Solving a New Mathematical Model for a Vehicle Routing Problem with Simultaneous Pickup and Delivery by a Multi-Objective Differential Algorithm

The model presented in this research belongs to a class of vehicle routing problems with backhaul, which the pickup and delivery process is carried out simultaneously. This problem is formulated in a bi-objective model, whose objectives are to minimize transportation costs (including the fixed cost of using vehicles and the variable cost of travelled distances) and increase the driver’s satisfaction by balanced distribution of the product. Due to the NP-hardness of the problem, a multi-objective differential evaluation (MODE) algorithm is proposed to solve of the VRP with simultaneous pickup and delivery (VRPSPD). To show the performance of the proposed MODE, its results are compared with the results obtained by a multi-objective harmony search. Additionally, a computational test is carried out on a number of test problems taken from the literature. The computational results show the good efficiency of the proposed MODE in terms of solutions quality and time.