A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery

•The vehicle routing problem with simultaneous pickup and delivery is studied.•The problem is considered with heterogeneous fleet of vehicles.•An adaptive local search integrated with tabu search is developed for its solution.•Proposed approach performs well on the randomly generated problem instances. The Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) is a variant of the classical Vehicle Routing Problem (VRP) where the vehicles serve a set of customers demanding pickup and delivery services at the same time. The VRPSPD can arise in many transportation systems involving both distribution and collection operations. Originally, the VRPSPD assumes a homogeneous fleet of vehicles to serve the customers. However, in many practical situations, there are different types of vehicles available to perform the pickup and delivery operations. In this study, the original version of the VRPSPD is extended by assuming the fleet of vehicles to be heterogeneous. The Heterogeneous Vehicle Routing Problem with Simultaneous Pickup and Delivery (HVRPSPD) is considered to be an NP-hard problem because it generalizes the classical VRP. For its solution, we develop a hybrid local search algorithm in which a non-monotone threshold adjusting strategy is integrated with tabu search. The threshold function used in the algorithm has an adaptive nature which makes it self-tuning. Additionally, its implementation is very simple as it requires no parameter tuning except for the tabu list length. The proposed algorithm is applied to a set of randomly generated problem instances. The results indicate that the developed approach can produce efficient and effective solutions.