Application of a Hybrid Genetic Algorithm to Solve the Multi-Depots Vehicle Routing Problem with Simultaneous Delivery and Pickup and Inventory Restrictions

Due to the recent environmental regulations and the increased incentives for returning and reusing products, many companies turned to reverse logistics. One of the actions taken by those companies is to collect empty packaging and other reusable materials or end-of-life products from customers towards the productive system for either reuse or proper disposal. It is within this context that we are interested in a Multi-Depot Vehicle Routing Problem with Simultaneous Delivery and Pickup and Inventory Restrictions (MDVRPSDPIR). It is a closed-loop problem in witch constructs routes simultaneously for several vehicles from multiple depots to a set of customers, in a way that customers require simultaneous pick-up and delivery services. The objective of this paper is to find a solution at a minimal cost which is in terms of total travel distance and number of vehicles, without violating the capacity constraints of the vehicles and the depots. Therefore, we developed two hybrid GAs (HGAs) to solve the variant of VRP studied in this work. In HGA2, initial solutions are generated randomly, while in HGA1, the Petal Heuristic and the Nearest Neighbor Heuristic are incorporated for initialization procedure. The experiment results are compared with those obtained by the exact method for small instances