An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows and scheduled lines

The Pickup and Delivery Problem with Time Windows and Scheduled Lines (PDPTW-SL) concerns scheduling a set of vehicles to serve freight requests such that a part of the journey can be carried out on a scheduled public transportation line. Due to the complexity of the problem, which is NP-hard, we propose an Adaptive Large Neighborhood Search (ALNS) heuristic algorithm to solve the PDPTW-SL. Complex aspects such as fixed lines׳ schedules, synchronization and time-windows constraints are efficiently considered in the proposed algorithm. Results of extensive computational experiments show that the ALNS is highly effective in finding good-quality solutions on the generated PDPTW-SL instances with up to 100 freight requests that reasonably represent real life situations.