Green split multiple-commodity pickup and delivery vehicle routing problem

This paper studies a new version of the green split multiple-commodity pickup and delivery vehicle routing problem, in which the multiple commodity demands of each retail store could be split and each retail store could be visited multiple times. In addition, the reallocation of items collected from other retail stores, traffic congestion and time-windows for convenient pickup and delivery were considered when formulating the model. To solve this complex model, a two-stage search quantum particle swarm optimization (TSQPSO) algorithm is proposed. The two-stage search strategy of TSQPSO helps to find the optimization direction quickly. Meanwhile, the three designed neighbourhood structures help to prevent the algorithm from falling into local optimal solutions. We compared the results obtained by the GAMS optimization solver and our algorithm. The average gap between the results is 0.86%, but our algorithm can obtain the optimal solution much faster. The computational results show that the model is capable of offering more reasonable and economical solutions. Furthermore, we found that with the lower unit operating commodity cost at the depot, the total cost is lower when the commodities are allowed to distribute from the depot. Conversely, when it is higher, the total cost is lower when the commodities collected from the supply retail stores are reallocated.