A hybrid heuristic algorithm for urban distribution with simultaneous pickup-delivery and time window

With the continuous development of urban distribution services, customers have increasingly strict requirements for the delivery time windows. Therefore it is necessary to study the vehicle routing problem with simultaneous pickup-delivery and time windows (VRPSPDTW) in urban distribution. However, as one of the most important classification of the much anticipated reverse logistics, the VRPSPDTW problem has not received much attention, and lacks an efficient and simple implementation. Our method combines the enhanced Late Acceptance Hill Climbing algorithm (enhanced LAHC) to ensure the diversity of solutions and the Multi-armed Bandit Algorithm (MAB) to choose a neighborhood structure which has the best performance. In order to enhance its search ability at a later stage, a perturbation strategy is designed to effectively prevent premature convergence. To our best knowledge, the proposed h_LAHC (hybrid LAHC) algorithm is applied to the VRPSPDTW for the first time. We provide abundant experiments were conducted on 93 benchmark instances, and the results demonstrated that our algorithm can achieve better, totally equal or approximately equal results in 97.85%, 56.99% and 73.12% instances compared with the latest three mainstream algorithms respectively. In particular, the proposed algorithm has a prominent performance in scenarios with relatively narrow time windows. Moreover, we conduct an empirical analysis on critical components of the algorithm to highlight their impact on the performance of the proposed algorithm.