The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this opaper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.
OPEN ACCESSCitation: Qi X, Fu Z, Xiong J, Zha W (2020) Multistart heuristic approaches for one-to-one pickup and delivery problems with shortest-path transport along real-life paths. PLoS ONE 15(2): e0227702.
A variation of the One-to-one Pickup and Delivery Problem (OPDP) in connected graphs, the Split Demand One-to-one Pickup and Delivery Problem with the Shortest-path Transport along Real-life Paths (SDOPDPSTRP) is abstracted from passenger train operation plans based on networks. Unlike the classical OPDP, in the SDOPDPSTRP: the demands can be split and must be transported along the shortest path according to passengers requirements and vehicles should travel along a real-life path. A new kind of integer programming model is formulated for the SDOPDPSTRP based on the connection relationship between pickup-delivery demands (pd-pairs). Two different categories of splitting strategies are proposed to solve the SDOPDPSTRP: split the demands before the calculation and split the demands during the calculation. Two Multi-Start Variable Neighborhood Descent (a MS_VND originating from the other literature and a new MS_VND' IN developed in this paper) and seven neighborhood operators are proposed for these two splitting strategies to solve the SDOPDPSTRP. The results show that Approach III outperforms Approach I and Approach II in terms of average solutions with the same algorithm termination conditions and in terms of time efficiency, which has great practical significance for real-life transport organizations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.