A Fast Decomposition and Reconstruction Framework for the Pickup and Delivery Problem With Time Windows and LIFO Loading

The pickup and delivery problem with time windows and last-in-first-out (LIFO) loading (PDPTWL) is a combinational optimization problem extended from the well-known vehicle routing problem (VRP), in which the type of customer point is no longer single and the loading order of the requests must meet the LIFO constraint. Due to its NP-hard nature, it is difficult for exact algorithms and heuristics with a linear structure to solve a large-scale problem in a reasonable time. In this paper, we propose a fast decomposition and reconstruction framework (D&R) to solve the PDPTWL with high quality in a relatively short time. An angle-based sweep method is used to decompose a complete solution into multiple sub-solutions, each of which is assigned to a tabu search for optimization. To speed up the whole process, the optimization procedure of sub-solutions is performed by different processors of multi-core CPU in parallel. Three neighborhood operators and three strategies to reduce the number of vehicles are designed to cope with the tabu search for further improvement. Moreover, the adaptive memory mechanism is added to provide a better start when the optimization procedure falls into the local optima. We compare our framework against the best known solutions on 119 instances with up to 300 requests, the results show that our framework is able to improve over 85% (107 out of 119) of the best known solutions. More specifically, the number of vehicles is optimized by about 60% (74 out of 119) and the driving distance by about 50% (59 out of 119). In addition on instances with the largest size of requests, the computational time of our framework can be 1/50 of the comparative results, confirming its efficiency.