An iterative biased-randomized heuristic for the fleet size and mix vehicle-routing problem with backhauls

This paper analyzes the fleet mixed vehicle-routing problem with backhauls, a rich and realistic variant of the popular vehicle-routing problem in which both delivery and pick-up customers are served from a central depot using a heterogeneous and configurable fleet of vehicles. After a literature review on the issue and a detailed description of the problem, a solution based on a multistart biased-randomized heuristic is proposed. Our algorithm uses an iterative method that relies on solving a series of smaller instances of the homogeneous-fleet version of the problem and then using these subsolutions as partial solutions for the original heterogeneous instance. In order to better guide the exploration of the solutions space, the algorithm employs several biased-randomized processes: a first one for selecting a vehicle type; a second one for sorting the savings list; and a third one to define the number of routes that must be selected from the homogenous-fleet subsolution. The computational experiments show that our approach is competitive and able to provide 20 new best-known solutions for a 36-instance benchmark recently proposed in the literature.