A Multi-stage Algorithm for the Capacitated Vehicle Routing Problem with Two-dimensional Loading and Time Windows

The capacitated vehicle routing problem with two-dimensional loading and time windows (2L-CVRPTW) is an extension of the vehicle routing problem, in which customers have the requirements of time windows and two-dimensional loading constraints. It aims at planning a shortest trip that can visit all customers and satisfy customers' demands, using a series of homogeneous vehicles. In this paper, we propose a multi-stage algorithm to solve the 2L-CVRPTW of customers whose geographical data is clustered (C-type). To accelerate the solving process, we merge the multiple customers into a few customers. Then, an improved ant colony algorithm incorporated with the skyline heuristic algorithm is used to solve the shortest route of merged customers. The results show that the algorithm can reduce the size of the points well for the C-type dataset, and obtain a solution closing to the optimal solution.