A Multi-Objective Learning Whale Optimization Algorithm for Open Vehicle Routing Problem with Two-Dimensional Loading Constraints

With the rapid development of the sharing economy, the distribution in third-party logistics (3PL) can be modeled as a variant of the open vehicle routing problem (OVRP). However, very few papers have studied 3PL with loading constraints. In this work, a two-dimensional loading open vehicle routing problem with time windows (2L-OVRPTW) is described, and a multi-objective learning whale optimization algorithm (MLWOA) is proposed to solve it. As the 2L-OVRPTW is integrated by the routing subproblem and the loading subproblem, the MLWOA is designed as a two-phase algorithm to deal with these subproblems. In the routing phase, the exploration mechanisms and learning strategy in the MLWOA are used to search the population globally. Then, a local search method based on four neighborhood operations is designed for the exploitation of the non-dominant solutions. In the loading phase, in order to avoid discarding non-dominant solutions due to loading failure, a skyline-based loading strategy with a scoring method is designed to reasonably adjust the loading scheme. From the simulation analysis of different instances, it can be seen that the MLWOA algorithm has an absolute advantage in comparison with the standard WOA and other heuristic algorithms, regardless of the running results at the scale of 25, 50, or 100 datasets.