Learning Whale Optimization Algorithm for Open Vehicle Routing Problem with Loading Constraints

This paper addresses the two-dimensional loading open vehicle routing problem with time window (2L-OVRPTW). We propose a learning whale optimization algorithm (LWOA) to minimize the total distance; an improved skyline filling algorithm (ISFA) is designed to solve the two-dimensional loading problem. In LWOA, the whale optimization algorithm is used to search the solution space and get the high-quality solution. Then, by learning and accumulating the block structure and customer location information in the high-quality solution individuals, a three-dimensional matrix is designed to guide the updating of the population. Finally, according to the problem characteristics, the local search method based on fleet and vehicle is designed and performed on the high-quality solution region. IFSA is used to optimize the optimal individual. The computational results show that the proposed algorithm can effectively solve 2L-OVRPTW.