problem appears in transportation logistics, where the flow of demands can be aggregated, resulting in economies of scale, and the orientations of arcs model a one way flow direction, which speeds up the distribution. We propose a Biased Random-Key Genetic Algorithm (BRKGA) metaheuristic, where the parameters have been calibrated using a machine learning package, which makes use of a machine learning mechanism. The results obtained using the BRKGA metaheuristic are of high quality compared to the ones found in the literature, improving solutions for instances with unknown optimal values.